*5.1 Inventing a lexicon*

and transmits the meaning he thus obtained. If this meaning is the one that the speaker originally had in mind the game succeeds, otherwise the game fails. When the game fails, the speaker communicates the meaning directly so that the hearer can acquire a new form-meaning pair for later conversations. When a speaker does not have a word yet for a meaning he wants to communicate, he may create a new one.

#### **5.1.1 Representing lexical associations**

What cognitive architecture do agents need to engage in naming games? Clearly they need some sort of associative memory to store their individual lexicons. Let us assume that agents can construct and recognise arbitrary consonant-vowel combinations, like *coba* or *wabidu*, for forming words, and that they have a repertoire of possible meanings in the form of categories, for example [left], [dark], [large], etc. The contents of the associative memory of a single agent can be displayed in a table as follows:

As an agent is acquiring his lexicon, there are going to be stages when he is not yet sure about the meaning of a certain form. So it must be possible for the agent to store different meanings for the same form and different forms for the same meaning. This can easily be done by extending the memory capacity to cross-associate multiple items. Agents can then handle ambiguity (one word can have different meanings) and synonymy (one meaning can be associated with many different words).

A speaker can only transmit a single choice for expressing the meaning. When there are alternative words for the same meaning in his lexicon, he must decide which one to use and this decision should be such that it maximises success in the game. To estimate this success, each agent should monitor for each form-meaning association how successful it has been, which could be implemented by associating with every form-meaning pair a score. The score of a form-meaning pair is specific to an agent and based only on his own local interactions with other agents, in line with the principle that no single agent has a complete overview of the lexicon nor controls the others. An example of a lexicon with multiple associations and a score for every association is illustrated in Table 5.2.

From this table we see that the agent prefers to use the word *pama* for [dark] and *limiri* for [large].

#### *5 The Naming Game*

Table 5.2: Example lexicon with multiple associations

#### **5.1.2 Updating the score**

One of the crucial aspects of the Naming Game model is how scores are updated based on the outcome of a game. Intuitively the score should be related to use and success. The more a word is used and the more success it has, the higher the score should be. Moreover there should be a time dimension, as recent use and success should obviously contribute more to the current score. The following is a scheme that captures these characteristics.

Every time an agent successfully uses a form-meaning pair for speaking, he increments the score with a specific increment *δ*. *δ* is relatively high, typically equal to 0.1. The scores of competing associations, i.e. associations that used another form for the same meaning are decremented with *δ*. The score remains however bounded between 0.0 and 1.0. This way the "best" form-meaning pair stands out more clearly next time around.3

When an agent plays the role of hearer, he also increments the association that was successful with *δ*, and decrements competing associations, i.e. associations that related another meaning to the same form. When a game fails, the associations used by the speaker and the hearer that contained the transmitted word form are both decremented.

The operations of speaker and hearer are summarised in Figure 5.1 assuming that speaker and hearer use both the score table above (in reality they of course always have different score tables). The speaker collects all possible forms for a given meaning [dark], chooses the one with the highest score (*pama*), and transmits that form. The hearer collects all possible meanings for the transmitted form ([dark], [large]) and again chooses the one with the highest score. If the hearer's meaning is equal to that of the speaker's, the game succeeds. The score of two used associations increases and the others decrease, implementing lateral inhibition. If the game fails, only the two used associations go down.4

It is possible to impose an even stronger lateral inhibition, by assuming that in the case of success, the speaker decreases the score of all the associations that imply the word used in the game but with another meaning, and the hearer decreases the score of

3 A systematic investigation of alternatives for the updating function is contained in Oliphant (1997). The dynamics of the mechanisms used in the Talking Heads experiments are being investigated in the Ph.D thesis of Frederic Kaplan.

4 More or less neural realism can be introduced to model this associative memory. In our experiments we have a perfectly working memory that can store an association as soon as it has seen it once. This makes theoretical investigation easier and makes it possible to better follow the simulations and experiments. An example of a neural network solution to lexical memory is discussed in Cangelosi & Parisi (1996).

Figure 5.1: Score adjustments after a successful game. Scores of used associations go up and their competitors go down.

all the associations that imply the same meaning but with another word. This obviously requires additional processing from the side of the agents.

### **5.1.3 Constructing and acquiring words**

When virgin agents start playing naming games, their associative memories are completely empty. Each agent needs two additional activities to get a lexicon emerging:

These rates are not critical but must of course be positive. Experiments continue to work when agents always make a new word (*wc* = 1) and always absorb the word of the other (*wa* = 1).

#### **5.1.4 The Naming Game in action**

To become more familiar with the Naming Game, I will now go through a few examples of its application, assuming a group of five agents: *A* = *{***a1**,**a2**, **a3**, **a4**, **a5***}* and five possible shared meanings: *M* = *{*[dark]*,* [large]*,* [light]*,* [small]*,* [red]*}*.

Here is a trace of a first game as reported by the commentator, when the agents do not have any lexicon at all.

```
Game 0
  a5 is the speaker. a3 is the hearer.
  a5 categorises the topic as [LIGHT]
  a5 does not have a word for [LIGHT]
```
This trace lists the number of the game, the speaker, the hearer and the categorisation of the topic. The speaker did not have a word and did not create one (because the word creation probability is *wc* = 0*.*1): the game has failed. In the beginning most games fail if the word creation rate has been set to a low rate.

In the next game shown below, the speaker is **a4**, the hearer **a5** and the topic [small]. Now the speaker is successful in creating a word, namely *di*. The hearer receives the word, does not know it, but stores it in association with [small]. The game still fails.

```
Game 29
   a4 is the speaker. a5 is the hearer.
   a4 categorises the topic as [SMALL]
   a4 creates a new word: di
   a5 does not know di
   a4 points to the topic
   a5 categorises the topic as [SMALL]
   a5 stores di as [SMALL]
```
In game 32, something similar happens. This time **a5** creates a new word *pida* for [large]. **a3** does not know the word but stores it.

```
Game 32
   a5 is the speaker. a3 is the hearer.
   a5 categorises the topic as [LARGE]
   a5 creates a new word: pida
   a5 says: pida
   a3 does not know pida
   a5 points to the topic
   a3 categorises the topic as [LARGE]
   a3 stores pida as [LARGE]
```
A first success occurs in game 43, when **a5** uses again *pida* for [large]. **a3** hears *pida*, has associated it in his lexicon with [large], and so the game succeeds.

*5.1 Inventing a lexicon*

```
Game 43
   a5 is the speaker. a3 is the hearer.
   a5 categorises the topic as [LARGE]
   a5 says: pida
   a3 interprets pida as [LARGE]
   a3 points to the topic
   a5 signals OK
```
It is quite tedious to go through such games by hand. For large populations of agents or meanings, even the most diligent researcher soon loses patience. Fortunately it is not so difficult to implement the Naming Game model on a computer. This makes large-scale simulations, even with hundreds of agents and meanings feasible, and ensures that they have been done correctly. All traces and graphs of games reported in this book have been produced by computer simulations or physical experiments with the Talking Heads.

#### **5.1.5 Characterising the lexicon**

The individual lexicon of one agent, **a5**, after 100 games is shown in 5.3.

Table 5.3: Associative memory of a single agent after 100 games.

Both the words *di* and *pida* are present but with weak scores. There are two synonyms for [large]: *pida* and *fobu*, but *pida* is preferred. There is a word *gi* who is available for [light] but does not have a positive score, because successive trials failed to yield a successful game.

A table such as the one above only represents the lexicon of a single agent. It is highly unlikely that two agents share the same lexicon because each agent will have had different encounters and hence different language experiences. A picture of the lexicon of the group from the viewpoint of an outside observer can be obtained by inspecting the internal states of each agent to construct the group lexicon. It groups the dominating meaning-form associations for all possible meanings and the frequency of each association. It gives a picture of "the" lexicon in the group. The group lexicon for the complete population of five agents after 50 language games is shown in Table 5.4.

This reflects a situation where 40 % of the agents prefers to name [large] with *pida*. 60 % of the agents use *gi* for [light], and 40 % *di* for [small]. The other meanings ([dark] and [red]) do not have names yet.

#### *5 The Naming Game*

Table 5.4: Population lexicon after 50 games

Note that the group lexicon is not known by the agents and is not stored anywhere in the total system. The only information which is locally stored in each agent is his own lexicon, which might be quite different from that of the group lexicon. For example, the lexicon of **a5** shown earlier is different from the group lexicon. **a5**'s score for *gi* is 0.0 even though the word is already preferred by 60 % of the agents according to the group lexicon. The group lexicon is a macroscopic structure that we as observers construct from inspecting the internal states of the agents.

Let us now continue the simulation. Here are two additional games showing how *ga* propagates from **a4** to **a2** in game 101 and from **a2** to **a1** in game 104.

```
Game 104
   a4 is the speaker. a2 is the hearer.
   a4 categorises the topic as [RED]
   a4 says: ga
   a2 does not know ga
   a4 points to the topic
   a2 categorises the topic as [RED]
   a2 stores ga as [RED]
Game 104
   a2 is the speaker. a1 is the hearer.
   a2 categorises the topic as [RED]
   a1 says: ga
   a1 does not know ga
   a2 points to the topic
   a1 categorises the topic as [RED]
   a1 stores ga as [RED]
```
After a total of 250 games, the consensus is complete. The group lexicon is shown in Table 5.5.

Once the agents have reached this stage, the lexicon does not change anymore, because all agents now prefer the same word for each possible meaning and would never choose another one nor encounter another one.

The lexicons of individual agents contain quite a few form-meaning pairs that did not make it in the shared lexicon that gradually emerged. It is entirely feasible to envision

*5.1 Inventing a lexicon*

Table 5.5: Consensus in group lexicon, reached after 250 games.

a pruning mechanism that would eliminate from memory those form-meaning pairs whose success has been non-existent (for example because an agent created it as speaker but it was never picked up by anybody else), or whose score has become zero (because another word became dominant). The impact of such a forgetting function has not been explored yet in our experiments.

#### **5.1.6 Monitoring**

I use various measures both for actual lexicon use and for the coherence and evolution of the lexicons of the individuals to see better what is happening. The first and easiest measure is the average game success, also called the communicative success, of a population of agents *A* in a set of *n* language games. When this measure is graphed continuously for consecutive sets of games, the progress in the population towards successful communication can be followed easily. This is shown in Figure 5.2 which plots data from the games discussed in the previous paragraphs. We see at once that average success climbs from a starting point of zero to a maximum of 1.0. This can only be because a shared lexicon emerged in the population.

When the population (both of meanings and agents) is larger, one would expect that it takes longer to reach total average success. This is indeed the case (Figure 5.3).

We see for example that for 20 agents and 20 meanings success climbs to total success after about 10,000 games. This is still surprisingly low particularly as success is are already above 95 % after about 5000 games. Games can be played in parallel by different agents because the system is entirely distributed. If we divide the number of agents by the number of games, we see that about 250 games are needed by the agents to get 95 % success, which means that every meaning needs to appear about 10 times for each agent. Interestingly enough, the larger the population of agents, the more the success curve approximates an S-shape, which has been observed empirically in the spreading of new linguistic conventions. The same curve shape is familiar to biologists studying models of competitive growth, suggesting a strong relationships between ecological dynamics and language spreading.5

5 The S-shaped curve is discussed in McMahon (1994) p. 52. For examples of biological models with similar properties, see May (1976).

Figure 5.2: The graph displays on the y-axis the average success every 10 games in a population of five agents lexicalising five different meanings. The x-axis shows the number of games. Average success rapidly climbs until it reaches total success after about 180 games.

Figure 5.3: The graph displays the evolution of communicative success for larger and larger populations. The number of games on the x-axis is divided by the number of agents.

*5.1 Inventing a lexicon*

#### **5.1.7 Measuring lexical coherence**

To monitor to what extent the agents share the same lexicon, I propose a second measure, the lexical coherence. The lexical coherence is defined as the average of the frequencies of all the form-meaning pairs in the group lexicon. If all agents prefer the same form-meaning pair for all meanings, lexical coherence is 1.0. If they agree on none, it is 0.0.

Consider the following group lexicon after 3000 games for the previous simulation (with 20 agents), shown in Table 5.6.

The lexical coherence is at this point equal to 0.835.

Lexical coherence can be graphed alongside average success (see Figure 5.4). As expected, lexical coherence increases and we can see that as coherence increases the success rate increases.

Does total success imply that all agents use the same lexicon? Not really. To have success, the hearer must associate the form used by the speaker with the same meaning. But it is not required that the hearer himself prefers to use the same form for the same meaning, synonyms may occur. A speaker of British English typically uses the word *pavement*, whereas an American prefers*sidewalk*, even though he understands *pavement*. Thus there can be several forms active in the same population, even though the outcome of a game is always successful. We will see later that synonyms do get damped, as is the case in human natural lexicons.

