In the first edition of this book (Müller 2016a), I followed the view of Evans & Klein and Tomasello, but I want to revise my view here. The criticism applies to things like part of speech (Section 13.1.7) since it is true that the claim that 400 and more parts of speech are part of our genetic endowment Cinque & Rizzi (2010: 55, 57) cannot really be falsified, but the situation is different here. All grammar formalisms that were covered in this book are capable of analyzing recursive structures (see Section 18.3). If Pirahã lacks recursive structures one could use a grammar formalism with lower generative capacity (see Chapter 17 on generative capacity) to model the grammar of Pirahã. Parts of the development of theoretical linguistics were driven by the desire to find formalisms of the right computational complexity to describe human languages. GPSG (with certain assumptions) was equivalent to context-sensitive grammars. When Shieber (1985) and Culy (1985) discovered data from Swiss German and Bambara it was clear that context free grammars are not sufficiently powerful to describe all known languages. Hence, GPSG was not powerful enough and researchers moved on to more powerful formalisms like HPSG. Other frameworks like CCG, TAG, and Minimalist Grammars were shown to be powerful enough to handle so-called *mildly context-sensitive grammars*, which are needed for Swiss German and Bambara. Now, we are working on languages like English using grammar formalisms that can deal with mildly context-sensitive grammars even though English may be context free (Pullum & Rawlins 2007). This is similar to the situation with Pirahã: even though English does not have cross-serial dependencies like Swiss German, linguists use tools that could license them. Even though Pirahã does not have recursive structures, linguists use tools that could license them. In general there are two possibilities: one can have very general combinatory rules and rich specifications in the lexicon or one can have very specific combinatory rules and less information in the lexicon.28 If one assumes that the basic combinatory rules are abstract (Minimalism, HPSG, TAG, CG), the difference between Pirahã and English is represented in the lexicon only. Pirahã uses the combinatory potential differently. In this sense, Chomsky (2014) is right

28Personally, I argue for a middle way: Structures like Jackendoff's N-P-N constructions (2008) are analyzed by concrete phrasal constructions. Verb-argument combinations of the kind discussed in the first part of this book are analyzed with abstract combinatory schemata. See Müller (2013c) and Chapter 21.

### 13 The innateness of linguistic knowledge

in saying that the existence of Pirahã is irrelevant to the discussion of what languages can do. Chomsky also notes that Pirahã people are able to learn other languages that have recursive structures. So in principle, they can understand and produce more complex structures in much the same way as children of English parents are able to learn Swiss German.

So the claim that all languages are infinite and make use of self-embedding recursive structures is probably falsified by languages like Pirahã, but using recursive rules for the description of all languages is probably a good decision. But even if we assume that recursive rules play a role in the analysis of all natural languages, would this mean that the respective rules and capacities are part of our genetic, language-specific endowment? This question is dealt with in the next subsection.

### **<IP_ADDRESS> Recursion in other areas of cognition**

There are also phenomena in domains outside of language that can be described with recursive rules: Hauser, Chomsky & Fitch (2002: 1571) mention navigation, family relations and counting systems.29 One could perhaps argue that the relevant abilities are acquired late and that higher mathematics is a matter of individual accomplishments that do not have anything to do with the cognitive capacities of the majority, but even children at the age of 3 years and 9 months are already able to produce recursive structures: In 2008, there were newspaper reports about an indigenous Brazilian tribe that was photographed from a plane. I showed this picture to my son and told him that Native Americans shot at the plane with a bow and arrow. He then asked me what kind of plane it was. I told him that you cannot see that because the people who took the photograph were sitting in the plane. He then answered that you would then need another plane if you wanted to take a photo that contained both the plane and the Native Americans. He was pleased with his idea and said "And then another one. And then another one. One after the other". He was therefore very much able to imagine the consequence of embeddings.

Culicover & Jackendoff (2005: 113–114) discuss visual perception and music as recursive systems that are independent of language. Jackendoff (2011) extends the discussion of visual perception and music and adds the domains of planning (with the example of making coffee) and wordless comic strips. Chomsky (2007: 7–8) claims that examples from visual perception are irrelevant but then admits that the ability to build up recursive structures could belong to general cognitive abilities (p. 8). He still attributes this ability to UG. He views UG as a subset of the Faculty of Language, that is, as a subset of non domain-specific abilities (Faculty of Language in the Broad Sense = FLB) and the

29Pinker & Jackendoff (2005: 230) note, however, that navigation differs from the kind of recursive system described by Chomsky and that recursion is not part of counting systems in all cultures. They assume that those cultures that have developed infinite counting systems could do this because of their linguistic capabilities. This is also assumed by Fitch, Hauser & Chomsky (2005: 203). The latter authors claim that all forms of recursion in other domains depend on language. For more on this point, see Chomsky (2007: 7– 8). Luuk & Luuk (2011) note that natural numbers are defined recursively, but the mathematical definition does not necessarily play a role for the kinds of arithmetic operations carried out by humans.

13.2 Speed of language acquisition

domain-specific abilities (Faculty of Language in the Narrow Sense = FLN) required for language.

### **13.1.9 Summary**

In sum, we can say that there are no linguistic universals for which there is a consensus that one has to assume domain-specific innate knowledge to explain them. At the 2008 meeting of the *Deutsche Gesellschaft für Sprachwissenschaft*, Wolfgang Klein promised e 100 to anyone who could name a non-trivial property that all languages share (see Klein 2009). This begs the question of what is meant by 'trivial'. It seems clear that all languages share predicate-argument structures and dependency relations in some sense (Hudson 2010b; Longobardi & Roberts 2010: 2701) and, all languages have complex expressions whose meaning can be determined compositionally (Manfred Krifka was promised 20 e for coming up with compositionality). However, as has been noted at various points, universality by no means implies innateness (Bates 1984: 189; Newmeyer 2005: 205): Newmeyer gives the example that words for sun and moon probably exist in all languages. This has to do with the fact that these celestial bodies play an important role in everyone's lives and thus one needs words to refer to them. It cannot be concluded from this that the corresponding concepts have to be innate. Similarly, a word that is used to express a relation between two objects (e.g., *catch*) has to be connected to the words describing both of these objects (*I*, *elephant*) in a transparent way. However, this does not necessarily entail that this property of language is innate.

Even if we can find structural properties shared by all languages, this is still not proof of innate linguistic knowledge, as these similarities could be traced back to other factors. It is argued that all languages must be made in such a way as to be acquirable with the paucity of resource available to small children (Hurford 2002: Section 10.7.2; Behrens 2009: 433). It follows from this that, in the relevant phases of its development, our brain is a constraining factor. Languages have to fit into our brains and since our brains are similar, languages are also similar in certain respects (see Kluender 1992: 251).

### **13.2 Speed of language acquisition**

It is often argued that children learn language extraordinarily quickly and this can only be explained by assuming that they already possess knowledge about language that does not have to be acquired (e.g., Chomsky 1976b: 144; Hornstein 2013: 395). In order for this argument to hold up to closer scrutiny, it must be demonstrated that other areas of knowledge with a comparable degree of complexity require longer to acquire (Sampson 1989: 214–218). This has not yet been shown. Language acquisition spans several years and it is not possible to simply state that language is acquired following *brief exposure*. Chomsky compares languages to physics and points out that it is considerably more difficult for us to acquire knowledge about physics. Sampson (1989: 215) notes, however, that the knowledge about physics one acquires at school or university is not a basis for comparison and one should instead consider the acquisition of everyday knowledge

### 13 The innateness of linguistic knowledge

about the physical world around us. For example, the kind of knowledge we need when we want to pour liquids into a container, skip with a skipping rope or the knowledge we have about the ballistic properties of objects. The complexity in comparing these domains of knowledge in order to be able to make claims about language acquisition may turn out to be far from trivial. For an in-depth discussion of this aspect, see Sampson (1989: 214–218). Müller & Riemer (1998: 1) point out that children at the age of six can understand 23,700 words and use over 5000. It follows from this that, in the space of four and a half years, they learn on average 14 new words every day. This is indeed an impressive feat, but cannot be used as an argument for innate linguistic knowledge as all theories of acquisition assume that words have to be learned from data rather than being predetermined by a genetically-determined Universal Grammar. In any case the assumption of genetic encoding would be highly implausible for newly created words such as *fax*, *iPod*, *e-mail*, *Tamagotchi*.

Furthermore, the claim that first language acquisition is effortless and rapid when compared to second language acquisition is a myth as has been shown by estimations by Klein (1986: 9): if we assume that children hear linguistic utterances for five hours a day (as a conservative estimate), then in the first five years of their lives, they have 9100 hours of linguistic training. But at the age of five, they have still not acquired all complex constructions. In comparison, second-language learners, assuming the necessary motivation, can learn the grammar of a language rather well in a six-week crash course with twelve hours a day (500 hours in total).

### **13.3 Critical period for acquisition**

Among ducks, there is a critical phase in which their behavior towards parent figures is influenced significantly. Normally, baby ducks follow their mother. If, however, a human is present rather than the mother during a particular time span, the ducks will follow the human. After the critical period, this influence on their behavior can no longer be identified (Lorenz 1970). This kind of critical period can also be identified in other animals and in other areas of cognition, for example the acquisition of visual abilities among primates. Certain abilities are acquired in a given time frame, whereby the presence of the relevant input is important for determining the start of this time frame.

Lenneberg (1964) claims that language acquisition is only possible up to the age of twelve and concludes from the fact that children can learn language much better than adults that this is also due to a critical period and that language acquisition must have similar properties to the behavior of ducks and hence, the predisposition for language acquisition must be innate (Lenneberg 1967: Chapter 4).

The assumptions about the length of the critical period for language acquisition vary considerably. It is possible to find suggestions for 5, 6, 12 and even 15 years (Hakuta et al. 2003: 31). Meisel (2013: 79) talks about "different points of development between 4 and 16 years". An alternative assumption to a critical period would be to assume that the ability to acquire languages decreases continuously over time. Johnson & Newport (1989) tried to determine a critical period for second-language acquisition and they claim

### 13.4 Lack of acquisition among non-human primates

that a second language is learned significantly worse from the age of 15. Elman, Bates, Johnson, Karmiloff-Smith, Parisi & Plunkett (1996: 187–188) have, however, pointed out that there is a different curve for Johnson and Newport's data that fits the individual data better. The alternative curve shows no abrupt change but rather a steady decrease in the ability to learn language and therefore offers no proof of an effect created by a critical period.

Hakuta, Bialystok & Wiley (2003) evaluate data from a questionnaire of 2,016,317 Spanish speakers and 324,444 speakers of Mandarin Chinese that immigrated to the United States. They investigated which correlations there were between age, the point at immigration, the general level of education of the speakers and the level of English they acquired. They could not identify a critical point in time after which language acquisition was severely restricted. Instead, there is a steady decline in the ability to learn as age increases. This can also be observed in other domains: for example, learning to drive at an older age is much harder.