Initially lexical coherence is higher than success, because a game fails if the hearer is acquiring the form-meaning association used by the speaker. So two agents could have stored the same association, and thus coherence would have increased, without already having enjoyed the benefit in a successful communication. However, once success is total, agents no longer make changes based on negative feedback from failure, simply because there is no failure, even the less common forms are understood correctly by

Figure 5.4: This figure shows the evolution of both average success and lexical coherence for a group of 20 agents and 20 meanings. Total lexical coherence climbs more slowly once the population has reached a high average success.

everybody. Further progress towards more coherence is therefore only due to the fact that the more common forms occur more often so that their scores keep going up as they are used more.

## **5.2 Scaling up**

The associative memory and the score updating introduced in the previous section appears to allow a group of distributed agents to establish a shared repertoire of formmeaning pairs. Of course, I still need to show that this mechanism remains adequate when it is incorporated in a complete game, in which case there is no direct feedback about meaning. But before doing so, let us see whether the mechanisms are adequate from the viewpoint of scaling: Can they handle variation in the set of meanings to be expressed? Do they cope with a changing population?

### **5.2.1 Coping with new meanings**

In natural languages, new meanings arise every day while other meanings become irrelevant. For example, none of the terms used for talking about the Internet (e-mail, surfing, home page, etc.) would have made sense to anyone a few decades ago. On the other

#### *5.2 Scaling up*

hand, most of us now have lost many categories and concepts for classifying plants, simply because they are no longer such a prominent part of our urbanised environments. It follows that a mechanism claiming to explain the origins and acquisition of a lexicon in a population of agents should cope with a fluctuating set of meanings as well. This property is moreover crucial in the Talking Heads experiment because new meanings will continuously arise as the agents encounter new situations in the environment.

Because the Naming Game included ways to handle new meanings from the start, nothing should have to be changed to handle an increased set of meanings. Let us see whether the Naming Game indeed copes through the next simulation (see Figure 5.5), using arbitrary labeled meanings ([M1], [M2], etc.). In a first phase, the system is closed and a shared lexicon emerges for the initial set of 20 meanings, as expected. The group's lexicon is now as in Table 5.7.

Table 5.7: Group lexicon after first phase.

In phase 2, a relatively small meaning flux is introduced (one new meaning every 1000 games). As can be seen from Figure 5.5, the population copes with the change. New words are created and propagate in the population. The following group lexicon shows that for newcomers like [M22] or [M25] a total consensus has emerged. Words for the latest new meanings, [M28] and [M29], still have low frequencies.

Next (phase 3 in Figure 5.5) a much higher meaning flux is imposed (one new meaning every 100 games). Lexical coherence decreases and average success plummets. There is not enough time to propagate the new conventions in the group. Note that lexical coherence drops slower than success when the lexicon disintegrates. Coherence is based on the average for all meanings, thus only the new ones are therefore affecting overall coherence. Success drops more rapidly because of the high rate of failure of new meanings.

The system restores itself when the flux of meaning is brought back to 1/1000 games (phase 4). Interestingly enough, coherence now increases slower than success. The in-

Table 5.8: Group lexicon after second phase.

Figure 5.5: Both average success (every 100 games) and lexical coherence is shown in cases of an inflow of meanings for a population of 20 agents starting with 20 meanings (phase 1). The inflow is 1/1000 in phase 2, 1/100 in phase 3 and 1/1000 in phase 4.

*5.2 Scaling up*

stability caused by a rapid influx of new meanings has lead to many new forms for the same meanings. These synonyms now spread in the population and lead to a rapid increase in communicative success. Coherence climbs up more slowly because competing synonyms are only gradually weeded out, based on their frequency of use.

We can conclude that the agent architecture manages to handle an influx of meaning, as long as the flux stays within certain bounds.

#### **5.2.2 Lexicon acquisition by virgin agents**

The next question we need to investigate is whether the mechanisms explain how a lexicon, once it has formed, can be preserved from one generation to the next. This clearly happens in human populations. Although lexicons show profound change, large parts get preserved even over very large periods of time. Some linguists even claim that the roots of certain words still in use today go back to the very beginnings of language which is hypothesised to have been around 50,000 years ago, see Ruhlen (1994). A genetic solution, where the lexicon is stored in the genetic code and thus transmitted from parent to child, seems clearly out of the question. Nevertheless, a lot of the early work on computational modeling of language origins relied on a genetic approach for transmitting the lexicon, possibly with some additional adaptation. See for example: MacLennan & Burghardt (1993: 603–631). This approach sheds light on the issue how signaling systems may evolve in animals but is not applicable to the transmission of human lexicons. The lexicon of human languages is too diverse and changes too quickly to allow genetic transmission. So lexicons must somehow be transmitted in a cultural process.

It turns out that the agent architecture I introduced in the previous sections does not need to be changed at all to obtain a cultural transmission of a lexicon, illustrating the explanatory power of the model despite its simplicity. New virgin agents entering the group may occasionally create a new word, if they do not have one themselves, but if a particular set of words with particular meanings is already strongly entrenched in the population, these new words have a very low probability to survive. Instead, the virgin agents will adopt the words that they abundantly hear in their environment, and the score of these words goes up quickly.

Here is a computer simulation testing whether this is indeed the case (see Figure 5.6). We begin with a population of 20 agents and let them develop a shared lexicon for 20 meanings (phase 1). Then I *add* new virgin agents at regular time intervals, at a rate of 1 every 1000 games (phase 2). A new agent has no knowledge of the existing lexicon and therefore must acquire the lexicon present in the rest of the group. Figure 5.6 (phase 2) shows that the population indeed copes. A new member initially causes some failures in communication, but he quickly picks up the lexicon of the community and success moves back up. The lexicon does not change, it is stable against minor perturbations.

However, when the birth rate is increased to 1/100 games (phase 3) the population is less able to cope. Success stays relatively high (70 %), but there are too many new agents coming in too fast. The lexicon cannot spread sufficiently quickly to the new agents and therefore starts to disintegrate. In a final stage (phase 4), the birth rate is set again to 1

Figure 5.6: Evolution of communicative success with different birth-rates, starting from a population of 20 agents (phase 1). Next the birth rate is increased from 1 new agent every 1000 games (phase 2) to 1 new agent every 100 games (phase 3), and then to 1 every 50 games (phase 4).

new agent every 50 games. The population is no longer able to cope with the influx of new members and disintegrates. If inflow is brought back to a lower rate, the population would again establish a shared lexicon. However, the lexicon is now a different one from the one that was established before. The dynamical process has moved from one stable lexical state to another one.

We have seen earlier that the Naming Game scales up with respect to the size of possible meanings. Now we see that it scales up with respect to the size of the population. As long as the rate of influx is not too high, the population can keep expanding. The only constraining factor is that new agents must have sufficient opportunities to acquire the lexicon present in the group.

#### **5.2.3 Preservation in changing populations**

In human populations, there is not only an influx of new members but also an outflux. When somebody leaves the community knowledge about the lexicon should disappear as well. Nevertheless, a lexicon clearly gets preserved from one generation to the next, which implies that the know-how is distributed robustly over the agents.

The next computer simulation tests whether this is also true in the Naming Game model. The simulation starts with a population of 20 agents who are left to develop a shared lexicon for 20 meanings (phase 1). Then an in- *and* out-flux is introduced (phase

#### *5.2 Scaling up*

2 in Figure 5.7) with one new virgin agent coming in and another agent leaving the population every 1000 games. The new agent has to acquire the lexicon present in the group. Average success therefore dips but is quickly regained. In fact, the population can be completely renewed without affecting the lexicon at all. After 16000 games nine agents (50 %) have been replaced, but the lexicon has not changed. So, the Naming Game model not only explains the formation of a lexicon but also its transmission: This transmission is entirely cultural. New agents enter the population with no prior knowledge.

Figure 5.7: Success and population size is shown for a series of 35,000 language games. The population starts with 20 agents and 20 meanings (phase 1). Then an influx and outflux is introduced at the rate of 1/1000 games (phase 2). The lexicon maintains itself. In phase 3 agents enter and leave at the rate of 1/100 games. Success lowers. In phase 4 the rate of change is brought back to 1/1000 games and success is regained.

Can we increase the flux in the population indefinitely? This is examined in phase 3 of Figure 5.7. In this phase a higher flux has been introduced. One agent is added and removed every 100 games. Success goes down, although it is still maintained at a high level. The lexicon is still not changing. However, previous examples have already shown us that if we continue to increase the rate, the lexicon would disintegrate. Too many new agents would be flowing in, who do not have a lexicon yet. On the other hand, if we bring the rate of change back down to 1/1000 games (phase 4 in figure 5.7), success regenerates.

These simulation illustrates how we can study lexicon transmission using a language game approach. We have to set up an in- and outflow of the agents and study the impact on their communicative success and their lexicon. In principle, we should not have to change the architecture of the individual agents, and indeed I have not done so. Language acquisition is such an integral part of language use that a realistic agent architecture must intimately integrate both capacities from the start. Of course, at this stage we have only tested this with the agents getting direct feedback about meaning, we still must that whether it will continue to work with the physically instantiated Talking Heads.

## **5.3 Self-organisation**

These various simulations show that the Naming Game embodies robust mechanisms for the emergence of a lexicon and we will use it as a core component for the Talking Heads experiment. In retrospect, the following mechanisms are crucial for the success of the model:

When any of these characteristics of the agent architecture or the game are eliminated, the system does not work. Communicative success does not climb, convergence will not go beyond a small percentage, the size of the lexicon explodes, and so on. The fact that these architectural properties are crucial and non-trivial to discover strongly suggests that similar mechanisms must be in place in the emergence of human lexicons.

*5.3 Self-organisation*

It is also important to stress what is not in the model. The mechanisms used by the agents are deliberately kept as simple as possible. Complexity should arise only from the enactment of simple construction rules. Agents do not go through complex reasoning about words, they simply store the new associations they encounter and rely on the updating processes to weed out wrong hypotheses.

#### **5.3.1 Winner-take-all processes**

The most remarkable and at first mysterious property of the Naming Game model is that the agents somehow reach a consensus without any central supervisor. They do *not* do this by having a general overview or by changing their internal parameters so as to become more conservative as the lexicon solidifies. It is solely due to the subtle interaction between language use, which gradually becomes uniform, and each agent's adaptation to the language heard in the environment. If a certain word comes to be preferred by a group of agents for a certain meaning, its frequency of use goes up so that others encounter this word more often and hence their scores for that word continue to increase as well. The more agents use a word, the higher its chance of success and the more it will be used. This effect is still enforced by lateral inhibition. The scores of competing associations decrease, making it less likely that they will win in the future. This positive feedback therefore introduces an autocatalytic (self-enforcing) effect until the population locks into an equilibrium state.6

To follow better how a consensus gradually emerges, I will visualise the competition between different words for the same meaning in a meaning-form (MF) competition diagram, such as the one in Figure 5.8, which monitors the frequencies of the different forms in use for one meaning. The diagram shows clearly the struggle between different forms until one form (*pe*) emerges as the winner. When we later study grounded lexicon formation processes, we will see that the competition becomes much more complex and the whole system is in constant evolution. A form-meaning pair which is dominating may become weaker because its meaning fails to pick up the right referent in a new context. This in turn may trigger the creation of new words or the resurgence of existing words.

#### **5.3.2 Collective behaviour and self-organisation**

Biology is full of examples where structures spontaneously self-organise from the uncoordinated activity of distributed elements through a winner-take-all process. Each time the same basic components as in the Naming Game model are seen: Random behaviour creates various possibilities and the reinforcement of some of these variations through positive feedback creates an autocatalytic effect. Perhaps the clearest examples can be found in the collective behaviour of social insects, such as the formation of nests by termites, although beautiful explanations have also been reported for the formation of

6 Such positive feedback loops and the stability criteria associated with them have been widely studied in non-linear dynamical systems and applied to chemical and biological processes. See Babloyantz (1986).

#### *5 The Naming Game*

Figure 5.8: Simulation with a population of 20 agents. The meaning-form competition diagram shows the frequency of all competing forms for a single meaning. We see a winner-take-all situation with one word (*pe*) dominating.

patterns on sea shells, the growth of cell tissue, the aggregation of individual cellular slime mold amoebae into a slug, the flocking and collective movement of birds or mammals, etc., Meinhardt (1982). A classical example for collective behaviour, first developed by Jean-Louis Deneubourg, is the formation of paths in an ant society through mass recruitment, Pasteels & Deneuborg (1987).

When ants carry food or other materials, they organise themselves in a chain which is typically the shortest path between the source and the nest. These chains can sometimes be surprisingly long (20 meters is quite common for European ants) and are maintained as long as the food supply lasts. The whole process has many intriguing properties. First of all, there is no central planning agency that regulates which food sources are to be explored. The coherence and co-ordination between hundreds or sometimes thousands of ants is established in a completely distributed fashion. There is no dependence on individual ants. Ants can be removed from a path or new ones can be introduced randomly without too much interference for the stability of the path as a whole. The paths are robust. If objects are put in the way or if the path is destroyed, the ants manage to reestablish it in a relatively short time span. The paths are adaptive. If the food supply terminates, the path disintegrates and a new path will appear linking the ants to an alternative food source.

We see here many of the properties found in natural languages and integrated in the

#### *5.3 Self-organisation*

Naming Game model: absence of central planning, no critical dependence on a single element, resilience to influx or outflux of elements, and adaptation to changing circumstances. Even more interestingly, the ants manage to establish these dynamic paths by a process which is similar to the language formation process used in the Naming Game, namely a positive feedback loop having an autocatalytic effect. An individual ant appears to move around in a random fashion while searching for a source of food. When a food source is discovered, the ant returns to the nest using a global landmark like the sun. The food-carrying ant also deposits a chemical substance known as a pheromone as he travels back to the nest. This pheromone influences the otherwise random movement of the other ants, in that ants are attracted by the pheromone. Thus more ants are drawn to the path and hence led to the food source. As these ants in turn go back to the nest they also deposit pheromone. This gives the self-enforcing, autocatalytic effect: The more ants are on the path, the more pheromone is deposited, and therefore the stronger the attraction to the other ants. Very soon all the ants which were sufficiently close to the path form a chain. There is no central planning agency needed and the whole system does not depend on an individual ant. The order is emergent.

These simple mechanisms also explain other features of the process. When the food source is depleted, the ants going back no longer deposit pheromone. And because the pheromone is a chemical that evaporates, it will soon have disappeared and consequently the ants will return to a random movement. When a path is interrupted because obstacles are put in the way or because the pheromone is temporarily removed by an experimenter, the ants resort back to a random movement. This introduces a random search process which will eventually lead to the discovery of a connection and the reestablishment of the path. When two ants find two food sources one closer than the other, the society will go for the closest source. Not because they exchange sophisticated signals but because the trail leading to the closest source will be amplified faster. Adaptivity is explained in terms of errors in following the path. Although ants are attracted to the pheromone, the attraction is only partial and very often (how often depends on the species) they will go astray. This sloppiness is however a source of new discoveries. When a lost ant hits upon a new food source the path formed by the whole society may gradually shift particularly if it is more abundant.

#### **5.3.3 Increasing-returns economics**

Self-organisation is not unique to biological phenomena, on the contrary, similar situations have been intensively studied in economics, where the complex adaptive systems paradigm has recently also led to many interesting new insights, as discussed in Arthur (1996). For certain types of products, particularly in information technology where the cost of manufacturing and distribution is neglectible compared to the cost of design, a winner-take-all situation can be observed. One product, for example a particular operating system or a particular microprocessor, comes to dominate the market.

Brian Arthur and others have analysed these economic situations and identified a positive feedback loop as being the ultimate cause. The more customers choose a product,

#### *5 The Naming Game*

the more others are attracted to it, particularly because other suppliers develop useful derivative products. Prices can be decreased keeping newcomers out of the market and customers get locked in, unable to move to other suppliers because they have invested too much and became dependent. For the companies who manage to manoeuver their products in such a situation there is a bonanza of increasing returns. This contrasts with the decreasing returns familiar from traditional equilibrium economics, where there is a damping of profits due to proliferating production and distribution cost as a product's market share increases.

#### **5.3.4 Lessons from nature**

The analogies between self-organisation in language and other fields is important for three reasons. First of all, if self-organisation is ubiquitous in nature and has successfully explained so many phenomena, its incorporation into a model of language becomes independently motivated, and therefore the explanatory force of the model increases. What is new and different is that the principle is applied to a non-material self-organising entity, but nevertheless the same sort of dynamics can be seen.

Second, the large arsenal of mathematical tools and analysis techniques developed in the sciences of complexity over the past decades can be carried over to the study of language. For example, the mathematical models of economists like Arthur or biologists like Deneubourg help us develop mathematical explanations why language reaches coherence if autocatalysis is present.

Third it suggests many aspects of the mechanisms which might be relevant for language. For example, the errors ants make in following a trail allow them to discover occasionally better food sources. Could such stochasticity also play a role in the adaptive capabilities of language? The chaotic regime seen in many natural systems is known to be a source of new order (Kaneko 1996). Could language innovation also be explained that way? In other words, is it possible that language may occasionally exhibit a chaotic dynamics out of which new order emerges?

## **5.4 Lexical dynamics**

This discussion begins to illustrate a major theme of the present book, namely that language as a macroscopic phenomenon can be viewed as a complex adaptive system with the same characteristics as other complex adaptive systems.

It is well known that the dynamics of language change are related to the dynamics of the underlying population. Basically we can see two phenomena. On the one hand, human populations are not fixed for ever. New children without any knowledge of the language are born and other members die, taking knowledge about the language away with them. Populations renew at a certain rate which is known to have a significant impact on language. If the population changes quickly a language evolves more quickly and subsystems may even destabilise. For example, linguists have argued that English

#### *5.4 Lexical dynamics*

lost its case system due to the Black Plague which decimated the population so that there was not enough opportunity for children to acquire the existing conventions.

Second, human populations mix. Throughout the history of mankind there have been migrations or intense contact between geographically diverse groups. This again impacts then the languages of the groups. When a given population splits into groups that have no longer contact, their languages start to deviate. Conversely when there is an intense and prolonged contact between languages, structures from one language get adopted by the other and vice-versa. The degree of adoption depends on which group is dominant. Sometimes groups adopt another lexicon while retaining their own syntax, and sometimes they take over the syntax while retaining their own lexicon.7

These phenomena are fascinating and interesting from the viewpoint of language evolution, and may even explain some of the characteristics of human languages. Linguistic systems must be such that they can be transmitted from one generation to the next, otherwise they will not survive. In the Talking Heads experiment, new agents may enter into the group at any time and agents are geographically distributed. The local interactions with humans at a particular site, which is a kind of language contact between human and artificial populations, may impact the evolving lexicons and ontologies.

#### **5.4.1 Spatially distributed naming games**

Language game models provide us with new fantastic tools to study language transmission and language contact: We can introduce a particular dynamics in the population in a controlled way and then study the impact on the dynamics of the language itself. I now focus on such a model to investigate the impact of the migratory dynamics of a population on the dynamics of language. We can introduce a two-dimensional grid and assign every agent randomly a position on this grid. The position assignment can be modulated so that the agents form clusters (Figure 5.9). Such a population structure can be thought of as a geographical distribution in space but might as well represent a social, genetic or economical structure. We could even envision models integrating several of these alternate dimensions. The physical Talking Heads network connecting installations in different geographical locations allows to do these experiments for real.

In earlier simulations agents were randomly picked out of the population. Now we can base the probability with which two agents interact on their respective distance and on an interaction factor, which determines the weight of the distance. If the interaction factor increases, the role of distance becomes more important and interactions tend to reflect the spatial clustering more. Based on this parameter we can study the evolution of language when communications between clusters of agents increase.

Initially we let each subgroup evolve towards a shared communication. Success is never total because there are occasional interactions with members of other communities, however inner-cluster communication reaches total success. However inspection of the agent lexicons reveals that agents will develop a stable language within their cluster,

7 A representative example of empirical investigations into language dynamics is contained in Nichols (1992). See also Romaine (1988).

*5 The Naming Game*

Figure 5.9: The figure shows the spatial distribution of a set of 20 agents. There is clustering around three centers.

but also a second language, an interlingua, which is weaker but shared among the different clusters. This interlingua will become stronger as more agents interact between clusters. Thus we observe language diversity due to the spatial distribution but at the same time the rise of an interlingua.

The following vocabularies illustrate this point clearly. The first vocabulary is taken from an agent from the leftmost cluster in Figure 5.9. All the words associated with a particular meaning are shown together with their score.

```
{}[M0]: kube[0.88] gutida[0.00] moko[0.00]
{}[M1]: nugini[0.97] gi[0.83] majiba[0.00]
{}[M2]: go[0.98] ta[0.00]
{}[M3]: moma[0.98] ti[0.00] nudo[0.00] kene[0.00]
{}[M4]: nebu[0.98] me[0.83]
{}[M5]: tine[0.98]
{}[M6]: bo[0.94] babige[0.82]
{}[M7]: mepabo[0.97] jabeto[0.71] di[0.00]
{}[M8]: kude[0.90] nado[0.00]
{}[M9]: pe[0.94] da[0.00]
{}[M10]: na[0.94] nuguge[0.90] pa[0.80] ne[0.00]
{}[M11]: mu[0.98] gite[0.00] paku[0.00]
{}[M12]: gema[0.96] do[0.33] gapu[0.00]
{}[M13]: ja[0.67] jo[0.00]
{}[M14]: dodine[0.88] pibo[0.83] gije[0.00] pupeto[0.00]
{}[M15]: jiti[0.94] gato[0.64]
{}[M16]: bimogu[0.98] ba[0.00]
{}[M17]: bapi[0.96] ki[0.81] damuti[1,0,0.00]
```
*5.4 Lexical dynamics*

{}[M18]: kutume [0.94] bu [0.00] ni[0.00] {}[M19]: mugu[0.95] NINU[0.50] pi[0.43] ji[0.00] tu[0.00]

This is the vocabulary for an agent taken from the rightmost cluster in Figure 5.9:

```
{}[M0]: gutida[0.79] kube[0.00]
{}[M1]: gi[0.89] matu[0.85] pumoni[0.00]
{}[M2]: go[0.95] ta[0.20]
{}[M3]: kene[0.89] moma[0.82] nudo[0.00] koko[0.00]
{}[M4]: nebu[0.97] me[0.00] bukugo[0.00]
{}[M5]: tine[0.90]
{}[M6]: babige[0.93] bo[0.00]
{}[M7]: mepabo[0.90] junipe[0.75] di[0.00]
{}[M8]: nado[0.96] kude[0.80] puto[0.00]
{}[M9]: da[0.86] nine[0.71]
{}[M10]: pa[0.87]
{}[M11]: gite[0.88]
{}[M12]: gema[0.90] gapu[0.87]
{}[M13]: jo[0.96] ji[0.89] ja[0.00]
{}[M14]: dodine[0.96] pupeto[0.56] pibo[0.00] gije[0.00]
{}[M15]: jiti[0.97] gato[0.46]
{}[M16]: bimogu[0.97] ba[0.83] pipebe[0.00]
{}[M17]: ki[0.97] bapi[0.00] ke[,0.00]
{}[M18]: ni[0.94] kutume[0.80] moko[0.80] mekami[0.00]
{}[M19]: ninu[0.81] mugu[0.00] pi[0.00]
```
Some words (for example *tine* for [M5] or *go* for [M2]) are shared. But generally there are at least two words. One word is used preferentially inside the cluster, the other is known but preferentially used by members of another cluster. Thus the word *mugu* for [M19] is preferred for the first object in the first cluster and known but not preferentially used by the agent in the second cluster. Conversely, *ninu* is preferred for the same meaning by the agent in the second cluster, although he also knows *mugu*. *mepabo* for [M7] belongs to the interlingua. Both agents know and use it but they have a strong alternative *jabeto* for the first and *junipe* for the second agent.

### **5.4.2 Language contact**

When the interaction factor increases, we see further differentiation because there is less communication between clusters. When it is decreased, we see more coherence because there is more intercluster communication. Thus we can effectively tune divergence or convergence in the simulations based on the probability of interaction between communities (clusters) of agents. The effect of increased language contact and hence convergence is demonstrated in Figure 5.10. The simulation starts from the situation described

#### *5 The Naming Game*

earlier with three clusters of agents that have each evolved a lexicon. The interaction between clusters is initially very weak. At some point (after 4000 games) the intercluster communication is increased drastically. At first there is a drop in communicative success but then total communicative success is again reached.

Figure 5.10: Evolution of average communicative success per 25 games in a group of agents with first weak (phase 1) and then strong interactions (phase 2).

However, this general evolution hides the more interesting developments. Figure 5.11 shows the evolution of coherence for each cluster (a, b, c) separately and also for the total set of agents. As long as the agents have relatively little contact, total coherence is low although the lexical coherence within each cluster is high. Total coherence starts to increase with increased contact. Coherence in each cluster diminishes somewhat because the agents in the cluster are in the process of accommodating to the global lexicon. This means that the languages of the different groups are in the process of merging due to the increased language contact.

Simulations show that, just as in human languages, increased contact causes at first a rapid increase in bilingualism, then a gradual mixing of the languages, and, if the contact continues, an evolution towards complete coherence. The more rapid the contact is increased, the faster the three phases can be observed.

Figure 5.11: Evolution of coherence in the total population and in the individual clusters is shown on the same scale as the previous figure. When contact is increased (phase 2), global coherence begins to rise steadily.

## **5.5 Conclusions**

A population of agents following a simple set of behaviour rules and using an associative memory can give rise to a shared repertoire of form-meaning associations, giving the agents a total average success in communication. Once a shared repertoire comes into existence, it locks into an equilibrium state and gets transmitted from one generation to the next in a cultural process, as long as the rate of population change is not too high. The population can also cope with an in- and outflux of meanings, in the sense that the lexicon constracts or expands in relation to the demands from an evolving set of possible meanings.

The mechanisms I have proposed here for the Naming Game are remarkable in many ways. It clearly shows that a shared set of conventions can arise without an omniscient central co-ordinator and without any prior knowledge of the lexicon built into the agents. The Naming Game also demonstrates a new way to model and thus investigate linguistic phenomena. Existing formal models of language, such as generative grammars, only model static competence of a single idealised speaker in a homogeneous language community. Using the framework of language games played by populations of agents, we can model the emergence and evolution of language in an inhomogeneous community and study language use as well as change through language contact.