Summing up, it seems to be relatively clear that a critical period cannot be proven to exist for second-language acquisition. Sometimes, it is assumed anyway that secondlanguage acquisition is not driven by an innate UG, but is in fact a learning process that accesses knowledge already acquired during the critical period (Lenneberg 1967: 176). One would therefore have to show that there is a critical period for first-language acquisition. This is, however, not straightforward as, for ethical reasons, one cannot experimentally manipulate the point at which the input is available. We cannot, say, take 20 children and let them grow up without linguistic input to the age of 3, 4, 5, 6, … or 15 and then compare the results. This kind of research is dependent on thankfully very rare cases of neglect. For example, Curtiss (1977) studied a girl called Genie. At the time, Genie was 13 years old and had grown up in isolation. She is a so-called feral child. As Curtiss showed, she was no longer able to learn certain linguistic rules. For an objective comparison, one would need other test subjects that had not grown up in complete isolation and in inhumane conditions. The only possibility of gaining relevant experimental data is to study deaf subjects that did not receive any input from a sign language up to a certain age. Johnson & Newport (1989: 63) carried out relevant experiments with learners of American Sign Language. It was also shown here that there is a linear decline in the ability to learn, however nothing like a sudden drop after a certain age or even a complete loss of the ability to acquire language.

### **13.4 Lack of acquisition among non-human primates**

The fact that non-human primates cannot learn natural language is viewed as evidence for the genetic determination of our linguistic ability. All scientists agree on the fact that there are genetically-determined differences between humans and primates and that these are relevant for linguistic ability. Friederici (2009) offers an overview of the literature that claims that in chimpanzees and macaques (and small children), the connections between parts of the brain are not as developed as in adult humans. The connected regions of the brain are together responsible for the processing of lexical-semantic knowl-

### 13 The innateness of linguistic knowledge

edge and could constitute an important prerequisite for the development of language (p. 179).

The question is, however, whether we differ from other primates in having special cognitive capabilities that are specific to language or whether our capability to acquire languages is due to domain-general differences in cognition. Fanselow (1992b: Section 2) speaks of a human-specific formal competence that does not necessarily have to be specific to language, however. Similarly, Chomsky (2007: 7–8) has considered whether Merge (the only structure-building operation, in his opinion), does not belong to language-specific innate abilities, but rather to general human-specific competence (see, however, Section 13.1.8, in particular footnote 29).

One can ascertain that non-human primates do not understand particular pointing gestures. Humans like to imitate things. Other primates also imitate, however, not for social reasons (Tomasello 2006b: 9–10). According to Tomasello et al. (2005: 676), only humans have the ability and motivation to carry out coordinated activities with common goals and socially-coordinated action plans. Primates do understand intentional actions, however, only humans act with a common goal in mind (*shared intentionality*). Only humans use and understand hand gestures (Tomasello et al. 2005: 685, 724, 726). Language is collaborative to a high degree: symbols are used to refer to objects and sometimes also to the speaker or hearer. In order to be able to use this kind of communication system, one has to be able to put oneself in the shoes of the interlocutor and develop common expectations and goals (Tomasello et al. 2005: 683). Non-human primates could thus lack the social and cognitive prerequisites for language, that is, the difference between humans and other primates does not have to be explained by innate linguistic knowledge (Tomasello 2003: Section 8.1.2; Tomasello et al. 2005).

### **13.5 Creole and sign languages**

When speakers that do not share a common language wish to communicate with each other, they develop so-called pidgin languages. These are languages that use parts of the vocabularies of the languages involved but have a very rudimentary grammar. It has been noted that children of pidgin speakers regularize these languages. The next generation of speakers creates a new language with an independent grammar. These languages are referred to as *creole languages*. One hypothesis is that the form of languages that develop from creolization is restricted by an innate UG (Bickerton 1984b). It is assumed that the parameter setting of creole languages corresponds to the default values of parameters (Bickerton 1984a: 217; 1984b: 178), that is, parameters already have values at birth and these correspond to the values that creole languages have. These default values would have to be modified when learning other languages.30 Bickerton claims that creole languages contain elements that language learners could not have acquired from the input, that is from the pidgin languages. His argumentation is a variant of the classic Poverty of the Stimulus Argument that will be discussed in more detail in Section 13.8.

30For problems that can arise from the assumption of defaults values, see Meisel (1995: 17). Bickerton (1997: 56, fn. 13) distances himself from the claim that creole languages have the default values of parameters.

### 13.6 Localization in special parts of the brain

Bickerton's claims have been criticized as it cannot be verified whether children had input in the individual languages of the adults (Samarin 1984: 207; Seuren 1984: 209). All that can be said considering this lack of evidence is that there are a number of demographic facts that suggest that this was the case for at least some creole languages (Arends 2008). This means that children did not only have the strings from the pidgin languages as an input but also sentences from the individual languages spoken by parents and others around them. Many creolists assume that adults contribute specific grammatical forms to the emerging language. For example, in the case of Hawaiian Creole English one can observe that there are influences from the mother tongues of the speakers involved: Japanese speakers use SOV order as well as SVO and Philippinos use VOS order as well as SVO order. In total, there is quite a lot of variation in the language that can be traced back to the various native languages of the individual speakers.

It is also possible to explain the effects observed for creolization without the assumption of innate language-specific knowledge: the fact that children regularize language can be attributed to a phenomenon independent of language. In experiments, participants were shown two light bulbs and the test subjects had to predict which of the light bulbs would be turned on next. If one of the bulbs was switched on 70% of the time, the participants also picked this one 70% of the time (although they would have actually had a higher success rate if they had always chosen the bulb turned on with 70% probability). This behavior is known as *Probability Matching*. If we add another light bulb to this scenario and then turn this lamp on in 70% of cases and the other two each 15% of the time, then participants choose the more frequently lit one 80–90% of the time, that is, they regularize in the direction of the most frequent occurrence (Gardner 1957; Weir 1964).

Like creolization, a similar situation can be found in certain social contexts with the acquisition of sign language: Singleton & Newport (2004) have shown that a child (Simon) that learned American Sign Language (ASL) makes considerably less mistakes than his parents. The parents first learned ASL at the age of 15 or 16 and performed particular obligatory movements only 70% of the time. Simon made these movements 90% of the time. He regularized the input from his parents, whereby the consistent use of form-meaning pairs plays an important role, that is, he does not simply use Probability Matching, but learns selectively. Singleton & Newport (2004: 401) suspect that these kinds of regularizations also play a role for the emergence of creole and sign languages. However, the relevant statistical data that one would need to confirm this hypothesis are not available.

### **13.6 Localization in special parts of the brain**

By measuring brain activity during speech production/processing and also by investigating patients with brain damage, one can identify special parts of the brain (Broca's area and Wernicke's area) that play an important role for language production and pro-

### 13 The innateness of linguistic knowledge

cessing (see Friederici (2009) for a current overview). Chomsky talks about there being a center of language and even calls this (metaphorically) an *organ* (Chomsky 1977: 164; Chomsky 2005: 1; Chomsky 2008: 133). This localization was seen as evidence for the innate basis for our linguistic knowledge (see also Pinker 1994: 297–314).

However, it is the case that if these parts are damaged, other areas of the brain can take over the relevant functions. If the damage occurs in early childhood, language can also be learned without these special areas of the brain (for sources, see Dąbrowska 2004: Section 4.1).

Apart from that, it can also be observed that a particular area of the brain is activated when reading. If the conclusion about the localization of processing in a particular part of the brain leading to the innateness of linguistic knowledge were valid, then the activation of certain areas of the brain during reading should also lead us to conclude that the ability to read is innate (Elman et al. 1996: 242; Bishop 2002: 57). This is, however, not assumed (see also Fitch, Hauser & Chomsky 2005: 196).

It should also be noted that language processing affects several areas of the brain and not just Broca's and Wernicke's areas (Fisher & Marcus 2005: 11; Friederici 2009). On the other hand, Broca's and Wernicke's areas are also active during non-linguistic tasks such as imitation, motoric coordination and processing of music (Maess et al. 2001). For an overview and further sources, see Fisher & Marcus (2005).

Musso et al. (2003) investigated brain activity during second-language acquisition. They gave German native speakers data from Italian and Japanese and noticed that there was activation in Broca's area. They then compared this to artificial languages that used Italian and Japanese words but did not correspond to the principles of Universal Grammar as assumed by the authors. An example of the processes assumed in their artificial language is the formation of questions by reversing of word order as shown in (39).

	- b. Statement a is this?

The authors then observed that different areas of the brain were activated when learning this artificial language. This is an interesting result, but does not show that we have innate linguistic knowledge. It only shows that the areas that are active when processing our native languages are also active when we learn other languages and that playing around with words such as reversing the order of words in a sentence affects other areas of the brain.

A detailed discussion of localization of languages in particular parts of the brain can be found in Dąbrowska (2004: Chapter 4).

### **13.7 Differences between language and general cognition**

Researchers who believe that there is no such thing as innate linguistic knowledge assume that language can be acquired with general cognitive means. If it can be shown that humans with severely impaired cognition can still acquire normal linguistic abilities or that there are people of normal intelligence whose linguistic ability is restricted, then one can show that language and general cognition are independent.

13.7 Differences between language and general cognition

### **13.7.1 Williams Syndrome**

There are people with a relatively low IQ, who can nevertheless produce grammatical utterances. Among these are people with Williams Syndrome (see Bellugi, Lichtenberger, Jones, Lai & George (2000) for a discussion of the abilities of people with Williams Syndrome). Yamada (1981) takes the existence of such cases as evidence for a separate module of grammar, independent of the remaining intelligence.

IQ is determined by dividing a score in an intelligence test (the mental age) by chronological age. The teenagers that were studied all had a mental age corresponding to that of a four to six year-old child. Yet children at this age already boast impressive linguistic ability that comes close to that of adults in many respects. Gosch, Städing & Pankau (1994: 295) have shown that children with Williams Syndrome do show a linguistic deficit and that their language ability corresponds to what would be expected from their mental age. For problems of sufferers of Williams Syndrome in the area of morphosyntax, see Karmiloff-Smith et al. (1997). The discussion about Williams Syndrome is summarized nicely in Karmiloff-Smith (1998).

### **13.7.2 KE family with FoxP2 mutation**

There is a British family – the so-called KE family – that has problems with language. The members of this family who suffer from these linguistic problems have a genetic defect. Fisher et al. (1998) and Lai et al. (2001) discovered that this is due to a mutation of the FoxP2 gene (FoxP2 stands for *Forkhead-Box P2*). Gopnik & Cargo (1991) conclude from the fact that deficits in the realm of morphology are inherited with genetic defects that there must be a gene that is responsible for a particular module of grammar (morphology). Vargha-Khadem et al. (1995: 930) have demonstrated, however, that the KE family did not just have problems with morphosyntax: the affected family members have intellectual and linguistic problems together with motoric problems with facial muscles. Due to the considerably restricted motion in their facial muscles, it would make sense to assume that their linguistic difficulties also stem from motory problems (Tomasello 2003: 285). The linguistic problems in the KE family are not just limited to production problems, however, but also comprehension problems (Bishop 2002: 58). Nevertheless, one cannot associate linguistic deficiencies directly with FoxP2 as there are a number of other abilities that are affected by the FoxP2 mutation: as well as hindering pronunciation, morphology and syntax, it also has an effect on non-verbal IQ and motory problems with the facial muscles, dealing with non-linguistic tasks, too (Vargha-Khadem et al. 1995).

Furthermore, FoxP2 also occurs in other body tissues: it is also responsible for the development of the lungs, the heart, the intestine and various regions of the brain (Marcus & Fisher 2003). Marcus & Fisher (2003: 260–261) point out that FoxP2 is probably not directly responsible for the development of organs or areas of organs but rather regulates a cascade of different genes. FoxP2 can therefore not be referred to as the language gene, it is just a gene that interacts with other genes in complex ways. It is, among other things, important for our language ability, however, in the same way that it does not make sense to call FoxP2 a language gene, nobody would connect a hereditary muscle disorder with a 'walking gene' just because this myopathy prevents upright walking

### 13 The innateness of linguistic knowledge

(Bishop 2002: 58). A similar argument can be found in Karmiloff-Smith (1998: 392): there is a genetic defect that leads some people to begin to lose their hearing from the age of ten and become completely deaf by age thirty. This genetic defect causes changes in the hairs inside the ear that one requires for hearing. In this case, one would also not want to talk about a 'hearing gene'.

Fitch, Hauser & Chomsky (2005: 190) are also of the opinion that FoxP2 cannot be responsible for linguistic knowledge. For an overview of this topic, see Bishop (2002) and Dąbrowska (2004: Section <IP_ADDRESS>) and for genetic questions in general, see Fisher & Marcus (2005).

### **13.8 Poverty of the Stimulus**

An important argument for the innateness of the linguistic knowledge is the so-called Poverty of the Stimulus Argument (PSA) (Chomsky 1980: 34). Different versions of it can be found in the literature and have been carefully discussed by Pullum & Scholz (2002). After discussing these variants, they summarize the logical structure of the argument as follows (p. 18):

	- b. If children learn their first language by data-driven learning, then they could not acquire anything for which they did not have the necessary evidence (the definition of data-driven learning)
	- c. However, children do in fact learn things that they do not seem to have decisive evidence for (empirical prerequisite)
	- d. Therefore, children do not learn their first language by data-driven learning. (*modus tollens* of b and c)
	- e. Conclusion: children learn language through a learning process supported by innate knowledge. (disjunctive syllogism of a and d)

Pullum and Scholz then discuss four phenomena that have been claimed to constitute evidence for there being innate linguistic knowledge. These are plurals as initial parts of compounds in English (Gordon 1985), sequences of auxiliaries in English (Kimball 1973), anaphoric *one* in English (Baker 1978) and the position of auxiliaries in English (Chomsky 1971: 29–33). Before I turn to these cases in Section 13.8.2, I will discuss a variant of the PSA that refers to the formal properties of phrase structure grammars.

### **13.8.1 Gold's Theorem**

In theories of formal languages, a language is viewed as a set containing all the expressions belonging to a particular language. This kind of set can be captured using various

### 13.8 Poverty of the Stimulus

complex rewrite grammars. A kind of rewrite grammar – so-called context-free grammars – was presented in Chapter 2. In context-free grammars, there is always exactly one symbol on the left-hand side of the rule (a so-called non-terminal symbol) and there can be more of these on the right-hand side of the rule. On the right side there can be symbols (so-called non-terminal symbols) or words/morphemes of the language in question (so-called terminal symbols). The words in a grammar are also referred to as vocabulary (V). Part of a formal grammar is a start symbol, which is usually S. In the literature, this has been criticized since not all expressions are sentences (see Deppermann 2006: 44). It is, however, not necessary to assume this. It is possible to use Utterance as the start symbol and define rules that derive S, NP, VP or whatever else one wishes to class as an utterance from Utterance.31

Beginning with the start symbol, one can keep applying phrase structure rules in a grammar until one arrives at sequences that only contain words (terminal symbols). The set of all sequences that one can generate are the expressions that belong to the language that is licensed by the grammar. This set is a subset of all sequences of words or morphemes that can be created by arbitrary combination. The set that contains all possible sequences is referred to as V∗ .

Gold (1967) has shown that in an environment E, it is not possible to solve the identification problem for any language from particular languages classes, given a finite amount of linguistic input, without additional knowledge. Gold is concerned with the identification of a language from a given class of languages. A language L counts as identified if at a given point in time t*n* , a learner can determine that L is the language in question and does not change this hypothesis. This point in time is not determined in advance, however, identification has to take place at some point. Gold calls this *identification in the limit*. The environments are arbitrary infinite sequences of sentences ⟨ *a*1 *, a*2 *, a*3 *, …*⟩, whereby each sentence in the language must occur at least once in this sequence. In order to show that the identification problem cannot be solved for even very simple language classes, Gold considers the class of languages that contain all possible sequences of words from the vocabulary V expect for one sequence: let V be the vocabulary and x1 , x2 , x3 , … the sequences of words from this vocabulary. The set of all strings from this vocabulary is V∗ . For the class of languages in (41), which consist of all possible sequences of elements in V with the exception of one sequence, it is possible to state a process of how one could learn these languages from a text.

(41) L1 = V∗ − *x*1 , L2 = V∗ − *x*2 , L3 = V∗ − *x*3 , …

After every input, one can guess that the language is V∗ − *σ*, where *σ* stands for the alphabetically first sequence with the shortest length that has not yet been seen. If the sequence in question occurs later, then this hypothesis is revised accordingly. In this way, one will eventually arrive at the correct language.

31On page 279, I discussed a description that corresponds to the S symbol in phrase structure grammars. If one omits the specification of head features in this description, then one gets a description of all complete phrases, that is, also *the man* or *now*. See also Ginzburg & Sag (2000: Section 8.1.4) for a unary branching rule that projects an utterance fragment to a sentential category incorporating the utterance context. See Nykiel & Kim (2019) for further details and references on ellipsis in HPSG.

### 13 The innateness of linguistic knowledge

If we expand the set of languages from which we have to choose by V∗ , then our learning process will no longer work since, if V∗ is the target language, then the guessing will perpetually yield incorrect results. If there were a procedure capable of learning this language class, then it would have to correctly identify V∗ after a certain number of inputs. Let us assume that this input is x*k* . How can the learning procedure tell us at this point that the language we are looking for is not V∗ − *xj* for *j* , *k*? If x*k* causes one to guess the wrong grammar V∗ , then every input that comes after that will be compatible with both the correct (V∗ − *xj* ) and incorrect (V∗ ) result. Since we only have positive data, no input allows us to distinguish between either of the hypotheses and provide the information that we have found a superset of the language we are looking for. Gold has shown that none of the classes of grammars assumed in the theory of formal languages (for example, regular, context-free and context-sensitive languages) can be identified after a finite amount of steps given the input of a text with example utterances. This is true for all classes of languages that contain all finite languages and at least one infinite language. The situation is different if positive and negative data are used for learning instead of text.

The conclusion that has been drawn from Gold's results is that, for language acquisition, one requires knowledge that helps to avoid particular hypotheses from the start. Pullum (2003) criticizes the use of Gold's findings as evidence for the fact that linguistic knowledge must be innate. He lists a number of assumptions that have to be made in order for Gold's results to be relevant for the acquisition of natural languages. He then shows that each of these is not uncontroversial.

### 13.8 Poverty of the Stimulus

5. Language acquisition does not necessarily constitute the acquisition of knowledge about a particular set of sequences, that is, the acquisition of a generative grammar capable of creating this set. The situation is completely different if grammars are viewed as a set of constraints that partially describe linguistic structures, but not necessarily a unique set of linguistic structures (for more on this point, see Section 6.7 and Chapter 14).

Furthermore, Pullum notes that it is also possible to learn the class of context-sensitive grammars with Gold's procedure with positive input only in a finite number of steps if there is an upper bound *k* for the number of rules, where *k* is an arbitrary number. It is possible to make *k* so big that the cognitive abilities of the human brain would not be able to use a grammar with more rules than this. Since it is normally assumed that natural languages can be described by context-sensitive grammars, it can therefore be shown that the syntax of natural languages in Gold's sense can be learned from texts (see also Scholz & Pullum 2002: 195–196).

Johnson (2004) adds that there is another important point that has been overlooked in the discussion about language acquisition. Gold's problem of identifiability is different from the problem of language acquisition that has played an important role in the nativism debate. In order to make the difference clear, Johnson differentiates between identifiability (in the Goldian sense) and learnability in the sense of language acquisition. Identifiability for a language class C means that there must be a function *f* that for each environment *E* for each language *L* in *C* permanently converges on hypothesis *L* as the target language in a finite amount of time.

Johnson proposes the following as the definition of *learnability* (p. 585): *A class C of natural languages is learnable iff, given almost any normal human child and almost any normal linguistic environment for any language L in C, the child will acquire L (or something sufficiently similar to L) as a native language between the ages of one and five.* Johnson adds the caveat that this definition does not correspond to any theory of learnability in psycholinguistics, but rather it is a hint in the direction of a realistic conception of acquisition.

Johnson notes that in most interpretations of Gold's theorem, identifiability and learnability are viewed as one and the same and shows that this is not logically correct: the main difference between the two depends on the use of two quantifiers. Identifiability of *one* language *L* from a class *C* requires that the learner converges on *L* in *every* environment after a finite amount of time. This time can differ greatly from environment to environment. There is not even an upper bound for the time in question. It is straightforward to construct a sequence of environments *E*1 , *E*2 , … for *L*, so that a learner in the environment *Ei* will not guess *L* earlier than the time *t i* . Unlike identifiability, learnability means that there is a point in time after which in every normal environment, *every* normal child has converged on the correct language. This means that children acquire their language after a particular time span. Johnson quotes Morgan (1989: 352) claiming that children learn their native language after they have heard approximately 4,280,000 sentences. If we assume that the concept of learnability has a finite upper-bound for available time, then very few language classes can be identified in the limit. Johnson has shown this as follows: let *C* be a class of languages containing *L* and *L* ′ , where *L* and *L* ′

### 13 The innateness of linguistic knowledge

have some elements in common. It is possible to construct a text such that the first *n* sentences are contained both in *L* and in *L* ′ . If the learner has *L* as its working hypothesis then continue the text with sentences from *L* ′ , if he has *L* ′ as his hypothesis, then continue with sentences from *L*. In each case, the learner has entertained a false hypothesis after *n* steps. This means that identifiability is not a plausible model for language acquisition.

Aside from the fact that identifiability is psychologically unrealistic, it is not compatible with learnability (Johnson 2004: 586). For identifiability, only one learner has to be found (the function *f* mentioned above), learnability, however, quantifies over (almost) all normal children. If one keeps all factors constant, then it is easier to show the identifiability of a language class rather than its learnability. On the one hand, identifiability quantifies universally over all environments, regardless of whether these may seem odd or of how many repetitions these may contain. Learnability, on the other hand, has (almost) universal quantification exclusively over normal environments. Therefore, learnability refers to fewer environments than identifiability, such that there are less possibilities for problematic texts that could occur as an input and render a language unlearnable. Furthermore, learnability is defined in such a way that the learner does not have to learn *L* exactly, but rather learn something sufficiently similar to *L*. With respect to this aspect, learnability is a weaker property of a language class than identifiability. Therefore, learnability does not follow from identifiability nor the reverse.