#### *5 The Naming Game*

The Naming Game is a minimal model of communication between agents and far removed from the full complexity of human natural language. Moreover we made a number of simplifying assumptions, thus putting up scaffolds to construct this initial model. The most important assumption was that the meaning of a word can be unambiguously known by the speaker and hearer independently of language. This assumption is of course not valid for human beings, and neither is it valid for the Talking Heads.

## **6 The Guessing Game**

The problem how a physically embodied situated agent might refer to objects using language is extraordinarily difficult. If we then further want to find out how a group of such agents might autonomously bootstrap a language system, the task seems almost unsurmountable. That is why I proposed earlier on to start by dividing this task into its three main subtasks along the lines of the semiotic square (Figure 6.1). The previous chapters each focused on one of these tasks. Chapter 5 has introduced perceptual mechanisms to process the raw image, segment the scene, derive characteristics about each segment, and give feedback by pointing to the referent. Chapter 4 studied categorisation mechanisms needed for conceptualising a scene and thus for generating the possible meanings of a verbal communication. Chapter 5 looked at how agents can lexicalise meanings and build up a sufficiently shared lexicon to engage in verbal interactions.

Given that we now have reasonable solutions for these basic processes, at least for its most simple instantiations, we can now start to put the pieces together and thus study the complete guessing game. I will proceed in two steps. First I will but the lexical layer and the conceptualisation layer together in this chapter, and then I will ground the whole system by coupling the conceptualisation layer to the perceptual layer in Chapter 7.

Another technique I proposed earlier on for handling the enormous challenges addressed in this book, is to scale up gradually. I will follow this strategy as well. In this chapter, I will assume that the referent and the perceived image are the same. This implies that we are really dealing with semiotic triangles as opposed to semiotic squares (Figure 6.1). I will start simulations with only 2 agents and then scale up to a larger number. This increases the degree of synonymy in the lexicon. I will furthermore start by letting the agents consider only the most salient channel, so that they much more easily guess the same category for the same scene. Then I will scale this up so that the agents now consider more sensory channels and hence more categories. This increases the degree of ambiguity in the lexicon. Both synonymy and ambiguity are sources of incoherence and we will have to make sure that agents still manage to be successful despite of these.

This chapter shows that agents still manage to bootstrap a shared lexicon due to carefully established feedback couplings between the different processing layers introduced in the previous chapters. The language game gives feedback to the lexical layer so that words become preferred that are understood by others. The lexical layer gives feedback to the conceptual layer so that categories become preferred that have been successfully lexicalised. Each layer is a selectionist system that generates possible ways to solve a subproblem, of which some are kept and others discarded based on feedback of their use. I will examine in this chapter whether these couplings indeed cause a coordination of

*6 The Guessing Game*

the different internal layers in a single agent and whether they lead to shared ontologies and lexicons.

## **6.1 Defining the Guessing Game**

The guessing game was already introduced in Chapter 2. Here is a first example game, game 500. **a2** plays the role of speaker and **a1** the role of hearer. The game is about the scene in Figure 6.2. The topic is the rectangle labeled 1. The grayscale channel is the most salient channel. The different sensory values (after sensor-scaling) for the segments in Figure 6.2 are shown in Table 6.1. The last line shows the saliency of the topic segment 1. Clearly the grayscale channel is the most salient.

Table 6.1: Sensory data for the scene shown in Figure 6.2.

All rectangles are relatively close to each other and have more or less the same height and width. But the grayscale is clearly the more salient because rectangle-1 is much darker than the others. I assume that there are only two agents in the population and that they always use only the most salient to conceptualise the scene. The speaker and hearer have to traverse only two sides of the semiotic square (Figure 6.1) because we assume that perceived image and object being referred to are identical for both agents.

Figure 6.1: The semiotic square becomes a triangle when the perceived image and the referent in the real world are assumed to be identical.

*6.1 Defining the Guessing Game*

#### **6.1.1 Example of a coupled game**

The speaker first plays a Discrimination Game traversing the semantic side of the square going from the referent *rectangle-1* to a possible meaning [gray 0.5–1.0]. He then plays a Naming Game traversing the lexical side of of the square to find the word *pokuneso* for this chosen meaning. The hearer traverses the lexical side of the triangle in the other direction to interpret the word *pokuneso* as [gray 0.5–1.0], and then identifies the referent by filtering the objects in the context with this meaning. Only rectangle-1 remains, so the game succeeds. The whole game is reported by the commentator as follows:

```
Game 500
```

```
a2 is the speaker. a1 is the hearer.
a2 segments the context into 3 objects:
     rectangle-0 rectangle-1 rectangle-2
a2 chooses rectangle-1 as the topic
a2 categorises the topic as [GRAY 0.5–1.0]
a2 says: pokuneso
a1 interprets pokuneso as [GRAY 0.5–1.0]
a1 points to rectangle-1
a2 signals OK
```
The game is perfectly successful because both agents associate the word *okuneso* with [gray 0.5–1.0] (dark) and they perceive the scene in the same way.

Figure 6.2: Example scene used in game 500.

Before examining the architecture behind these games in more detail, we can already see from Figure 6.4 that **a1** and **a2** clearly manage to build autonomously a communication system and its underlying ontology from scratch by playing the guessing game. The communicative success moves up to reach almost 100 % after a mere 500 games. Given that the environment keeps generating novel situations, there is always a chance that a scene occurs which requires new categories. So there is always a chance of failure, but it will further trigger expansion of the discrimination trees and of the lexicon.

*6 The Guessing Game*

Figure 6.3: Semiotic triangle underlying game 500.

Figure 6.4: Success (left y-axis) and average ontology size (right y-axis) for two agents playing 500 guessing games.

#### *6.1 Defining the Guessing Game*

Figure 6.4 also shows the average number of categories in each agent. There is a steep rise in the early phases, when no categories exist, but then the creation of new categories levels off as discrimination mostly succeeds. When the environment becomes more complex, possibly exercising additional sensory channels, the discrimination trees would start to expand again, as we have seen in the previous chapter and then the lexicon would start to expand as well. Obviously the lexicon can only start to develop when there is an adequate ontology which explains some of the delay before the communicativesuccess curve starts to climb.

Table 6.2 displays the complete lexicon of the two agents after 100 games, together with the score for each assocation for **a1** and **a2**. Only associations where the score is above 0.0 for at least one agent are shown. A dash (-) indicates that the agent has not stored this association yet.

Table 6.2: Complete lexicon of **a1** and **a2** after 100 games

We see that, at this point, the agents have lexicalised only the most general distinctions, such as 'dark' (*pokuneso*) versus 'light' (*fesasado*) or 'short' (*suwaxugo*) versus 'tall' (*kusone*). Words for the grayscale and height dimensions have the strongest scores, although this is purely accidental. When we would start another simulation from scratch, we would end up with different words and perhaps other distinctions would be more successful.

Table 6.3 is the complete lexicon after 500 games and Table 6.4 after 1000 games.

We see that words for basic distinctions have further established themselves. Words for 'short' (*suwaxugo*) and 'tall' (*kusone*), or 'light' (*fesasado*) and 'dark' (*pokuneso*) now have scores of 1.0. Words for more refined categories, like 'very short' (*tawube*) or 'very narrow' (*kutaki*), are beginning to establish themselves.

Two steps in the evolution of the discrimination trees underlying this lexicon are shown in Figure 6.5. There is a progressive refinement of all trees as time goes on, because all sensory channels have the same chance of being most salient. But the trees are

Table 6.3: Lexicon of **a1** and **a2** after 500 games

Table 6.4: Lexicon of **a1** and **a2** after 1000 games

not the same for the two agents at every stage of development because even though they prefer to expand the salient channel, the agents have encountered different environmental situations in which different channels were salient. For example, after 100 games, **a1** has less refinements for the width channel than **a2**. After 500 games, all trees have at least one level of refinement. Not all categories have been lexicalised. For example, the width channel is three levels deep in both agents but no words exist yet for the deepest level.

Figure 6.5: Evolution of the discrimination trees of **a1** (left) and **a2** (right). Snapshots have been taken after 100 games (top) and 500 games (bottom).

Note that this simulation is very different from the ones shown in the previous chapter. The agents now get only feedback through overt selection of the referent. The hearer points to the identified referent and the speaker decides on the outcome of the game based on this non-verbal information, but speaker and hearer do not know whether they have used the same meaning or not. Very often there are alternative ways to conceptualise reality, so even if agents would have completely shared ontologies, there is still the possibility of guessing the wrong meaning. I have called this the gavagai-problem, inspired by the philosopherQuine, who tells the story of the anthropologist puzzled by the word *gavagai* uttered by a native in an undecoded language. Does *gavagai* mean rabit, animal scurrying by, the direction in which I will go now, or white furry object? The child who is acquiring a lexicon has exactly the same problem. It explains why overex*6 The Guessing Game*

tensions or underextensions are seen in a child's first words. For example, the word for orange is applied to any small circular round object, including a ball, or a doorknob.

#### **6.1.2 Input-output coupling**

Obviously the first thing I had to do to get these results, is make the inputs of one layer the outputs of the other (Figure 6.6). When the speaker has conceptualised the scene, the possible solutions enter the lexical layer for lexicon lookup. The resulting words get into a competition and the one with the highest score wins. In a more complete system with a syntactic layer, different lexicalisations would be considered by the syntactic layer to find the one that fits with the rest of the grammatical structure.

Figure 6.6: Flow of solutions through coupled layers from perception to conceptualisation and lexicalisation with re-entry links between them.

The importance of having re-entry links now becomes clear. The choice which conceptualisation is finally chosen as the best one will depend on the lexical layer because the speaker should prefer those categories whose lexicalisation is best established, if he wants to maximise success in the game. Due to the constant evolution of the lexicon and the presence of synonyms, the conceptual layer cannot know once and for all what the most appropriate conceptualisation from the viewpoint of language will be. And it needs to know the outcome of the lexical layer to later update the scores of participating categorisers.

The hearer uses the same layers but now with solutions flowing in the other direction. He gets a set of words which generate possible conceptualisations through lexicon lookup and these then are applied to the scene to find the referent (Figure 6.7). Because layers have this dual mode of operations, it is perfectly possible that the hearer has already guessed words and thus strong expectations based on the scene and his own conceptualisation of it, although this has not been implemented in the Talking Heads yet.

*6.1 Defining the Guessing Game*

Figure 6.7: Layers operate in two directions. The flow of solutions in the hearer is shown from words to categories and perceptions and in the other direction through re-entry.

Also for the hearer, the re-entrant flow is important. A hearer can only know which meaning was intended for a particular word after trying out the meaning on the scene. He therefore uses the context to determine the meaning of the utterance. For example, a particular word may mean both [large] and [dark], particularly during the phase of early language acquisition. However if only one of these categories picks out a single referent, it is chosen as the meaning, and the hearer will act upon this choice by pointing to the object it singles out from the scene.

This architecture takes care of synonymy and ambiguity and makes sure that the most plausible form/meaning/referent chain stands out. A similar architecture may explain how humans effortlessly pick out the appropriate meanings from the many possible meanings a word typically has and not even be aware of the alternatives. If our language sytems could not cope this way with ambiguity and ambiguity we would have had to use a lexicon where every word can have only a single meaning. Language has had to recruit whatever capacity was already available.

#### **6.1.3 Updating the scores**

The next thing I had to do is reconsider the score updating mechanisms, even though they are basically the same as used earlier (Figure 6.8). For a given referent, there are multiple meanings possible (in case more than one channel is considered to be sufficiently salient), and for each meaning there are multiple words. The best one of this whole lot is chosen by the speaker and used for the utterance transmitted to the hearer. We have seen that it is important for the hearer to use lateral inhibition based on the outcome of a game. But although the speaker is considering *all* the possible conceptualisations, lateral inhibition should only take place between the lexicalisations of the meaning that was finally chosen.

#### *6 The Guessing Game*

So when the game was successful, the speaker increases the association that was used with *δ* and decreases all the other associations *with the same meaning*. *delta* is still set to a reasonable low value, namely *delta* = 0.1. The hearer does the same as explained earlier in the Naming Game. The score of all the alternative meanings for the word (or words) that are used by the speaker are decreased. When the game fails, both the speaker and the hearer decrease the association that they used with *δ*. No change takes place to the scores of any of the other associations.

Figure 6.8: Score adjustments after a successful game. Used associations go up and competing associations go down. The game producing these relationships is discussed later as game 10008.

The scores of the categories and category combinations in the discrimination trees should also be updated. When a category or category combination is used as part of the communication in the game (as meaning for the speaker or the hearer), its use counter goes up. When the game is successful, its success counter goes up. To know the score of a particular category or category-set, the agent simply divides success by use. Because the score of the categories thus depends on their success in the language game, a strong coordination gradually arises between conceptualisation and lexicalisations. After a while, categorisations will be preferred that are amenable to yield successful language games

*6.1 Defining the Guessing Game*

and of course the language only lexicalises categories that are nodes in discrimination trees. We thus get a progressive coordination of both the repertoire of categories and the lexicon, as I will discuss in more detail later.