Finally, Gold is dealing with the acquisition of syntactic knowledge without taking semantic knowledge into consideration. However, children possess a vast amount of information from the context that they employ when acquiring a language (Tomasello et al. 2005). As pointed out by Klein (1986: 44), humans do not learn anything if they are placed in a room and sentences in Mandarin Chinese are played to them. Language is acquired in a social and cultural context.

In sum, one should note that the existence of innate linguistic knowledge cannot be derived from mathematical findings about the learnability of languages.

### **13.8.2 Four case studies**

Pullum & Scholz (2002) have investigated four prominent instances of the Poverty of the Stimulus Argument in more detail. These will be discussed in what follows. Pullum and Scholz's article appeared in a discussion volume. Arguments against their article are addressed by Scholz & Pullum (2002) in the same volume. Further PoS arguments from Chomsky (1986b) and from literature in German have been disproved by Eisenberg (1992).

### **<IP_ADDRESS> Plurals in noun-noun compounding**

Gordon (1985) claims that compounds in English only allow irregular plurals in compounds, that is, *mice-eater* but ostensibly not *\* rats-eater*. Gordon claims that compounds with irregular plurals as first element are so rare that children could not have learned the fact that such compounds are possible purely from data.

13.8 Poverty of the Stimulus

On pages 25–26, Pullum & Scholz discuss data from English that show that regular plurals can indeed occur as the first element of a compound (*chemicals-maker*, *forms-reader*, *generics-maker*, *securities-dealer*, *drinks trolley*, *rules committee*, *publications catalogue*).32 This shows that what could have allegedly not been learned from data is in fact not linguistically adequate and one therefore does not have to explain its acquisition.

### **<IP_ADDRESS> Position of auxiliaries**

The second study deals with the position of modal and auxiliary verbs. Kimball (1973: 73–75) discusses the data in (42) and the rule in (43) that is similar to one of the rules suggested by Chomsky (1957: 39) and is designed to capture the following data:

	- b. It may rain.
	- c. It may have rained.
	- d. It may be raining.
	- e. It has rained.
	- f. It has been raining.
	- g. It is raining.
	- h. It may have been raining.

T stands for tense, M for a modal verb and *en* stands for the participle morpheme (-*en* in *been*/*seen*/… and -*ed* in *rained*). The brackets here indicate the optionality of the expressions. Kimball notes that it is only possible to formulate this rule if (42h) is wellformed. If this were not the case, then one would have to reorganize the material in rules such that the three cases (M)(have+en), (M)(be+ing) and (have+en)(be+ing) would be covered. Kimball assumes that children master the complex rule since they know that sentences such as (42h) are well-formed and since they know the order in which modal and auxiliary verbs must occur. Kimball assumes that children do not have positive evidence for the order in (42h) and concludes from this that the knowledge about the rule in (43) must be innate.

Pullum and Scholz note two problems with this Poverty of the Stimulus Argument: first, they have found hundreds of examples, among them some from children's stories, so that the Kimball's claim that sentences such as (42h) are "vanishingly rare" should be called into question. For PSA arguments, one should at least specify how many occurrences there are allowed to be if one still wants to claim that nothing can be learned from them (Pullum & Scholz 2002: 29).

The second problem is that it does not make sense to assume that the rule in (42h) plays a role in our linguistic knowledge. Empirical findings have shown that this rule is not descriptively adequate. If the rule in (43) is not descriptively adequate, then it cannot

32Also, see Abney (1996: 7) for examples from the Wall Street Journal.

### 13 The innateness of linguistic knowledge

achieve explanatory adequacy and therefore, one no longer has to explain how it can be acquired.

Instead of a rule such as (43), all theories discussed here currently assume that auxiliary or modal verbs embed a phrase, that is, one does not have an Aux node containing all auxiliary and modal verbs, but rather a structure for (42h) that looks as follows:

```
(44) It [may [have [been raining]]].
```
Here, the auxiliary or modal verb always selects the embedded phrase. The acquisition problem now looks completely different: a speaker has to learn the form of the head verb in the verbal projection selected by the auxiliary or modal verb. If this information has been learned, then it is irrelevant how complex the embedded verbal projections are: *may* can be combined with a non-finite lexical verb (42b) or a non-finite auxiliary (42c,d).

### **<IP_ADDRESS> Reference of** *one*

The third case study investigated by Pullum and Scholz deals with the pronoun *one* in English. Baker (1978: 413–425, 327–340) claims that children cannot learn that *one* can refer to constituents larger than a single word as in (45).

	- b. The old man from France was more erudite than the young *one*.

Baker (416–417) claims that *one* can never refer to single nouns inside of NPs and supports this with examples such as (46):

(46) \* The student of chemistry was more thoroughly prepared than the one of physics.

According to Baker, learners would require negative data in order to acquire this knowledge about ungrammaticality. Since learners – following his argumentation – never have access to negative evidence, they cannot possibly have learned the relevant knowledge and must therefore already possess it.

Pullum & Scholz (2002: 33) point out that there are acceptable examples with the same structure as the examples in (46):

	- b. An advocate of Linux got into a heated discussion with one of Windows NT and the rest of the evening was nerd talk.

This means that there is nothing to learn with regard to the well-formedness of the structure in (46). Furthermore, the available data for acquiring the fact that *one* can refer to larger constituents is not as hopeless as Baker (p. 416) claims: there are examples that only allow an interpretation where *one* refers to a larger string of words. Pullum and Scholz offer examples from various corpora. They also provide examples from the CHILDES corpus, a corpus that contains communication with children (MacWhinney 1995). The following example is from a daytime TV show:

13.8 Poverty of the Stimulus

	- B: "Maybe I will, someday. But he'd have to be somebody very special. Sensitive and supportive, giving. Hey, wait a minute, where do they make guys like this?"
		- A: "I don't know. I've never seen one up close."

Here, it is clear that *one* cannot refer to *guys* since A has certainly already seen *guys*. Instead, it refers to *guys like this*, that is, men who are sensitive and supportive.

Once again, the question arises here as to how many instances a learner has to hear for it to count as evidence in the eyes of proponents of the PSA.

### **<IP_ADDRESS> Position of auxiliaries in polar questions**

The fourth PoS argument discussed by Pullum and Scholz comes from Chomsky and pertains to the position of the auxiliary in polar interrogatives in English. As shown on page 97, it was assumed in GB theory that a polar question is derived by movement of the auxiliary from the I position to the initial position C of the sentence. In early versions of Transformational Grammar, the exact analyses were different, but the main point was that the highest auxiliary is moved to the beginning of the clause. Chomsky (1971: 29–33) discusses the sentences in (49) and claims that children know that they have to move the highest auxiliary verb even without having positive evidence for this.33 If, for example, they entertained the hypothesis that one simply places the first auxiliary at the beginning of the sentence, then this hypothesis would deliver the correct result (49b) for (49a), but not for (49c) since the polar question should be (49d) and not (49e).

	- b. Is the dog in the corner hungry?
	- c. The dog that is in the corner is hungry.
	- d. Is the dog that is in the corner hungry?
	- e. \* Is the dog that in the corner is hungry?

Chomsky claims that children do not have any evidence for the fact that the hypothesis that one simply fronts the linearly first auxiliary is wrong, which is why they could pursue this hypothesis in a data-driven learning process. He even goes so far as to claim that speakers of English only rarely or even never produce examples such as (49d) (Chomsky in Piattelli-Palmarini (1980: 114–115)). With the help of corpus data and plausibly constructed examples, Pullum (1996) has shown that this claim is clearly wrong. Pullum (1996) provides examples from the Wall Street Journal and Pullum & Scholz (2002) discuss the relevant examples in more detail and add to them with examples from the CHILDES corpus showing that adult speakers cannot only produce the relevant kinds of

33Examples with auxiliary inversion are used in more recent PoS arguments too, for example in Berwick, Pietroski, Yankama & Chomsky (2011) and Chomsky (2013: 39). Work by Bod (2009b) is not discussed by the authors. For more on Bod's approach, see Section 13.8.3.

### 13 The innateness of linguistic knowledge

sentences, but also that these occur in the child's input.34 Examples from CHILDES that disprove the hypothesis that the first auxiliary has to be fronted are given in (50):35

	- b.
	- c. While you're sleeping, shall I make the breakfast?

Pullum and Scholz point out that *wh*-questions such as (50b) are also relevant if one assumes that these are derived from polar questions (see page 97 in this book) and if one wishes to show how the child can learn the structure-dependent hypothesis. This can be explained with the examples in (51): the base form from which (51a) is derived is (51b). If we were to front the first auxiliary in (51b), we would produce (51c).

	- b. the application Mark [AUX PAST] promised to fill out [AUX is] there
	- c. \* Where did the application Mark promised to fill out is?

Evidence for the fact that (51c) is not correct can, however, also be found in language addressed to children. Pullum and Scholz provide the examples in (52):37

	- b. Where's the other dolly that was in here?
	- c. Where's the other doll that goes in there?

These questions have the form *Where's NP?*, where NP contains a relative clause.

In (50c), there is another clause preceding the actual interrogative, an adjunct clause containing an auxiliary as well. This sentence therefore provides evidence for falsehood of the hypothesis that the linearly first auxiliary must be fronted (Sampson 1989: 223).

In total, there are a number of attested sentence types in the input of children that would allow them to choose between the two hypotheses. Once again, the question arises as to how much evidence should be viewed as sufficient.

Pullum und Scholz's article has been criticized by Lasnik & Uriagereka (2002) and Legate & Yang (2002). Lasnik and Uriagereka argue that the acquisition problem is much bigger than presented by Pullum and Scholz since a learner without any knowledge about the language he was going to acquire could not just have the hypothesis in (53) that were discussed already but also the additional hypotheses in (54):

	- b. Place the first auxiliary in matrix-Infl at the front of the clause.

34For more on this point, see Sampson (1989: 223). Sampson cites part of a poem by William Blake, that is studied in English schools, as well as a children's encyclopedia. These examples surely do not play a role in acquisition of auxiliary position since this order is learned at the age of 3;2, that is, it has already been learned by the time children reach school age.

35See Lewis & Elman (2001). Researchers on language acquisition agree that the frequency of this kind of examples in communication with children is in fact very low. See Ambridge et al. (2008: 223).

36From the transcription of a TV program in the CHILDES corpus.

37These sentences are taken from NINA05.CHA in DATABASE/ENG/SUPPES/.

13.8 Poverty of the Stimulus

(54) a. Place any auxiliary at the front of the clause. b. Place any finite auxiliary at the front of the clause.

Both hypotheses in (54) would be permitted by the sentences in (55):

	- b. Is the dog that is in the corner hungry?

They would, however, also allow sentences such as (56):

(56) \* Is the dog that in the corner is hungry?

The question that must now be addressed is why all hypotheses that allow (56) should be discarded since the learners do not have any information in their natural-linguistic input about the fact that (56) is not possible. They are lacking negative evidence. If (55b) is present as positive evidence, then this by no means implies that the hypothesis in (53b) has to be the correct one. Lasnik and Uriagereka present the following hypotheses that would also be compatible with (55b):

	- b. Place the first auxiliary in initial position (that follows the first complete constituent).
		- c. Place the first auxiliary in initial position (that follows the first parsed semantic unit).

These hypotheses do not hold for sentences such as (58) that contain a conjunction:

(58) Will those who are coming and those who are not coming raise their hands?

The hypotheses in (57) would also allow for sentences such as (59):

(59) \* Are those who are coming and those who not coming will raise their hands?

Speakers hearing sentences such as (58) can reject the hypotheses (57) and thereby rule out (59), however, it is still possible to think of analogous implausible hypotheses that are compatible with all data previously discussed.

Legate & Yang (2002) take up the challenge of Pullum and Scholz and explicitly state how many occurrences one needs to acquire a particular phenomenon. They write the following:

Suppose we have two independent problems of acquisition, P1 and P2 , each of which involves a binary decision. For P1 , let F1 be the frequency of the data that can settle P1 one way or another, and for P2 , F2 . Suppose further that children successfully acquire P1 and P2 at roughly the same developmental stage. Then, under any theory that makes quantitative predictions of language development, we expect F1 and F2 to be roughly the same. Conversely, if F1 and F2 turn out significantly different, then P1 and P2 must represent qualitatively different learning problems.

Now let P1 be the auxiliary inversion problem. The two choices are the structuredependent hypothesis (3b-i) and the first auxiliary hypothesis (3a-i). (Legate & Yang 2002: 155)

### 13 The innateness of linguistic knowledge

The position of auxiliaries in English is learned by children at the age of 3;2. According to Legate and Yang, another acquisition phenomenon that is learned at the age of 3;2 is needed for comparison. The authors focus on subject drop38, that is learned at 36 months (two months earlier than auxiliary inversion). According to the authors, acquisition problems involve a binary decision: in the first case, one has to choose between the two hypotheses in (53). In the second case, the learner has to determine whether a language uses overt subjects. The authors assume that the use of expletives such as *there* serves as evidence for learners that the language they are learning is not one with optional subjects. They then count the sentences in the CHILDES corpus that contain *there*-subjects and estimate F2 at 1.2 % of the sentences heard by the learner. Since, in their opinion, we are dealing with equally difficult phenomena here, sentences such as (49d) and (52) should constitute 1.2 % of the input in order for auxiliary inversion to be learnable.

The authors then searched in the Nina and Adam corpora (both part of CHILDES) and note that 0.068 to 0.045 % of utterances have the form of (52) and none have the form of (49d). They conclude that this number is not sufficient as positive evidence.

Legate and Yang are right in pointing out that Pullum and Scholz's data from the Wall Street Journal are not necessarily relevant for language acquisition and also in pointing out that examples with complex subject noun phrases do not occur in the data or at least to a negligible degree. There are, however, three serious problems with their argumentation: first, there is no correlation between the occurrence of expletive subjects and the property of being a pro-drop language: Galician (Raposo & Uriagereka 1990: Section 2.5) is a pro-drop language with subject expletive pronouns, in Italian there is an existential expletive *ci*, 39 even though Italian counts as a pro-drop language, Franks (1995) lists Upper and Lower Sorbian as pro-drop languages that have expletives in subject position. Since therefore expletive pronouns have nothing to do with the pro-drop parameter, their frequency is irrelevant for the acquisition of a parameter value. If there were a correlation between the possibility of omitting subjects and the occurrence of subject expletives, then Norwegian and Danish children should learn that there has to be a subject in their languages earlier than children learning English since expletives occur a higher percentage of the time in Danish and Norwegian (Scholz & Pullum 2002: 220). In Danish, the constructions corresponding to *there*-constructions in English are twice as frequent. It is still unclear whether there are actually differences in rate of acquisition (Pullum 2009: 246).

Second, in constructing their Poverty of the Stimulus argument, Legate and Yang assume that there is innate linguistic knowledge (the pro-drop parameter). Therefore their argument is circular since it is supposed to show that the assumption of innate linguistic knowledge is indispensable (Scholz & Pullum 2002: 220).

The third problem in Legate and Yang's argumentation is that they assume that a transformational analysis is the only possibility. This becomes clear from the following citation (Legate & Yang 2002: 153):

38This phenomenon is also called *pro-drop*. For a detailed discussion of the pro-drop parameter see Section 16.1.

39However, *ci* is not treated as an expletive by all authors. See Remberger (2009) for an overview.

13.8 Poverty of the Stimulus

The correct operation for question formation is, of course, structure dependent: it involves parsing the sentence into structurally organized phrases, and fronting the auxiliary that follows the subject NP, which can be arbitrarily long:

	- b. Has [the man that is reading a book] e eaten supper?

The analysis put forward by Chomsky (see page 97) is a transformation-based one, that is, a learner has to learn exactly what Legate and Yang describe: the auxiliary must move in front of the subject noun phrase. There are, however, alternative analyses that do not require transformations or equivalent mechanisms. If our linguistic knowledge does not contain any information about transformations, then their claim about what has to be learned is wrong. For example, one can assume, as in Categorial Grammar, that auxiliaries form a word class with particular distributional properties. One possible placement for them is initial positions as observed in questions, the alternative is after the subject (Villavicencio 2002: 104). There would then be the need to acquire information about whether the subject is realized to the left or to the right of its head. As an alternative to this lexicon-based analysis, one could pursue a Construction Grammar (Fillmore 1988: 44; 1999; Kay & Fillmore 1999: 18), Cognitive Grammar (Dąbrowska 2004: Chapter 9), or HPSG (Ginzburg & Sag 2000; Sag 2013) approach. In these frameworks, there are simply two40 schemata for the two sequences that assign different meanings according to the order of verb and subject. The acquisition problem is then that the learners have to identify the corresponding phrasal patterns in the input. They have to realize that Aux NP VP is a well-formed structure in English that has interrogative semantics. The relevant theories of acquisition in the Construction Grammar-oriented literature have been very well worked out (see Section 16.3 and 16.4). Construction-based theories of acquisition are also supported by the fact that one can see that there are frequency effects, that is, auxiliary inversion is first produced by children for just a few auxiliaries and only in later phases of development is it then extended to all auxiliaries. If speakers have learned that auxiliary constructions have the pattern Aux NP VP, then the coordination data provided by Lasnik and Uriagereka in (58) no longer pose a problem since, if we only assign the first conjunct to the NP in the pattern Aux NP VP, then the rest of the coordinate structure (*and those who are not coming*) remains unanalyzed and cannot be incorporated into the entire sentence. The hearer is thereby forced to revise his assumption that *will those who are coming* corresponds to the sequence Aux NP in Aux NP VP and instead to use the entire NP *those who are coming and those who are not coming*. For acquisition, it is therefore enough to simply learn the pattern Aux NP VP first for some and then eventually for all auxiliaries in English. This has also been shown by Lewis & Elman (2001), who trained a neural network exclusively with data that did not contain NPs with relative clauses in auxiliary constructions. Relative clauses were, however, present in other structures. The complexity of the training material was increased bit by

40Fillmore (1999) assumes subtypes of the Subject Auxiliary Inversion Construction since this kind of inversion does not only occur in questions.

### 13 The innateness of linguistic knowledge

bit just as is the case for the linguistic input that children receive (Elman 1993).41 The neural network can predict the next symbol after a sequence of words. For sentences with interrogative word order, the predictions are correct. Even the relative pronoun in (60) is predicted despite the sequence Aux Det N Relp never occurring in the training material.

(60) Is the boy who is smoking crazy?

Furthermore, the system signals an error if the network is presented with the ungrammatical sentence (61):

(61) \* Is the boy who smoking is crazy?

A present participle is not expected after the relative pronoun, but rather a finite verb. The constructed neural network is of course not yet an adequate model of what is going on in our heads during acquisition and speech production.42 The experiment shows, however, that the input that the learner receives contains rich statistical information that can be used when acquiring language. Lewis and Elman point out that the statistical information about the distribution of words in the input is not the only information that speakers have. In addition to information about distribution, they are also exposed to information about the context and can make use of phonological similarities in words.

In connection to the ungrammatical sentences in (61), it has been claimed that the fact that such sentences can never be produced shows that children already know that grammatical operations are structure-dependent and this is why they do not entertain the hypothesis that it is simply the linearly first verb that is moved (Crain & Nakayama 1987). The claim simply cannot be verified since children do not normally form the relevant complex utterances. It is therefore only possible to experimentally illicit utterances where they could make the relevant mistakes. Crain & Nakayama (1987) have carried out such experiments. Their study has been criticized by Ambridge, Rowland & Pine (2008) since these authors could show that children do really make mistakes when fronting auxiliaries. The authors put the difference to the results of the first study by Crain and Nakayama down to unfortunate choice of auxiliary in Crain and Nakayama's study. Due to the use of the auxiliary *is*, the ungrammatical examples had pairs of words that never or only very rarely occur next to each other (*who running* in (62a)).

	- b. The boy who can run fast can jump high. → \* Can the boy who run fast can jump high?

41There are cultural differences. In some cultures, adults do not talk to children that have not attained full linguistic competence (Ochs 1982; Ochs & Schieffelin 1985) (also see Section 13.8.4). Children have to therefore learn the language from their environment, that is, the sentences that they hear reflect the full complexity of the language.

42See Hurford (2002: 324) and Jackendoff (2007: Section 6.2) for problems that arise for certain kinds of neural networks and Pulvermüller (2003; 2010) for an alternative architecture that does not have these problems.

### 13.8 Poverty of the Stimulus

If one uses the auxiliary *can*, this problem disappears since *who* and *run* certainly do appear together. This then leads to the children actually making mistakes that they should not have, as the incorrect utterances actually violate a constraint that is supposed to be part of innate linguistic knowledge.

Estigarribia (2009) investigated English polar questions in particular. He shows that not even half of the polar questions in children's input have the form Aux NP VP (p. 74). Instead, parents communicated with their children in a simplified form and used sentences such as:

	- b. He talking?
	- c. That taste pretty good?

Estigarribia divides the various patterns into complexity classes of the following kind: frag (*fragmentary*), spred (*subject predicate*) and aux-in (*auxiliary inversion*). (64) shows corresponding examples:

c. Are you coming tomorrow? (aux-in)

What we see is that the complexity increases from class to class. Estigarribia suggests a system of language acquisition where simpler classes are acquired before more complex ones and the latter ones develop from peripheral modifications of more simple classes (p. 76). He assumes that question forms are learned from right to left (*right to left elaboration*), that is, (64a) is learned first, then the pattern in (64b) containing a subject in addition to the material in (64a), and then in a third step, the pattern (64c) in which an additional auxiliary occurs (p. 82). In this kind of learning procedure, no auxiliary inversion is involved. This view is compatible with constraint-based analyses such as that of Ginzburg & Sag (2000). A similar approach to acquisition by Freudenthal, Pine, Aguado-Orea & Gobet (2007) will be discussed in Section 16.3.