The other criteria discussed earlier (simplicity of the categories and level of depth in the tree) are still used for ranking the possible conceptualisations coming out of the lexicon, particularly when none of the meanings has been lexicalised yet or whether there are multiple possibilities. The human brain is clearly capable to integrate many more criteria in lexical choice. For example, when talking to a child we might use more common words than we would use when talking to another adult.

#### **6.1.4 Repair processes**

Of course the other repair processes discussed earlier are still going on as well. Agents expand their discrimination trees when they fail to categorise and they invent new words or adopt words from the other if necessary. The task is more complicated compared to the simple Naming Game because the hearer now gets no direct feedback of the meaning only of the referent. In case of failure, the hearer must try to find himself a distinctive category or category set discriminating the referent from the other objects in the context.

Here is an example game illustrating this type of repair process. The data for game 77 (after sensor-scaling) is shown in Table 6.5.

Table 6.5: Sensory data for game 77 after sensor-scaling.

The speaker is again **a2**. height is the most salient channel. **a2** has a word for [height 0.75–1.0] (very tall), namely *bowaluro*, and uses it. The hearer **a1** does not know the word, conceptualises the scene, and arrives at the same category, so the hearer stores the new word with the same meaning as the speaker.

```
Game 77
  a2 is the speaker. a1 is the hearer.
  a2 segments the context into 3 objects:
       rectangle-0 rectangle-1 rectangle-2
  a2 chooses rectangle-1 as the topic
  a2 categorises the topic as [HEIGHT 0.75–1.0]
  a2 says: 'bowaluro'
  a1 does not know 'bowaluro'
  a1 says: 'bowaluro?'
```
*6 The Guessing Game*

```
a2 points to rectangle-1
a1 categorises the topic as [HEIGHT 0.75–1.0]
a1 stores 'bowaluro' as [HEIGHT 0.75–1.0]
```
The reason why **a1** has guessed the right meaning of *bowaluro* is because both agents use only the most salient channel and they both share the same perception of reality. We will soon see that if these constraints are not valid, agents are not always so lucky and hence multiple meanings start to circulate for the same word.

A similar repair action takes place when the hearer cannot guess a unique referent, as illustrated in game 96 drawn from the same simulation series. The scene contains three rectangles and the topic is the most narrow rectangle. The segments in the scene of game 279 have the characteristics (after sensor-scaling) shown in Table 6.6.

Table 6.6: Sensory data for game 279

The hearer guessed the meaning used by the speaker right away, because both share the same perception and both use the most salient channel as basis for categorisation.

```
Game 96
  a1 is the speaker. a2 is the hearer.
  a1 segments the context into 3 objects:
       rectangle-0 rectangle-1 rectangle-2
  a1 chooses rectangle-1 as the topic
  a1 categorises the topic as [WIDTH 0.0–0.25]
  a1 creates a new word: 'kutaki'
  a1 says: 'kutaki'
  a2 does not find a unique referent
  a2 says: 'kutaki?'
  a1 points to rectangle-1
  a2 categorises the topic as [WIDTH 0.0–0.25]
  a2 stores 'kutaki' as [WIDTH 0.0–0.25]
```
## **6.2 Synonymy**

When we scale up the population, synonyms (several words for the same meaning) will start to appear. Indeed, when there are only two agents, the hearer picks up a word as soon as the speaker has created it. With a larger group, it is much more likely that agents

*6.2 Synonymy*

create words not knowing that words already exist in the population, and it takes time for a new word to propagate.

Synonyms are not a positive feature of a language. They make it less efficient for the speaker to find the most appropriate word to express a meaning, they require more memory to store the lexicon, and confuse a new virgin agent coming into the group. In natural languages, synonyms get damped and we have seen in the previous chapter that the positive feedback loop between use and success (implemented by lateral inhibition in the agent's score updating process) has the same effect. Let us now see whether this is still the case if the hearer does not get any feedback about the meaning used.

The following simulation uses a group of ten agents. Each agent still only uses the most salient channel so that the agents can guess the meaning easily in case a word is not known. The evolution of communicative success for a series of 4000 games, which means about 800 games per agent, is shown in Figure 6.9. An effective lexicon and ontology is emerging because we see communicative success rise.

Figure 6.9: Communicative success (left y-axis) and average ontology size (right y-axis) is shown for a series of 4000 language games played by 10 agents.

Part of the lexicons of five of the ten agents after 2000 games (only those words which have positive scores) are shown in the Table 6.7. We see that synonymy does indeed occur. For example, two words are in the running for [hpos 0.5–1.0]: *rutaxese* and *xomupovi*, and three for [vpos 0.5–1.0]: *wavone*, *zaxawe*, and *dazofo*. Some words are already well established, for example *numefuli* for [gray 0.5–1.0] (dark).

I

#### *6 The Guessing Game*

Table 6.7: Lexicon of five agents after 2000 games.

Figure 6.10: In the case of synonymy, there are multiple words for the same meaning and hence the same referent.

*6.2 Synonymy*

The positive feedback loop between use and success has already dampened some synonyms. For some cases, like [gray 0.5–1.0] the competition has died out with one word *faluleru* being the winner. For others, like [hpos 0.5–1.0], the competition is still going on, although we can guess that *xomupovi* is probably going to be the winner.

It is instructive to follow the history of the words in use for a particular meaning. For example, let us look at the words for [gray 0.5–1.0] (dark) in the very early phases of lexicon development. Three different words are quickly created, and *faluleru* is the first one that has some success.

```
Game 76
 Speaker a4 creates 'notabefe' for [GRAY 0.5–1.0]
 Hearer a5 adopts 'notabefe' for [GRAY 0.5–1.0]
Game 79
 Speaker a2 creates 'vivevobo' for [GRAY 0.5–1.0]
 Hearer a7 does not adopt 'vivebo'
     (failed to discriminate)
Game 88
 Speaker a7 creates 'faluleru' for [GRAY 0.5–1.0]
 Hearer a4 adopts 'faluleru' for [GRAY 0.5–1.0]
Game 100
 Speaker a7 uses 'faluleru' for [GRAY 0.5–1.0]
 Hearer a4 correctly interprets 'faluleru'
```
The semiotic triangles existing at this point in the population are summarised in Figure 6.10. Agent **a4** is now already in a dilemma because he has created *notabefe* and picked up *faluleru* from **a7**.

With a lower word creation rate (*wc*), fewer new words would be created. The initial bootstrapping of the lexicon would then take a bit longer but the process of weeding out synonymy would be shorter. With a lower word adoption rate (*wa*), agents are less inclined to adopt a word and that again diminishes the chance that new words spread, if words already exist for the same meaning. But even with high word creation and word adoption rates, the whole system stabilises automatically. The stronger a lexicon is already in place, the fewer new synonyms arise because new words created by virgin agents entering the population have hardly any chance to propagate.

Note that the word creation rate can never be completely zero because then the agents would no longer be able to handle new meanings. The word adoption rate can never be equal to zero either because then new words cannot spread in the population and there would be a high chance that the lexicon does not become coherent with subgroups getting stuck with different words for the same meaning.

Because there are synonyms, agents must now choose which word to use. The one with the highest score should clearly be preferred because based on the evidence the agent has gathered so far, this gives the highest chance of success in the game. **a4** is faced with this kind of choice in the next game in the series involving the meaning [gray 0.5–1.0]. **a4** chooses *faluleru* because this word has the highest score. It is immediately picked up by **a1**:

```
Game 101
  a4 is the speaker. a1 is the hearer.
  a4 segments the context into 2 objects:
       rectangle-0 rectangle-1
  a4 chooses rectangle-1 as the topic
  a4 categorises the topic as [GRAY 0.5–1.0]
  a4 has two words for [GRAY 0.5–1.0]:
       'faluleru' (0.20)
       'notabefe' (0.00)
  a4 says: 'faluleru'
  a1 does not know 'faluleru'
  a1 says: 'faluleru?'
  a4 points to rectangle-1
  a1 categorises the topic as [GRAY 0.5–1.0]
  a1 stores 'faluleru' as [GRAY 0.5–1.0]
```
After this game, three agents "know" the word *faluleru* for [gray 0.5–1.0]: **a4**, **a1**, and **a7**. When we continue to inspect the simulation we see that *notabefe* takes a bit of a revenge. The next games with the meaning [gray 0.5–1.0] all involve the word *notabefe*:

```
Game 111
 Speaker a5 uses 'notabefe' for [GRAY 0.5–1.0]
 Hearer a4 correctly interprets 'notabefe'
Game 113
 Speaker a4 uses 'notabefe' for [GRAY 0.5–1.0]
 Hearer a9 adopts 'notabefe' for [GRAY 0.5–1.0]
Game 127
 Speaker a9 uses 'notabefe' for [GRAY 0.5–1.0]
 Hearer a6 adopts 'notabefe' for [GRAY 0.5–1.0]
```
But then there is another occurrence of *faluleru*:

```
Game 135
 Speaker a1 uses 'faluleru' for [GRAY 0.5–1.0]
 Hearer a2 adopts 'faluleru' for [GRAY 0.5–1.0]
```
And now **a6**, which has not been involved yet in any interaction concerning the meaning [gray 0.5–1.0], further confuses the situation by creating a new word, *sopine*, which **a5**, playing the role of hearer, adopts.

```
Game 140
 Speaker a6 creates 'sopine' for [GRAY 0.5–1.0]
 Hearer a5 adopts 'sopine' for [GRAY 0.5–1.0]
```
This kind of evolution continues with a struggle between *notabefe* and *faluleru*. The agents know both words so the games do not fail. But *faluleru*, just by chance, starts to occur a bit more often which causes its score to go up a bit more. This results in *faluleru* being used even more, and, due to lateral inhibition, *notabefe* used less. Gradually *faluleru* dominates for the whole population. After 2000 games, the competitors to *faluleru* have all disappeared from the group lexicon.

## **6.3 Ambiguity**

We now continue in small steps to scale up the challenge to the agents by progressively adding more realism to the simulation. So far I assumed that agents use only the most salient channel for categorising the topic and that their perception of the world is identical. Consequently a hearer can guess with 100 % success the meaning of an unknown word and it is therefore no wonder that the agents arrive at a shared communication system, even though neither the lexicon nor the repertoire of categories has been supplied in advance by a designer nor their development centrally coordinated. The main problem for them so far is the rise of synonyms which need to be damped to increase the probability of successful and efficient communication.

I now relax the saliency assumption. When there is a lower saliency threshold, more than one sensory channel is considered by the conceptual layer, possibly leading to several alternative conceptualisations of the scene. The question is then whether the agents are still able to reach a shared communication system despite the unavoidable word ambiguities that this generates.

We begin again by looking at simulations with two agents so that we can clearly see the impact of multiple conceptualisations. The architecture of the agents has not changed, I only lowered the saliency threshold. The scenes have become a bit more complex as well. They now not only contain rectangles but also squares, circles, and triangles. This has a limited impact because the same sensory channels are used as before and none of them is really sensitive to shape properties.

Figure 6.11: Scene used in game 3.

#### *6 The Guessing Game*

#### **6.3.1 How words may still get the same meaning**

When inspecting the simulation results, we see first of all that we may still accidentally get the same situation as before, i.e. one where the hearer selects the same channel as the speaker for conceptualising the scene, even though several channels are salient. This happens in the following game which involves a scene with a rectangle and a square (Figure 6.11).

The data for game 3, after sensor-scaling, are shown in Table 6.8.

Table 6.8: Sensory data for game 3 after scaling.

Values for vpos and gray are very close so they are not considered as sufficiently salient.

```
Game 3
  a1 is the speaker. a2 is the hearer.
  a1 segments the context into 2 objects:
       square-0 rectangle-1
  a1 chooses rectangle-1 as the topic
  a1 considers as salient AREA WIDTH HEIGHT HPOS
  a1 categorises the topic as [HEIGHT 0.0–0.5]
  a2 creates a new word: \smplenquote{mibati}
  a1 says: 'mibati'
  a2 does not know 'mibati'
  a2 says: 'mibati?'
  a1 points to rectangle-1
  a1 considers as salient AREA WIDTH HEIGHT HPOS
  a1 categorises the topic as [HEIGHT 0.0–0.5]
  a1 stores 'mibati' as [HEIGHT 0.0–0.5]
```
[height 0.0–0.5] has been chosen by the speaker because height was one of the salient channels (even though clearly not the only salient one) and because a successful distinction already existed in the ontology. The same distinction was chosen by chance by the hearer, but he could just as well have chosen a distinction based on the area, width or hpos.

In the next game of the simulation series, *mibati* is used again, now by **a2** as speaker. It is based on a scene with a triangle and a rectangle. The data for game 4 are shown in Table 6.9 (after scaling).

*6.3 Ambiguity*

Table 6.9: Lexicon of a1 and a2 after 500 games.

The rectangle is chosen as topic. Two alternative categories can be used by **a2** (and are listed by the commentator) but the one preferred is the one with the strongest lexicalisation, which is *mibati*.

```
Game 4
  a2 is the speaker. a1 is the hearer.
  a2 segments the context into 2 objects:
       triangle-0 rectangle-1
  a2 chooses rectangle-1 as the topic
  a2 considers as salient AREA GRAY HEIGHT HPOS
  a2 categorises the topic as [HEIGHT 0.0–0.5]
{}[GRAY 0.5–1.0]
  a2 has the word
       mibati for [HEIGHT 0.0–0.5] (1.0)
  a2 says: 'mibati'
  a1 interprets 'mibati' as [HEIGHT 0.0–0.5]
  a1 points to rectangle-1
  a2 signals OK
```
This example illustrates two points. First of all the language interpretation process influences which conceptualisation of the scene is preferred. For the speaker, both [height 0.0–0.5] (short) and [gray 0.5–1.0] (dark) are possible ways to distinguish the topic from the other objects in the context. But [height 0.0–0.5] is chosen because its lexicalisation has a higher score. Second, we begin to see why agents will manage to coordinate their ontologies, even though they do not have any direct feedback about each other's internal structures. The score of [height 0.0–0.5] goes up after this game and if the agent has to choose a category later purely based on the score of the categories themselves, [height 0.0–0.5] will be the one being preferred. Unless [gray 0.5–1.0] manages to become successfully lexicalised itself, it even risks to get pruned away.

#### **6.3.2 How words get different meanings**

Here is an example where ambiguity slips in the lexicon. The game involves two objects: a rectangle and a square (Figure 6.12). The data for game 9, after sensor-scaling, are shown in Table 6.10.

The discrimination trees of the two agents at this point are shown in Figure 6.13. The speaker uses a distinction based on the vpos channel namely [vpos 0.5–1.0] (top), cre-

#### *6 The Guessing Game*

Figure 6.12: Scene used in game 9. Square-1 is the topic. Several conceptualisations are possible so the agents get divergent meanings.

Figure 6.13: Discrimination trees of speaker a1 (left) and hearer a2 (right) available in game 9

Table 6.10: Data for game 9 after sensor-scaling.

*6.3 Ambiguity*

ates a word for it *puxazi*, and transmits this to the hearer. The hearer does not know the word, conceptualises the scene based on this non-verbal hint from the speaker, and identifies the category [gray 0.0–0.5] (light) as distinctive. So this meaning is stored and it is different from the one used by speaker. The current constellation of meanings is summarised in Figure 6.14.

Figure 6.14: Semiotic triangles underlying game 9. For the same referent and the same word, there are two different meanings. Dashed lines indicate the relations used by the speaker **a2**. Straight lines indicate those used by the hearer **a1**.

```
Game 9
  a1 is the speaker. a2 is the hearer.
  a1 segments the context into 2 objects:
       rectangle-0 square-1
  a1 chooses square-1 as the topic
  a1 considers as salient GRAY WIDTH VPOS HPOS
  a1 categorises the topic as [VPOS 0.5–1.0]
  a2 creates a new word: 'puxazi'
  a1 says: 'puxazi'
  a2 does not know 'puxazi'
  a2 says: 'puxazi?'
  a1 points to square-1
  a2 considers as salient GRAY WIDTH VPOS HPOS
  a2 categorises the topic as [GRAY 0.0–0.5]
  a2 stores 'puxazi' as [GRAY 0.0–0.5]
```
A subsequent game (game 11) illustrates that despite semantic incoherence, a game can still succeed. The agents do not know that each of them means something else by *puxazi* and if the meanings are compatible, they have no reason to change their internal lexicon:

*6 The Guessing Game*

```
Game 11
  a2 is the speaker. a1 is the hearer.
  a2 segments the context into 3 objects:
       circle-0 rectangle-1
  a2 chooses rectangle-1 as the topic
  a2 considers as salient AREA GRAY WIDTH HPOS
  a2 categorises the topic as [GRAY 0.0–0.5]
  a2 says: 'puxazi'
  a1 interprets 'puxazi' as [VPOS 0.5–1.0]
  a1 points to rectangle-1
  a2 signals OK
```
Figure 6.15: Semiotic triangles used in game 14. Dashed lines are the relations used by the hearer **a2**. Straight lines those of the speaker **a1**. After this game, **a1** adopts yet another meaning for *puxazi*, namely [height 0.5–1.0].

Here is next a game (game 14) where **a2** comes to adopt the other meaning of *puxazi*, because the first meaning does not work in the present context. The game involves three objects: two rectangles and a triangle (Figure 6.16). The data for game 14, before context scaling, are shown in Table 6.11.

Table 6.11: Sensory data for game 14 after scaling.

#### *6.3 Ambiguity*

**a1** conceptualises the scene using [vpos 0.5–1.0], which he has lexicalised as *puxazi*. For **a2**, *puxazi* means [gray 0.0–0.5] (light), but this meaning identifies both rectangle-2 and triangle-1 (Figure 6.15). The game therefore fails and the speaker points to the topic. The hearer conceptualises the scene based on this non-verbal hint from the speaker using the height dimension and adopts this as the second meaning of *puzaxi*.

```
Game 14
  a1 is the speaker. a2 is the hearer.
  a1 segments the context into 3 objects:
       rectangle-0 triangle-1 rectangle-2
  a1 chooses triangle-1 as the topic
  a1 considers as salient HEIGHT VPOS HPOS
  a1 categorises the topic as
{}[VPOS 0.5–1.0] [HEIGHT 0.5–1.0]
  a1 says: 'puxazi'
  a2 interprets 'puxazi' as [GRAY 0.0–0.5]
  a2 identifies rectangle-2 triangle-1
  a2 says: 'puxazi?'
  a1 points to triangle-1
  a2 considers as salient HEIGHT VPOS HPOS
  a2 categorises the topic as [HEIGHT 0.5–1.0]
  a2 stores 'puxazi' as [HEIGHT 0.5–1.0]
```
Note that the hearer could in principle also have categorised the scene using vpos and hpos, because they are equally salient. So there was absolutely no guarantee that *puxazi* would have been associated with [height 0.5–1.0] by **a2**. Moreover **a2** stores an association between *puxazi* and [height 0.5–1.0], even though there is already another word for [height 0.5–1.0] in his lexicon. The fact that several meanings are possible to distinguish the topic in a given context has not only the consequence that ambiguity arises but also that synonyms may enter into the lexicon, even with only two agents!

#### **6.3.3 Competition between word meanings**

Once a word has more than one meaning (ambiguity), and once several words exist for the same meaning (synonymy), a struggle between word-meaning pairs sharing the same word or the same meaning develops. The lateral inhibition carried out by the speaker in case of a successful game pushes down alternative lexicalisations for the same meaning, thus damping synonyms, and the lateral inhibition carried out by the hearer pushes down alternative meanings for the same word, thus damping ambiguity.

Game 25 illustrates this effect of lateral inhibition. The situation before the game is as depicted in Figure 6.17. Two words (with different meanings) are competing in **a2** to identify the referent: *puxazi* (meaning [gray 0.0–0.5], i.e. light) and *torigusu* (meaning [vpos 0.0–0.5], i.e. lower). *puxazi* has a higher score and wins the competition. Because the game was successful, the score of *puxazi* goes up. The score of *torigusu* does not

#### *6 The Guessing Game*

Figure 6.16: Scene used in game 14. Synonymy arises because the hearer conceptualises the scene differently from the speaker.

Figure 6.17: Semiotic triangles used in game 25. The score of the relation between [gray 0.0–0.5] and *puxazi* is increased in both agents. The relation between *puxazi* and [gray 0.0–0.5] gets damped.

change because it concerns another meaning. Two meanings for *puxazi* are competing in **a1**: [gray 0.0–0.5] (light) and [vpos 0.0–0.5] (down). [vpos 0.0–0.5] gets damped and the score of [gray 0.0–0.5] goes up, thus helping to further disambiguate *puxazi*.

```
Game 25
  a2 is the speaker. a1 is the hearer.
  a2 segments the context into 2 objects:
       rectangle-0 rectangle-1
  a2 chooses rectangle-1 as the topic
  a2 considers as salient GRAY VPOS
  a2 categorises the topic as [VPOS 0.0–0.5]
{}[GRAY 0.0–0.5] [GRAY 0.0–0.25]
  a2 has the words
```
*6.3 Ambiguity*

```
puxazi for [GRAY 0.0–0.5] (0.20)
       torigusu for [VPOS 0.0–0.5] (0.0)
  a2 says: 'puxazi'
  a1 interprets 'puxazi' as
{}[GRAY 0.0–0.5] (0.20)
{}[VPOS 0.0–0.5] (0.0)
  a1 points to rectangle-1
  a2 signals OK
```
After this game, the association between [gray 0.0–0.5] and *puxazi* will have a score of 0.3 in both agents. The association between *puxazi* and [vpos 0.0–0.5] in the hearer is decreased, but because it was already 0.0, it cannot decrease further.

Note that the speaker not only conceptualises the scene using the most generic distinctions ([gray 0.0–0.5], [vpos 0.0–0.5]) but also with more specific ones ([gray 0.0–0.25]). Indeed it may happen that there is no word for a more generic distinction, but there is one for a more specific one, in which case it should be used. So, all discriminative distinctions, whatever their level of detail, are transmitted from the categorisation layer to the lexical layer and it is up to the lexical layer to choose. Of course, everything else being equal, other criteria are still important. If there is a more abstract category (meaning one higher in the discrimination tree) it is preferred over a more specific one if they have equal lexical scores.

#### **6.3.4 Lexical and ontological development**

Despite additional complication of mutually compatible meanings for unknown words, the two agents nevertheless manage to build up a shared communication system, as can be seen from Figure 6.18. Each time the ontology is extended, communicative success dips because a new word needs to be acquired, but the agents clearly manage to become successful in the guessing game.

Success does not mean that the lexicons are completely identical. As we have seen in game 11, it is possible to have communicative success with different meanings for the same word as long as the different meanings pick out the same referent. Of course in the domain of the geom world, it is a pure coincidence that two categories pick out the same referent and therefore alternative meanings for the same word will get damped. However, if there are more regularities, ambiguity persists much longer. In fact, ambiguity may persist in natural languages if the different meanings of a word are so closely related that it is sufficiently often unclear which meaning is intended.

Here are some snapshots of the developing lexicon. After 30 games, the lexicon of the established words (i.e. associations with a score greater than 0.0 for at least one agent) is as in Table 6.12.

Note that there are two meanings for *puxazi*: [gray 0.0–0.5] (light) and [height 0.5– 1.0] (tall).

The lexicon after 200 games is shown in Table 6.13.

The second meaning of *puxazi* has now disappeared from the lexicon. So we basically see the same situation as before when only one most salient channel was considered by

Figure 6.18: Communicative success (left y-axis) and average ontology size (right y-axis) for a series of 2000 language games played by two agents.

the agents. Words for more general distinctions happen to be lexicalised first because they are more often useful in the game, but when needed words for more specific meanings start to develop.

Table 6.12: Group lexicon after 30 games.

*6.4 Scaling up*

Table 6.13: Group lexicon after 200 games.

## **6.4 Scaling up**

Conforted by having reached a new plateau in the challenges confronting the agents, I now go one more step further. First we scale up the population to see whether despite the ambiguity now persistently present, a larger group of agents still manages to develop a shared communication system.

#### **6.4.1 Increasing the population size**

We already know from the previous section that a larger population automatically increases the risk for synonymy. Figure 6.19 shows the evolution of communicative success and average ontology size in a population of ten agents. We see again a steady progression towards an effective communication system. Recall that these games are played with randomly generated scenes from the geom world.

It is instructive to examine in detail the lexicon that has emerged after this series, where every agent has on average played about 2000 games. The table shown in Table 6.14 shows word-meaning pairs whose frequency is larger than 0.8.

We see that for all the sensory channels, solid words exist for the top level categories. There is however one exception: there are no words in this group for area nor for [height 0.5–1.0]. We do find these words, and words for more refined notions as well, in the batch of word-meaning pairs whose scores are between 0.5 and 0.8, shown in Table 6.15.

Although most of these words are on their way towards total coherence, because the competition has already been damped completely, this is less the case for area/height words. Closer inspection reveals that there are two words competing for expressing area and height: *texiraxi* and *wixizode* (Figure 6.20). Both words have both meanings but there is a strong divergence of opinion in the population. Some prefer the area

Figure 6.19: Communicative success (left y-axis) and average ontology size (right y-axis) for a series of 20,000 language games played by ten agents.

Table 6.14: Group lexicon after 2000 games.

Table 6.15: Table of word meaning pairs and their average scores.

meaning, others prefer the height meaning. This can be seen from the scores of the different meanings.

For the word *texiraxi*, the scores of the different agents for the area and height categories is as in Table 6.16.