A further interesting study has been carried out by Bod (2009b). He shows that it is possible to learn auxiliary inversion assuming trees with any kind of branching even if there is no auxiliary inversion with complex noun phrases present in the input. The procedure he uses as well as the results he gains are very interesting and will be discussed in Section 13.8.3 in more detail.

In conclusion, we can say that children do make mistakes with regard to the position of auxiliaries that they probably should not make if the relevant knowledge were innate. Information about the statistical distribution of words in the input is enough to learn the structures of complex sentences without actually having this kind of complex sentences in the input.

### **<IP_ADDRESS> Summary**

Pullum & Scholz (2002: 19) show what an Argument from Poverty of the Stimulus (APS) would have to look like if it were constructed correctly:

### 13 The innateness of linguistic knowledge

	- a. ACQUIRENDUM CHARACTERIZATION: describe in detail what is alleged to be known.
	- b. LACUNA SPECIFICATION: identify a set of sentences such that if the learner had access to them, the claim of data-driven learning of the acquirendum would be supported.
	- c. INDISPENSABILITY ARGUMENT: give reason to think that if learning were data-driven, then the acquirendum could not be learned without access to sentences in the lacuna.
	- d. INACCESSIBILITY EVIDENCE: support the claim that tokens of sentences in the lacuna were not available to the learner during the acquisition process.
	- e. ACQUISITION EVIDENCE: give reason to believe that the acquirendum does in fact become known to learners during childhood.

As the four case studies have shown, there can be reasons for rejecting the acquirendum. If the acquirendum does not have to be acquired, than there is no longer any evidence for innate linguistic knowledge. The acquirendum must at least be descriptively adequate. This is an empirical question that can be answered by linguists. In three of the four PoS arguments discussed by Pullum and Scholz, there were parts which were not descriptively adequate. In previous sections, we already encountered other PoS arguments that involve claims regarding linguistic data that cannot be upheld empirically (for example, the Subjacency Principle). For the remaining points in (65), interdisciplinary work is required: the specification of the lacuna falls into the theory of formal language (the specification of a set of utterances), the argument of indispensability is a mathematical task from the realm of learning theory, the evidence for inaccessibility is an empirical question that can be approached by using corpora, and finally the evidence for acquisition is a question for experimental developmental psychologists (Pullum & Scholz 2002: 19–20).

Pullum & Scholz (2002: 46) point out an interesting paradox with regard to (65c): without results from mathematical theories of learning, one cannot achieve (65c). If one wishes to provide a valid Poverty of the Stimulus Argument, then this should automatically lead to improvements in theories of learning, that is, it is possible to learn more than was previously assumed.

### **13.8.3 Unsupervised Data-Oriented Parsing (U-DOP)**

Bod (2009b) has developed a procedure that does not require any information about word classes or relations between words contained in utterances. The only assumption that one has to make is that there is some kind of structure. The procedure consists of three steps:

13.8 Poverty of the Stimulus

This process will be explained using the sentences in (66):

	- b. The dog barks.

The trees that are assigned to these utterances only use the category symbol X since the categories for the relevant phrases are not (yet) known. In order to keep the example readable, the words themselves will not be given the category X, although one can of course do this. Figure 13.2 shows the trees for (66). In the next step, the trees are divided

Figure 13.2: Possible binary-branching structures for *Watch the dog* and *The dog barks*.

into subtrees. The trees in Figure 13.2 have the subtrees that can be seen in Figure 13.3 on the following page. In the third step, we now have to compute the best tree for each utterance. For *The dog barks.*, there are two trees in the set of the subtrees that correspond exactly to this utterance. But it is also possible to build structures out of subtrees. There are therefore multiple derivations possible for *The dog barks.* all of which use the trees in Figure 13.3: one the one hand, trivial derivations that use the entire tree, and on the other, derivations that build trees from smaller subtrees. Figure 13.4 gives an impression of how this construction of subtrees happens. If we now want to decide which of the analyses in (67) is the best, then we have to compute the probability of each tree.

	- b. [the [dog barks]]

The probability of a tree is the sum of the probabilities of all its analyses. There are two analyses for (67b), which can be found in Figure 13.4. The probability of the first analysis of (67b) corresponds to the probability of choosing exactly the complete tree for [the [dog barks]] from the set of all subtrees. Since there are twelve subtrees, the probability of choosing that one is 1/12. The probability of the second analysis is the product of the probabilities of the subtrees that are combined and is therefore 1/12 × 1/12 = 1/144. The

### 13 The innateness of linguistic knowledge

Figure 13.3: Subtrees for the trees in Figure 13.2

probability of the analysis in (67b) is therefore 1/12 + (1/12 × 1/12) = 13/144. One can then calculate the probability of the tree in (67a) in the same way. The only difference here is that the tree for [the dog] occurs twice in the set of subtrees. Its probability is therefore 2/12. The probability of the tree [[the dog] barks] is therefore: 1/12 + (1/12 × 2/12) = 14/144. We have thus extracted knowledge about plausible structures from the corpus. This knowledge can also be applied whenever one hears a new utterance for which there is no complete tree. It is then possible to use already known subtrees to calculate the probabilities of possible analyses of the new utterance. Bod's model can also be combined with weights: those sentences that were heard longer ago by the speaker, will receive a lower weight. One can thereby also account for the fact that children do not have all sentences that they have ever heard available simultaneously. This extension makes the UDOP model more plausible for language acquisition.

13.8 Poverty of the Stimulus

Figure 13.4: Analysis of *The dog barks* using subtrees from Figure 13.3

In the example above, we did not assign categories to the words. If we were to do this, then we would get the tree in Figure 13.5 as a possible subtree. These kinds of

Figure 13.5: Discontinuous partial tree

discontinuous subtrees are important if one wants to capture dependencies between elements that occur in different subtrees of a given tree. Some examples are the following sentences:

	- b. *What's* this scratch *doing* on the table?
	- c. Most software *companies* in Vietnam *are* small sized.

It is then also possible to learn auxiliary inversion in English with these kinds of discontinuous trees. All one needs are tree structures for the two sentences in (69) in order to prefer the correct sentence (70a) over the incorrect one (70b).

13 The innateness of linguistic knowledge

U-DOP can learn the structures for (69) in Figure 13.6 from the sentences in (71):

	- b. The man is hungry.
	- c. The man mumbled.
	- d. The boy is eating.

Note that these sentences do not contain any instance of the structure in (70a). With

Figure 13.6: Structures that U-DOP learned from the examples in (69) and (71)

the structures learned here, it is possible to show that the shortest possible derivation for the position of the auxiliary is also the correct one: the correct order *Is the man who is eating hungry?* only requires that the fragments in Figure 13.7 on the next page are combined, whereas the structure for \* *Is the man who eating is hungry?* requires at least four subtrees from Figure 13.6 to be combined with each other. This is shown by Figure 13.8 on the facing page.

The motivation for always taking the derivation that consists of the least subparts is that one maximizes similarity to already known material.

The tree for (72) containing one auxiliary too many can also be created from Figure 13.6 with just two subtrees (with the tree [X isX X] and the entire tree for *The man who is eating is hungry*).

13.8 Poverty of the Stimulus

Figure 13.7: Derivation of the correct structure for combination with an auxiliary using two subtrees from Figure 13.6

Figure 13.8: Derivation of the incorrect structure for the combination with an auxiliary using two subtrees from Figure 13.6

### (72) \* Is the man who is eating is hungry?

Interestingly, children do produce this kind of incorrect sentences (Crain & Nakayama 1987: 530; Ambridge, Rowland & Pine 2008). However, if we consider the probabilities of the subtrees in addition to the the number of combined subparts, we get the correct result, namely (70a) and not (72). This is due to the fact that *the man who is eating* occurs in the corpus twice, in (70a) and in (71a). Thus, the probability of *the man who is eating* is just as high as the probability of *the man who is eating is hungry* and thus derivation in Figure 13.7 is preferred over the one for (72). This works for the constructed examples here, however one can imagine that in a realistic corpus, sequences of the form *the man who is eating* are more frequent than sequences with further words since *the man who is eating* can also occur in other contexts. Bod has applied this process to corpora of adult language (English, German and Chinese) as well as applying it to the Eve corpus from the CHILDES database in order to see whether analogy formation constitutes a plausible model for human acquisition of language. He was able to show

### 13 The innateness of linguistic knowledge

that what we demonstrated for the sentences above also works for a larger corpus of naturally occurring language: although there were no examples for movement of an auxiliary across a complex NP in the Eve corpus, it is possible to learn by analogy that the auxiliary from a complex NP cannot be fronted.

It is therefore possible to learn syntactic structures from a corpus without any prior knowledge about parts of speech or abstract properties of language. The only assumption that Bod makes is that there are (binary-branching) structures. The assumption of binarity is not really necessary. But if one includes flat branching structures into the computation, the set of trees will become considerably bigger. Therefore, Bod only used binary-branching structures in his experiments. In his trees, X consists of two other X's or a word. We are therefore dealing with recursive structures. Therefore, Bod's work proposes a theory of the acquisition of syntactic structures that only requires recursion, something that is viewed by Hauser, Chomsky & Fitch (2002) as a basic property of language.

As shown in Section 13.1.8, there is evidence that recursion is not restricted to language and thus one can conclude that it is not necessary to assume innate linguistic knowledge in order to be able to learn syntactic structures from the given input.

Nevertheless, it is important to point out something here: what Bod shows is that syntactic structures can be learned. The information about the parts of speech of each word involved which are not yet included in his structures can also be derived using statistical methods (Redington et al. 1998; Clark 2000).43 In all probability, the structures that can be learned correspond to structures that surface-oriented linguistic theories would also assume. However, not all aspects of the linguistic analysis are acquired. In Bod's model, only occurrences of words in structures are evaluated. Nothing is said about whether words stand in a particular regular relationship to one another or not (for example, a lexical rule connecting a passive participle and perfect participle). Furthermore, nothing is said about how the meaning of expressions arise (are they rather holistic in the sense of Construction Grammar or projected from the lexicon?). These are questions that still concern theoretical linguists (see Chapter 21) and cannot straightforwardly be derived from the statistic distribution of words and the structures computed from them (see Section 21.8.1 for more on this point).

A second comment is also needed: we have seen that statistical information can be used to derive the structure of complex linguistic expressions. This now begs the question of how this relates to Chomsky's earlier argumentation against statistical approaches (Chomsky 1957: 16). Abney (1996: Section 4.2) discusses this in detail. The problem with his earlier argumentation is that Chomsky referred to Markov models. These are statistical versions of finite automatons. Finite automatons can only describe type 3 languages and are therefore not appropriate for analyzing natural language. However, Chomsky's criticism cannot be applied to statistical methods in general.

43Computational linguistic algorithms for determining parts of speech often look at an entire corpus. But children are always dealing with just a particular part of it. The corresponding learning process must then also include a curve of forgetting. See Braine (1987: 67).

13.8 Poverty of the Stimulus

### **13.8.4 Negative evidence**

In a number of works that assume innate linguistic knowledge, it is claimed that children do not have access to negative evidence, that is, nobody tells them that sentences such as (49e) – repeated here as (73) – are ungrammatical (Brown & Hanlon 1970: 42–52; Marcus 1993).