A game where the two meanings are compatible is shown below:

```
Game 10008
  a2 is the speaker. a4 is the hearer.
  a2 segments the context into 2 objects:
       circle-0 square-1
  a2 chooses square-1 as the topic
  a2 considers as salient AREA WIDTH HEIGHT
  a2 categorises the topic as
{}[HEIGHT 0.5–1.0] [HEIGHT 0.75–1.0]
```
#### *6 The Guessing Game*

Table 6.16: Scores for area and height categories.

```
{}[WIDTH 0.5–1.0] [WIDTH 0.75–1.0]
{}[AREA 0.5–1.0] [AREA 0.75–1.0]
{}[HEIGHT 0.5–1.0] [HEIGHT 0.75–1.0]
  a2 has the words
      wixizode for [HEIGHT 0.5–1.0] (1.0)
      kilokawe for [WIDTH 0.5–1.0] (1.0)
      texiraxi for [AREA 0.5–1.0] (1.0)
      powugeme for [HEIGHT 0.5–1.0] (0.8)
      wetami for [HEIGHT 0.75–1.0] (0.5)
      wofetizo for [WIDTH 0.5–1.0] (0.4)
      kufule for [HEIGHT 0.75–1.0] (0.1)
      lisexese for [HEIGHT 0.75–1.0] (0.1)
  a2 says: 'wixizode'
  a7 interprets 'wixizode' as
{}[AREA 0.5–1.0] (1.0)
{}[WIDTH 0.0–0.5] (0.0)
{}[HEIGHT 0.5–1.0] (0.0)
  a7 identifies square-1
  a2 signals OK
```
Note the abundance of choices for the speaker. He finally picks *wixizode*. The hearer interprets this using area and the game succeeds. A partial overview of the different choices and subsequent updating is given in Figure 6.8. The speaker decreases the score of *powugeme* which is also competing for expressing [height 0.5–1.0]. The hearer on the other hand damps the alternative meanings of *wixizode*, which includes the meaning [height 0.5–1.0] used by the speaker.

*6.4 Scaling up*

This example shows that there will be a divergence of opinion among the agents if the environment does not provide enough disambiguating cases. It is still possible of course that the semantic incoherence will disappear from the lexicon, but it is understandable that agents have difficulty in this domain to disentangle the meanings of words for tall and large. French has one word *grand* encapsulating both of these categories.

Here are the words in the lexicon with still lower frequencies in the population (between 0.2 and 0.5). We see more clearly several synonyms in heavy competition, for example *kodawika* and *togixa* for [gray <IP_ADDRESS>], or *vavuvosi* and *radude* for [width 0.75–1.0]. See Table 6.17.

Table 6.17: Lexicon with lower frequencies.

So all the mechanisms proposed earlier do what they are supposed to do, even when we scale up the population. The Discrimination Game generates the repertoire of distinctions necessary in this domain, the Naming Game generates the shared repertoire of form-meaning pairs. The coupling between the two based on feedback from the environment causes a convergence even if the agents do not have any direct knowledge about which meanings are used by the others.

#### **6.4.2 Lexicon acquisition by new agents**

We finally scale up on the same dimension but now towards an open population. The following simulation examines what happens when a new agent enters into the population. The agent has no prior ontology nor any knowledge of the existing lexicon in the

#### *6 The Guessing Game*

group and no additional components or processes are added, compared to the agents in the simulation so far. Introducing a new agent tests in how far the cognitive architecture put in place enables a new agent to acquire a lexicon that already exists.

The first words learned (after about a dozen games by the agent) are shown in Table 6.18.

Table 6.18: First words after about a dozen games.

As expected, the new agent sometimes creates new words (this is the case for*sakezomo* and *nopofi*). But these words are very short-lived. The new agent has already picked up *larubo* which is the word in use expressing the meaning of *sakezomo*. *larubo* has already a higher score so *sakezomo* will definitely disappear.

The most widespread words in the lexicon such as *tituroxu* or *legoka* are the ones that are most likely to be picked up because the chance that they will be heard is higher. This suggests that the entry of new agents in the population does not destabilise the lexicon but on the contrary it makes it more coherent 1

For example, the new agent has solidly associated the word *texiraxi* with [height 0.5– 1.0] and *wixizode* with [area 0.5–1.0] as the majority of the population. Thus resolving the incoherence shown in Figure 6.20.

Notice also that the new agent first acquires words for the more abstract categories. This is the case because (1) the discrimination trees are still developing and so more specific categories are not yet available, and (2) even if more specific categories are available, agents do not try to be more specific than needed in the game.

Table 6.19 is the set of words of the new agent with scores above 0.4 after 500 total games (which means more or less 100 games in which the new agent was involved).

The agent clearly picks up the lexicon circulating in the population and generally associates the same meanings to the words (compare with the lexicons given earlier for the total population). Occasionally there are still incoherences. For example, *fumetese*

1 The importance of a flux in the agent population for streamlining a language has been stressed by Simon Kirby, who has applied this principle in a remarkable simulation concerning the origins of hierarchical structure, Kirby (1999).

Table 6.19: Score of new agent after 500 games.

has been associated with [width 0.0–0.5] whereas the rest of the population uses this word for a distinction on the vpos-channel. The meaning of this word will later shift as the agent encounters disambiguating cases. We can conclude that the guessing game shows not only how a population may emerge a lexicon from scratch but also how new agents entering the group may acquire the existing lexicon.

## **6.5 Conclusions**

This chapter has coupled the Discrimination Game and the Naming Game, so that agents now can play language games without getting explicit feedback about meanings. As in the case of humans, feedback only comes through the non-verbal outcome of a game. This may generate semantic confusion because usually more than one conceptualisation is possible to distinguish a topic from the other objects in the context. However we have seen that despite this complication agents still manage to build up an ontology and a lexicon which is effective for communicating in their environment.

Although this chapter took away the assumption of direct meaning feedback, it still made a number of simplifying assumptions with respect to real world physical agents, in particular it assumed that the perception of the scene was identical for the speaker and the hearer. The next chapter takes away this assumption and thus sets the final step to test whether a perceptually grounded lexicon may emerge in a population of embodied distributed autonomous agents.

Ludwig Wittgenstein went through two major periods in his thinking. During the first period he worked within the framework of logical empiricism, initiated by Bertrand Russell and others at the end of the 19th century. The logicist approach defines a language by listing the elementary building blocks (the words), the combination rules (the syntax), and a mapping from words and syntactic structures to semantic interpretations (the semantics). It assumes that there is a universal, logical structure to the world which can be captured once and for all in a non-ambiguous logical language and that the permissible inferences can be catalogued exhaustively. This project has its roots in the 17th century dream of Leibniz and Descartes to streamline rational thinking so that it becomes as clear and non-controversial as numerical calculation. Wittgenstein enthusiastically participated in this project, which is still vigorously being pursued today by logicians and linguists alike, even though many of them do not necessarily subscribe to the universalist thesis motivating the early developments of logic.1

But some drastic events happened in Wittgenstein's life which caused a radical shift in his philosophical orientation. One of them was that he became headmaster of a small school in the Austrian mountains, without losing his interest for philosophising about language and meaning. By working with children and by seeing concretely how they engaged with language, Wittgenstein realised that the logicist approach did not address some basic questions one can ask about language, particularly how the semantics of a language might arise, or how people ever develop a shared communication system. Wittgenstein saw clearly that a language imposes a certain view on the world, which gives each language its own strength as well as its limitations. The logicist framework might be ideal as a tool for constructing a *post factum* formal description of the semantics of an (ideal) language, just as a structuralist grammar identifies the frozen state of its syntax, but not for modeling how language achieves its communicative purpose, comes about, or evolves.

Wittgenstein proposed to study the use of language in terms of games. This notion captures that the most basic form of language involves a social interaction between individuals within a specific setting, which acts as a context restricting the possible meanings. The interaction is played out along a conventionalised set of rules, as is chess or any other game. The notion of a game captures that a language interaction has a purpose, for example, to identify an object in a context, to gather information, to transmit emotion, to try and invoke an action by another person, etc. Words get their meaning as part of a language game. Language is a tool fully integrated in the rest of human social activity.2

It should be abundantly clear by now that the mechanisms explored in this book are

1 Wittgenstein's main work from this period is Wittgenstein (1922). A prototypical example of the logicist research program is found in Carnap (1928).

2 See in particular Wittgenstein (1953).

strongly indebted to a Wittgensteinian point of view. Of course, we studied only one relatively simple language game, but we have explored it at great depth so that there is now a framework for studying language games with the same rigor as the framework of classical logic or structural syntax.3

We are also exploring many issues that were not raised by Wittgenstein, the most important one being the origins of words and meanings and how they may spread in a population. In this chapter, I set the ultimate step on this path, which is to ground the cognitive architectures of the agents in the world through their perceptual and behavioral apparatus. I will show concrete examples from a series of language games played by autonomous robotic agents perceiving real world scenes and we will see that very similar phenomena as the ones observed in the previous chapter emerge.

The second goal of this chapter is to study the semiotic dynamics that thus unfolds in the population. Already in the beginning of this book, I introduced the notion of a semiotic square, which captures the relation between a referent, a perceived image, a meaning, and a form. The collection of semiotic squares that can be observed in an agent's behavior or in the behavior of a group of agents forms a semiotic landscape. This landscape undergoes continuous change as new words are created, word-meaning relations shift, and meanings are applied to new referents. This chapter introduces additional tools to study this dynamics, focusing in particular on how synonymy and ambiguity get introduced or damped and how language influences the conceptualisation of reality.

## **7.1 A first grounding experiment**

We have arrived at a point where experiments with physically embodied autonomous agents become conceivable. To do so, we first have to ground the language game, which means that we have to couple the conceptual layer to the sensory-motor layers of the agent.

#### **7.1.1 Integrating perception and action**

The coupling between the perceptual layer and the conceptual layer is from an architectural viewpoint very similar to the coupling of the conceptual layer and the lexical layer which we studied in the previous chapter. For the formulation of an utterance, the outputs of the perceptual layer are inputs to the conceptual layer which in turn provides inputs to the lexical layer (Figure 7.1). Just as the other layers, the perceptual layer generates a set of possibilities: a set of possible segmentations and a set of sensory characteristics about each segment. These possibilities are ranked based on various criteria such as saliency and made available to the conceptual layer which further expands on the best solutions. The conceptual layer in turn generates a set of possible solutions with different rankings which are then processed by the lexical layer. Re-entry is nec-

3 There have been several attempts to develop a more formal investigation of language games, see one of the earliest efforts in Hintikka (1998).

#### *7.1 A first grounding experiment*

essary because the final perception of the scene depends on the ontological and lexical repertoires of the agent and cannot be decided on the basis of sensory processing alone.

Figure 7.1: Flow of solutions through the different cognitive layers when an utterance is being produced. Re-entry is necessary because the decision at each layer depends on decisions at subsequent layers.

For the interpretation of an utterance, the main flow of information goes in the other direction. The lexical layer sends a variety of hypotheses to the conceptual layer and the conceptual layer makes use of data from the perceptual layer to see which conceptualisation yields a referent. Several solutions are considered by the conceptual layer because words are typically ambiguous and so the perceptual layer must produce the appropriate segmentations and sensory characteristics to test each solution. Even if a sensory channel was not considered to be very salient by the hearer, it may have been used by the speaker in his conceptualisation of the scene and hence the hearer's perceptual processes must actively try to seek in the image the information required to see whether it is applicable to the specific context. The interpretation of an utterance thus strongly takes the real world context into account. The utterance literally influences the way the hearer sees the world. The two-way flow (from perception to conceptualisation and language and from language and conceptualisation to perception) resolves one of the paradoxes of meaning discussed in Chapter 4. The clear picture of reality that we consciously experience results from a dynamical process in which local constraints keep propagating until a globally coherent solution emerges.4

Grounding language games in the real world not only requires a link between conceptualisation and real world perception. Of equal importance is the physical actions undertaken by the agents to point to the object they believe to be the topic. The accuracy of pointing heavily influences overall communicative success. Indeed, a game may

4 Dynamical systems which enter into an attractor based on a similar relaxation process have been widely studied, particularly in physics. One of the prototypical examples is a spin glass whose magnetic states keep switching until a globally coherent state is reached.

fail not because the speaker and the hearer did not agree on the meaning nor because they did not refer to the same object, but because the speaker misperceived which object the hearer has pointed to. These differences in perception leading to difficulties in communication do happen and may cause communicative failures despite a shared lexicon.

#### **7.1.2 Concept acquisition**

I now show a series of example games taken from an experiment in which two situated embodied agents, **a1** and **a2**, play grounded language games based on coloured figures pasted on the white board in front of them. The following channels are available to the agents in the experiments in this section: hpos (the horizontal position of the midpoint of the segment's bounding box), vpos (the vertical position of the midpoint of the segment's bounding box), height (the height of the bounding box), width (the width of the bounding box), area (the area of the segment, calculated by counting the number of pixels that belong to it), r (the average redness of the pixels in the segment), g (the average greenness of the pixels in the segment), b (the average blueness of the pixels in the segment). These "colour" channels are not to be confused with the human opponent colour channels so the distinctions that form of them are not directly perceivable by human observers.

Because there are only two agents, the risk of synonymy is almost non-existent. The saliency threshold is sufficiently low so that more than one sensory channel might be salient and hence ambiguity is unavoidable.

A first word is acquired by the agents in game 3 based on the segmented images shown in Figure 7.2 (top). The different sensory values (after sensor-scaling) for the segments in game 3 are shown in Table 7.1.