(73) \* Is the dog that in the corner is hungry?

It is indeed correct that adults do not wake up their children with the ungrammatical sentence of the day, however, children do in fact have access to negative evidence of various sorts. For example, Chouinard & Clark (2003) have shown that English and French speaking parents correct the utterances of their children that are not well-formed. For example, they repeat utterances where the verb was inflected incorrectly. Children can deduce from the fact that the utterance was repeated and from what was changed in the repetition that they made a mistake and Chouinard and Clark also showed that they actually do this. The authors looked at data from five children whose parents all had an academic qualification. They discuss the parent-child relationship in other cultures, too (see Ochs (1982); Ochs & Schieffelin (1985) and Marcus (1993: 71) for an overview) and refer to studies of America families with lower socio-economic status (page 660).

A further form of negative evidence is indirect negative evidence, which Chomsky (1981a: 9) also assumes could play a role in acquisition. Goldberg (1995: Section 5.2) gives the utterance in (74a) as an example:44

	- b. \* The magician disappeared the bird.

The child can conclude from the fact that adults use a more involved causative construction with *make* that the verb *disappear*, unlike other verbs such as *melt*, cannot be used transitively. An immediately instructive example for the role played by indirect negative evidence comes from morphology. There are certain productive rules that can however still not be applied if there is a word that blocks the application of the rule. An example is the -*er* nominalization suffix in German. By adding an -*er* to a verb stem, one can derive a noun that refers to someone who carries out a particular action (often habitually) (*Raucher* 'smoker', *Maler* 'painter', *Sänger* 'singer', *Tänzer* 'dancer'). However, *Stehler* 'stealer' is very unusual. The formation of *Stehler* is blocked by the existence of *Dieb* 'thief'. Language learners therefore have to infer from the non-existence of *Stehler* that the nominalization rule does not apply to *stehlen* 'to steal'.

Similarly, a speaker with a grammar of English that does not have any restrictions on the position of manner adverbs would expect that both orders in (75) are possible (Scholz & Pullum 2002: 206):

	- b. \* call immediately the police

44Also, see Tomasello (2006a: 277).

### 13 The innateness of linguistic knowledge

Learners can conclude indirectly from the fact that verb phrases such as (75b) (almost) never occur in the input that these are probably not part of the language. This can be modeled using the relevant statistical learning algorithms.

The examples for the existence of negative evidence provided so far are more arguments from plausibility. Stefanowitsch (2008) has combined corpus linguistic studies on the statistical distribution with acceptability experiments and has shown that negative evidence gained from expected frequencies correlates with acceptability judgments of speakers. This process will be discussed now briefly: Stefanowitsch assumes the following principle:

(76) Form expectations about the frequency of co-occurrence of linguistic features or elements on the basis of their individual frequency of occurrence and check these expectations against the actual frequency of co-occurrence. (Stefanowitsch 2008: 518)

Stefanowitsch works with the part of the *International Corpus of English* that contains British English (ICE-GB). In this corpus, the verb *say* occurs 3,333 times and sentences with ditransitive verbs (Subj Verb Obj Obj) occur 1,824 times. The entire total of verbs in the corpus is 136,551. If all verbs occurred in all kinds of sentences with the same frequencies, then we would expect *say* to occur 44.52 times (X / 1,824 = 3,333 / 136,551 and hence X = 1,824 × 3,333 / 136,551) in the ditransitive construction. But the number of actual occurrences is actually 0 since, unlike (77b), sentences such as (77a) are not used by speakers of English.

	- b. Dad said something nice to Sue.

Stefanowitsch shows that the non-occurrence of *say* in the ditransitive sentence pattern is significant. Furthermore, he investigated how acceptability judgments compare to the frequent occurrence or non-occurrence of verbs in certain constructions. In a first experiment, he was able to show that the frequent non-occurrence of elements in particular constructions correlates with the acceptability judgments of speakers, whereas this is not the case for the frequent occurrence of a verb in a construction.

In sum, we can say that indirect negative evidence can be derived from linguistic input and that it seems to play an important role in language acquisition.

### **13.9 Summary**

It follows from all this that not a single one of the arguments in favor of innate linguistic knowledge remains uncontroversial. This of course does not rule out there still being innate linguistic knowledge but those who wish to incorporate this assumption into their theories have to take more care than was previously the case to prove that what they assume to be innate is actually part of our linguistic knowledge and that it cannot be learned from the linguistic input alone.

13.9 Summary

### **Comprehension questions**

1. Which arguments are there for the assumption of innate linguistic knowledge?

### **Further reading**

Pinker's book (1994) is the best written book arguing for nativist models of language.

Elman, Bates, Johnson, Karmiloff-Smith, Parisi & Plunkett (1996) discuss all the arguments that have been proposed in favor of innate linguistic knowledge and show that the relevant phenomena can be explained differently. The authors adopt a connectionist view. They work with neuronal networks, which are assumed to model what is happening in our brains relatively accurately. The book also contains chapters about the basics of genetics and the structure of the brain, going into detail about why a direct encoding of linguistic knowledge in our genome is implausible.

Certain approaches using neuronal networks have been criticized because they cannot capture certain aspects of human abilities such as recursion or the multiple usage of the same words in an utterance. Pulvermüller (2010) discusses an architecture that has memory and uses this to analyze recursive structures. In his overview article, certain works are cited that show that the existence of more abstract rules or schemata of the kind theoretical linguists take for granted can be demonstrated on the neuronal level. Pulvermüller does not, however, assume that linguistic knowledge is innate (p. 173).

Pullum and Scholz have dealt with the Poverty-of-the-Stimulus argument in detail (Pullum & Scholz 2002; Scholz & Pullum 2002).

Goldberg (2006) and Tomasello (2003) are the most prominent proponents of Construction Grammar, a theory that explicitly tries to do without the assumption of innate linguistic knowledge.

## **14 Generative-enumerative vs. model-theoretic approaches**

Generative-enumerative approaches assume that a grammar generates a set of sequences of symbols (strings of words). This is where the term Generative Grammar comes from. Thus, it is possible to use the grammar on page 53, repeated here as (1), to derive the string *er das Buch dem Mann gibt* 'he the book the man gives'.

Beginning with the start symbol (S), symbols are replaced until one reaches a sequence of symbols only containing words. The set of all strings derived in this way is the language described by the grammar.

The following are classed as generative-enumerative approaches:

LFG was also originally designed to be a generative grammar.

The opposite of such theories of grammar are model-theoretic or constraint-based approaches (MTA). MTAs formulate well-formedness conditions on the expressions that the grammar describes. In Section 6.7, we already discussed a model-theoretic approach for theories that use feature structures to model phenomena. To illustrate this point, I will discuss another HPSG example: (2) shows the lexical item for *kennst* 'know'. In the description of (2), it is ensured that the phon value of the relevant linguistic sign is ⟨ *kennst* ⟩, that is, this value of phon is constrained. There are parallel restrictions for the features given in (2): the synsem value is given. In synsem, there are restrictions on the loc and nonloc value. In cat, there are individual restrictions for head and comps. The value of comps is a list with descriptions of dependent elements. The descriptions are given as abbreviations here, which actually stand for complex feature descriptions

### 14 Generative-enumerative vs. model-theoretic approaches

that also consist of feature-value pairs. For the first argument of *kennst*, a head value of type *noun* is required, the per value in the semantic index has to be *second* and the num value has to be *sg*. The structure sharings in (2) are a special kind of constraint. Values that are not specified in the descriptions of lexical entries can vary in accordance with the feature geometry given by the type system. In (2), neither the slash value of the nominative NP nor the one of the accusative NP is fixed. This means that slash can either be an empty or non-empty list.

The constraints in lexical items such as (2) interact with further constraints that hold for the signs of type *phrase*. For instance, in head-argument structures, the non-head daughter must correspond to an element from the comps list of the head daughter.

Generative-enumerative and model-theoretic approaches view the same problem from different sides: the generative side only allows what can be generated by a given set of rules, whereas the model-theoretic approach allows everything that is not ruled out by constraints.1

Pullum & Scholz (2001: 19–20) and Pullum (2007) list the following model-theoretic approaches:2

1Compare this to an old joke: in dictatorships, everything that is not allowed is banned, in democracies, everything that is not banned is allowed and in France, everything that is banned is allowed. Generativeenumerative approaches correspond to the dictatorships, model-theoretic approaches are the democracies and France is something that has no correlate in linguistics.

2 See Pullum (2007) for a historical overview of Model Theoretic Syntax (MTS) and for further references.

14.1 Graded acceptability

Categorial Grammars (Bouma & van Noord 1994), TAG (Rogers 1994) and Minimalist approaches (Veenstra 1998) can be formulated in model-theoretic terms.

Pullum & Scholz (2001) point out various differences between these points of view. In the following sections, I will focus on two of these differences.4 Section 14.3 deals with ten Hacken's objection to the model-theoretic view.

### **14.1 Graded acceptability**

Generative-enumerative approaches differ from model-theoretic approaches in how they deal with the varying degrees of acceptability of utterances. In generative-enumerative approaches, a particular string is either included in the set of well-formed expressions or it is not. This means that it is not straightforwardly possible to say something about the degree of deviance: the first sentence in (3) is judged grammatical and the following three are equally ungrammatical.

	- b. \* Du you kennen know.3pl diesen this.acc Aufsatz. essay
	- c. \* Du you kennen know.3pl dieser this.nom Aufsatz. essay
	- d. \* Du you kennen know.3pl Aufsatz essay dieser. this.nom

At this point, critics of this view raise the objection that it is in fact possible to determine degrees of wellformedness in (3b–d): in (3b), there is no agreement between the subject and the verb, in (3c), *dieser Aufsatz* 'this essay' has the wrong case in addition, and in (3d), *Aufsatz* 'essay' and *dieser* 'this' occur in the wrong order. Furthermore, the sentence in (4) violates grammatical rules of German, but is nevertheless still interpretable.

3According to Pullum (2013: Section 3.2), there seems to be a problem for model-theoretic formalizations of so-called *constraining equations*.

4The reader should take note here: there are differing views with regard to how generative-enumerative and MTS models are best formalized and not all of the assumptions discussed here are compatible with every formalism. The following sections mirror the important points in the general discussion.

### 14 Generative-enumerative vs. model-theoretic approaches

(4) Studenten students stürmen storm mit with Flugblättern flyers und and Megafon megaphone die the Mensa canteen und and rufen call alle all auf up zur to Vollversammlung plenary.meeting in in der the Glashalle glass.hall *zum* to.the *kommen*. come *Vielen* many.dat bleibt stays das the Essen food im in.the Mund mouth stecken stick und and *kommen* come *sofort* immediately *mit*. 5 with 'Students stormed into the university canteen with flyers and a megaphone calling

for everyone to come to a plenary meeting in the glass hall. For many, the food stuck in their throats and they immediately joined them.'