Table 7.1: First words after about a dozen games.

Figure 7.2: Three examples of segmented images. The topic is indicated by a dashed bounding box in the image of the speaker. Segments which are too small are ignored. The topics have all been conceptualised as being 'to the right' and so the same word *gofubo* has been used to refer to them.

hpos is the most salient channel. After sensor-scaling, the two values for hpos are still be drawn further apart with 1.0 for object-0 and 0.0 for object-1 so that the category [hpos 0.5–1.0] easily distinguishes the topic (object-0) from object-1.

The left image is that of the hearer **a1**, the right one that of the speaker, **a2**. **a2** had already invented the word *gofubo* for [hpos 0.5–1.0] (to the right) in an earlier game, but the word was not acquired in that game by **a1** because he still missed the appropriate distinction. Meanwhile the hpos category is available to **a1** due to an expansion of his discrimination networks and so he can store the word:

```
Game 3
```

```
a2 is the speaker. a1 is the hearer.
a2 segments the context into 2 objects:
     object-0 object-1
a2 chooses object-0 as the topic
a2 categorises the topic as [HPOS 0.5–1.0]
a2 says: gofubo
a1 does not know gofubo
a1 says: gofubo?
a2 points to object-0
a1 categorises the topic as [HPOS 0.5–1.0]
a1 stores gofubo as [HPOS 0.5–1.0]
```
This game proceeds essentially like in the computer simulations studied before. The major difference is that now real images have been used, the objects considered are the outcome of segmentation processes, the sensory characteristics have been derived from the image itself, and the pointing has been done by physically moving the cameras.

#### **7.1.3 Generalisation without learning**

Immediately the agents apply this word to very different scenes, such as the ones in Figure 7.2 (middle and bottom). The middle picture shows on the left the segmented scene from the speaker in game 5, and on the right the one from the hearer. In game 5, the figures are blue rectangles. They are much further apart than the two circles in game 3. Nevertheless, after scaling, they are categorised and conceptualised similarly and therefore the same word could be used effectively. The concept of [hpos 0.5–1.0] and hence the word *gofubo* is general *from the very start*. The agents do not need to see many examples because they do not use inductive generalisation. Instead, the hpos category is constructed in a top-down fashion as soon as the hpos channel has been salient and is immediately available for use in the discrimination game and hence in verbalising the scene. This explains why the word-meaning acquisition process observed in the experiments goes so amazingly fast.

The bottom of Figure 7.2 shows yet another scene where the word *gofubo* was used with success. The topic is the rightmost shape in the scene and so [hpos 0.5–1.0] is once more distinctive. To an outside observer it may look like the agents have performed a *7.1 A first grounding experiment*

gigantic inductive leap, but this is not the case at all. The agents do not try to abstract the commonalities from different examples but construct distinctions in a top down fashion and try to apply them to the perceived image.

After a mere 50 games, the lexicon shown in Table 7.2 has emerged. Only associations with scores greater than 0.0 are shown.

Table 7.2: First words after about a dozen games.

There is already a word (*gofubo*) which has a score of 1.0! After 100 games, the lexicon has become more solid and now looks as in Table 7.3.

Table 7.3: Population lexicon after 100 games.

Figure 7.3: The discrimination trees of two embodied agents **a1** (left) and **a2** (right) after playing 100 games (top) and after 200 games (bottom).

#### **7.1.4 The influence of the environment**

One thing is striking about this lexicon. It contains words for fine-grained distinctions along the horizontal position axis, but none for width or height. Indeed if we look at the discrimination trees as they exist at this point (figure 7.3 top) we see that there are no discrimination trees for the height and width channels. This is entirely due to the environment. There have simply been no situations on the white board yet where these distinctions are salient enough.

As human experimenters, we can stimulate conceptual development by configuring scenes where these channels are needed, for example, a scene which contains two objects with the same size, colour, and position but of significantly different width. The conceptual layer in each agent should then start to develop again and the lexical layer should follow with the construction of new words.

A game where this happens is game 126 with the segmented images shown in Figure 7.4 (top). Width is now the most salient channel. The segments and sensory data for game 126 (after sensor-scaling) are shown in Table 7.4.

Clearly width is the most salient channel for the speaker. It is therefore chosen and because the agents have already grown distinctions on this channel, discrimination succeeds and a new word can be constructed and stored.

```
Game 126
  a2 is the speaker. a1 is the hearer.
  a2 segments the context into 2 objects:
       object-0 object-1
  a2 chooses object-0 as the topic
```
Figure 7.4: Top and bottom: Examples of new segmented scenes that stimulate conceptual development and hence expansions of the lexicon. The most salient characteristic in the top scene is width and in the bottom scene height.

Table 7.4: Sensory data for game 126.

```
a2 categorises the topic as [WIDTH 0.5–1.0]
a2 creates a new word: vaviwumu
a2 says: vaviwumu
a1 does not know vaviwumu
a1 says: vaviwumu?
a2 points to object-0
a1 categorises the topic as [WIDTH 0.5–1.0]
a1 stores vaviwumu as [WIDTH 0.5–1.0]
```
Figure 7.4 (bottom) contains another example of segmented images which have stimulated conceptual growth and hence an expansion of the lexicon. In this case, categorisations on the height channel are relevant and a word developed for tall.

Figure 7.5 shows another series of image segments, where categorisations based on the area channel were effective and Figure 7.6 shows additional image segments exercising vpos, hpos and colour distinctions.

After 200 games, the lexicon of the population looks as in Table 7.5.

Table 7.5: Population lexicon after 200 games.

Note that new words have come into the lexicon for 'up' (*putuwenu*), 'down' (*wiwigapo*), and 'wide' (*vaviwumu*). The discrimination trees of the width and height channel have started to expand (Figure 7.3 bottom).

Figure 7.5: Segmented images where distinctions on the area channel have been used. The topic (with dashed bounding box) in the two top cases has been categorised as large. In the bottom case, a word meaning 'small' was used.

Figure 7.6: The image segments from the top game require distinctions on the vpos channel and caused the creation of a word for 'upper'. The image segments in the middle led to the use of refined distinctions on the hpos channel, so as to identify the middle square. The topic in the image segments at the bottom was done with a conjunction of categories: blue and tall.

*7.1 A first grounding experiment*

#### **7.1.5 Coping with perceptual anomalies**

Grounding language games in physical environments makes it obviously harder for the agents in a number of respects. First of all because perception and segmentation may differ, the salient characteristics of objects may not be the same and as a result the hearer may guess another meaning for an unknown word, compared to the one used by the speaker. This happens for example in the following game (game 128) which is based on the segmented images shown in Figure 7.7 (top). The speaker's perception is shown to the left and the hearer's to the right.

```
Game 128
  a1 is the speaker. a2 is the hearer.
  a1 segments the context into 3 objects:
       object-0 object-1 object-2
  a1 chooses object-0 as the topic
  a1 categorises the topic as
       [HPOS 0.0–0.25] [HPOS 0.0–0.125]
  a1 creates a new word: 'bagaxe' for [HPOS 0.0–0.25]
  a1 says: bagaxe
  a2 does not know bagaxe
  a2 says: bagaxe?
  a1 points to object-0
  a2 categorises the topic as [AREA 0.5–1.0]
  a2 stores bagaxe as [AREA 0.5–1.0]
```
Although the difference may not appear significant to the human eye, the topic (the left most rectangle) is in the raw perception of the speaker less wide as the same rectangle perceived by the hearer. The segments and sensory data of the speaker in game 128 (after sensor-scaling) are shown in the Table 7.6.

Table 7.6: Sensory data for game 128.

Figure 7.7: Examples of scenes causing confusion due to perceptual anomalies. In the top scene, the segmentation of the speaker (left) makes the topic's most salient characteristic the horizontal position, whereas for the hearer (right) the most salient characteristic of the same segment is its area. In the bottom scene, speaker and hearer have segmented the scene into two, respectively three segments. This causes the game to fail even though both agents had the same meaning for the word used by the speaker.

Context-scaling further amplifies this difference which shows that it is not always beneficial to do so. **a1** uses the horizontal axis, creating a new word *bagaxe* meaning 'very left' [hpos 0.0–0.25] whereas **a2**, for whom the area is the most salient characteristic, associates this word with [area 0.5–1.0] (large). This example shows that grounding introduces additional risks for the introduction of semantic incoherence in a group's lexicon.

Due to perceptual anomalies, a game may fail even though both agents already have the same meaning for the same word. This happens when this meaning yields different objects (or no objects at all) for the speaker and the hearer. As a consequence, the hearer adopts another meaning for the word which starts to compete with the one he already had. This happened in the following game (game 127) based on the segmented images shown in Figure 7.7 (bottom). The speaker (left image) has identified only two objects, but the hearer three. The speaker (left image) uses green as distinguishing characteristic which is indeed appropriate. but because the hearer's third object (the top rectangle) is also green, this distinction fails for him. Even though the hearer had already a well estab*7.1 A first grounding experiment*

lished meaning for *puxedu*, he associates a new meaning based on the width-channel with this word because this channel is now the most salient.

```
Game 127
  a1 is the speaker. a2 is the hearer.
  a1 segments the context into 2 objects:
       s-object-0 s-object-1
  a1 chooses object-0 as the topic
  a1 considers as salient G R AREA HPOS
  a1 categorises the topic as
       [HPOS 0.0–0.5] [HPOS 0.0–0.125]
       [AREA 0.0–0.5] [R 0.0–0.5] [G 0.5–1.0]
  a1 has the words
       puxedu for [G 0.5–1.0] (1.0)
       wawosido for [HPOS 0.0–0.5] (0.7)
       pesidimu for [AREA 0.0–0.5] (0.2)
       wefoto for [R 0.0–0.5] (0.2)
       buwonipo for [G 0.5–1.0] (0.0)
  a1 says: puxedu
  a2 segments the context into 3 objects:
       h-object-0 h-object-1 h-object-2
  a2 interprets puxedu as
       [G 0.5–1.0] (0.20)
  a2 identifies h-object-0 h-object-1
  a2 says: puxedu?
  a1 points to s-object-0
  a2 categorises the topic as [WIDTH 0.5–1.0]
  a2 stores puxedu as [WIDTH 0.5–1.0]
```
After 500 games, the lexicon is as in Table 7.7.

The global evolution of success and ontology is shown in the graph in Figure 7.8. The graph is not fundamentally different from the ones we have seen in the computer simulations in the previous chapter, except that more failures occur after a lexicon is established due to the contingencies of real world images and the unavoidable stochasticity associated with physical interactions.

So despite the difficulties caused by perceptual anomalies and errors in non-verbal realworld interaction, the mechanisms used by the agents appear sufficiently robust that a shared communication system manages to get off the ground. We have been able to take away all the scaffolds put up in earlier chapters and the complete language system now stands on its own feet. Of course we now need to further scale up the challenge to the agents, particularly along three dimensions: complexity of the environments, complexity of the sensori-motor apparatus (particularly the number of sensory channels available to the agents), and size of the agent population. Only the latter type of scale-up is studied in the remainder of this chapter.

Table 7.7: Population lexicon after 500 games.

Figure 7.8: Success (left y-axis) and average ontology size (right y-axis) for two agents playing 500 guessing games about real world scenes perceived through their cameras. Occasionally new situations have been introduced to stimulate conceptual development.

*7.2 Semiotic dynamics*

## **7.2 Semiotic dynamics**

Semiotic dynamics refers to the changing relationships between words, meanings, perceptions, and real world scenes observed while a group of autonomous distributed agents play language games about scenes from an open evolving environment. The possible utterances and possible meanings are not fixed but continuously changing as the agents autonomously evolve their communication systems and adapt to changing environments. Tracking and understanding these changes is a non-trivial task. It is comparable to the investigation of other non-linear complex dynamical systems and therefore similar tools are useful.5 The study of semiotic dynamics is an entirely new subject for linguistics, and I will give here only some examples to illustrate the approach.

### **7.2.1 Tracking language evolution**

The first thing we need is a systematic way to collect data. In studying the lexical and ontological development of the agents, I have so far played god, inspecting the internal states of the agents. With larger agent populations that are travelling over the Internet and engage in interactions in different physical sites, it becomes impossible to perform these computations, because ontologies and lexicons are distributed over many agent servers throughout the world and different language games are going on in parallel. We are forced in these circumstances to adopt the viewpoint of a linguist, who can only observe the overt linguistic behavior in the community, not the internal states of each individual. So we have built tools that track the language games as they take place in parallel on a world-wide scale. The tools are available to anyone who logs on through the Internet and wants to see for him or herself how the language system is evolving.6

Of course, an external observer's point of view is only partial. As we have seen in the previous chapters, many words and categories are latently known by the agents, without their being used in overt behavior, just as we carry genes in our bodies that are not being expressed. Nevertheless, observations of the actual behavior of the agents is in a sense a more natural way to characterise ontologies and lexicons and reflects well the semiotic dynamics in the population. For the remainder of this chapter, all data are taken from observing experiments with the Talking Heads as they play grounded language games.

#### **7.2.2 Semiotic landscapes**