Chomsky (1975: Chapter 5; 1964b) tried to use a string distance function to determine the relative acceptability of utterances. This function compares the string of an ungrammatical expression with that of a grammatical expression and assigns an ungrammaticality score of 1, 2 or 3 according to certain criteria. This treatment is not adequate, however, as there are much more fine-grained differences in acceptability and the string distance function also makes incorrect predictions. For examples of this and technical problems with calculating the function, see Pullum & Scholz (2001: 29).

In model-theoretic approaches, grammar is understood as a system of well-formedness conditions. An expression becomes worse, the more well-formedness conditions it violates (Pullum & Scholz 2001: 26–27). In (3b), the person and number requirements of the lexical item for the verb *kennst* are violated. In addition, the case requirements for the object have not been fulfilled in (3c). There is a further violation of a linearization rule for the noun phrase in (3d).

Well-formedness conditions can be weighted in such a way as to explain why certain violations lead to more severe deviations than others (Sorace & Keller 2005). Furthermore, performance factors also play a role when judging sentences (for more on the distinction between performance and competence, see Chapter 15). As we will see in Chapter 15, constraint-based approaches work very well as performance-compatible grammar models. If we combine the relevant grammatical theory with performance models, we will arrive at explanations for graded acceptability differences owing to performance factors.

### **14.2 Utterance fragments**

Pullum & Scholz (2001: Section 3.2) point out that generative-enumerative theories do not assign structure to fragments. For instance, neither the string *and of the* nor the string *the of and* would receive a structure since none of these sequences is well-formed as an utterance and they are therefore not elements of the set of sequences generated by the grammar. However, *and of the* can occur as part of the coordination of PPs in sentences such as (5) and would therefore have some structure in these cases, for example the one given in Figure 14.1 on the next page.

5 Streikzeitung der Universität Bremen, 04.12.2003, p. 2. The emphasis is mine.

### 14.2 Utterance fragments

(5) That cat is afraid of the dog and of the parrot.

Figure 14.1: Structure of the fragment *and of the* following Pullum & Scholz (2001: 32)

As a result of the interaction of various constraints in a constraint-based grammar, it emerges that *the* is part of an NP and this NP is an argument of *of* and furthermore *and* is combined with the relevant *of* -PP. In symmetric coordination, the first conjunct has the same syntactic properties as the second, which is why the partial structure of *and of the* allows one to draw conclusions about the category of the conjunct despite it not being part of the string.

Ewan Klein noted that Categorial Grammar and Minimalist Grammars, which build up more complex expressions from simpler ones, can sometimes create this kind of fragments (Pullum 2013: 507). This is certainly the case for Categorial Grammars with composition rules, which allow one to combine any sequence of words to form a constituent. If one views derivations as logical proofs, as is common in some variants of Categorial Grammar, then the actual derivation is irrelevant. What matters is whether a proof can be found or not. However, if one is interested in the derived structures, then the argument brought forward by Pullum and Scholz is still valid. For some variants of Categorial Grammar that motivate the combination of constituents based on their prosodic and information-structural properties (Steedman 1991: Section 3), the problem persists since fragments have a structure independent of the structure of the entire utterance and independent of their information-structural properties within this complete structure. This structure of the fragment can be such that it is not possible to analyze it with type-raising rules and composition rules.

In any case, this argument holds for Minimalist theories since it is not possible to have a combination of *the* with a nominal constituent if this constituent was not already built up from lexical material by Merge.

14 Generative-enumerative vs. model-theoretic approaches

### **14.3 A problem for model-theoretic approaches?**

Ten Hacken (2007: 237–238) discusses the formal assumptions of HPSG. In HPSG, feature descriptions are used to describe feature structures. Feature structures must contain all the features belonging to a structure of a certain type. Additionally, the features have to have a maximally-specific value (see Section 6.7). Ten Hacken discusses gender properties of the English noun *cousin*. In English, gender is important in order to ensure the correct binding of pronouns (see page 280 for German):

	- b. The woman*i* sleeps. He∗*i* snores.

While *he* in (6a) can refer to *man*, *woman* is not a possible antecedent. Ten Hacken's problem is that *cousin* is not marked with respect to gender. Thus, it is possible to use it to refer to both male and female relatives. As was explained in the discussion of the case value of *Frau* 'woman' in Section 6.7, it is possible for a value in a description to remain unspecified. Thus, in the relevant feature structures, any appropriate and maximally specific value is possible. The case of *Frau* can therefore be nominative, genitive, dative or accusative in an actual feature structure. Similarly, there are two possible genders for *cousin* corresponding to the usages in (7).

	- b. I have a cousin*i* . She*i* is very smart.

Ten Hacken refers to examples such as (8) and claims that these are problematic:

	- b. How many cousins does Niels have?

In plural usage, it is not possible to assume that *cousins* is feminine or masculine since the set of relatives can contain either women or men. It is interesting to note that (9a) is possible in English, whereas German is forced to use (9b) to express the same meaning.

	- b. Niels Niels und and Odette Odette sind are Cousin cousin.m und and Cousine. cousin.f

Ten Hacken concludes that the gender value has to remain unspecified and this shows, in his opinion, that model-theoretic analyses are unsuited to describing language.

If we consider what exactly ten Hacken noticed, then it becomes apparent how one can account for this in a model-theoretic approach: Ten Hacken claims that it does not make sense to specify a gender value for the plural form of *cousin*. In a model-theoretic approach, this can be captured in two ways. One can either assume that there are no gender features for referential indices in the plural, or that one can add a gender value that plural nouns can have.

The first approach is supported by the fact that there are no inflectional differences between the plural forms of pronouns with regard to gender. There is therefore no reason to distinguish genders in the plural.

14.3 A problem for model-theoretic approaches?

	- b. The cousins/brothers/sisters are standing over there. They are very smart.

No distinctions are found in plural when it comes to nominal inflection (*brothers*, *sisters*, *books*). In German, this is different. There are differences with both nominal inflection and the reference of (some) noun phrases with regard to the sexus of the referent. Examples of this are the previously mentioned examples *Cousin* 'male cousin' and *Cousine* 'female cousin' as well as forms with the suffix -*in* as in *Kindergärtnerin* 'female nursery teacher'. However, gender is normally a grammatical notion that has nothing to do with sexus. An example is the neuter noun *Mitglied* 'member', which can refer to both female and male persons.

The question that one has to ask when discussing Ten Hacken's problem is the following: does gender play a role for pronominal binding in German? If this is not the case, then the gender feature is only relevant within the morphology component, and here the gender value is determined for each noun in the lexicon. For the binding of personal pronouns, there is no gender difference in German.

(11) Die the Schwestern sisters.f / Brüder brothers.m / Vereinsmitglieder club.members.n / Geschwister siblings stehen stand dort. there Sie they lächeln. smile.

'The sisters/brothers/club members/siblings are standing there. They are smiling.'

Nevertheless, there are adverbials in German that agree in gender with the noun to which they refer (Höhle 1983: Chapter 6):

	- b. Die the Türen doors.f wurden were eine one.f nach after der the anderen other geschlossen. closed 'The doors were closed one after the other.'
	- c. Die the Riegel bolts.m wurden were einer one.m nach after dem the anderen other zugeschoben. closed
		- 'The bolts were closed one after the other.'

For animate nouns, it is possible to diverge from the gender of the noun in question and use a form of the adverbial that corresponds to the biological sex:

(13) a. Die the Mitglieder members.n des of.the Politbüros politburo wurden were eines one.n / einer one.m nach after dem the anderen other aus out.of dem the Saal hall getragen. carried

'The members of the politburo were carried out of the hall one after the other.'

### 14 Generative-enumerative vs. model-theoretic approaches

b. Die the Mitglieder members.n des of.the Frauentanzklubs women's.dance.club verließen left eines one.n / eine one.f nach after dem the.n / der the.f anderen other im in.the Schutze protection der of.the Dunkelheit dark den the Keller. basement 'The members of the women's dance club left the basement one after the other under cover of darkness.'

This deviation from gender in favor of sexus can also be seen with binding of personal and relative pronouns with nouns such as *Weib* 'woman' (pej.) and *Mädchen* 'girl':

(14) a. "Farbe color bringt brings die the meiste most Knete!" money verriet revealed ein a 14jähriges 14-year.old türkisches Turkish *Mädchen*, girl.n *die* who.f die the Mauerstückchen wall.pieces am in.the Nachmittag afternoon am at Checkpoint Checkpoint Charlie Charlie an at Japaner und US-Bürger verkauft.6

Japanese and US-citizens sells

' "Color gets the most money" said a 14-year old Turkish girl who sells pieces of the wall to Japanese and American citizens at Checkpoint Charlie.'

b. Es it ist is ein a junges young *Mädchen*, girl.n *die* who.f auf on der the Suche search nach for CDs CDs bei at Bolzes Bolzes reinschaut.7 stops.by

'It is a young girl looking for CDs that stops by Bolzes.'

For examples from Goethe, Kafka and Thomas Mann, see Müller (1999b: 417–418).

For inanimate nouns such as those in (12), agreement is obligatory. For the analysis of German, one therefore does in fact require a gender feature in the plural. In English, this is not the case since there are no parallel examples with pronouns inflecting for gender. One can therefore either assume that plural indices do not have a gender feature or that the gender value is *none*. In the latter case, the feature would have a value and hence fulfill the formal requirements. (15) shows the first solution: plural indices are modeled by feature structures of type *pl-ind* and the gender feature is just not appropriate for such objects.

(15) a. singular index: b. plural index: *sg-ind* per *per* num *sg*

num *pl*

gen *gender*

6 taz, 14.06.1990, p. 6.

7 taz, 13.03.1996, p. 11.

14.3 A problem for model-theoretic approaches?

The second solution requires the type hierarchy in Figure 14.2 for the subtypes of *gender*. With such a type hierarchy *none* is a possible value of the gen feature and no problem will arise.

Figure 14.2: Type hierarchy for one of the solutions of ten Hacken's problem

In general, it is clear that cases such as the one constructed by ten Hacken will never be a problem since there are either values that make sense, or there are contexts for which there is no value that makes sense and one therefore does not require the features.

So, while ten Hacken's problem is a non-issue, there are certain problems of a more technical nature. I have pointed out one such technical problem in Müller (1999b: Section 14.4). I show that spurious ambiguities arise for a particular analysis of verbal complexes in German when one resolves the values of a binary feature (flip). I also show how this problem can be avoided by the complicated stipulation of a value in certain contexts.

## **15 The competence/performance distinction**

The distinction between competence and performance (Chomsky 1965: Section 1.1), which is assumed by several theories of grammar, was already discussed in Section 12.6.3 about the analysis of scrambling and verbal complexes in TAG. Theories of competence are intended to describe linguistic knowledge and performance theories are assigned the task of explaining how linguistic knowledge is used as well as why mistakes are made in speech production and comprehension. A classic example in the competence/ performance discussion are cases of center self-embedding.  If one rearranges the material somewhat, it is possible to process the sentences and assign a meaning to them.1 For sentences such as (2b), it is often assumed that they fall within

1The sentence in (2a) can be continued following the pattern that was used to create the sentence. For instance by adding *die unter der Treppe lebte, die meine Freunde repariert haben* 'who lived under the staircase which my friends repaired'. This shows that a restriction of the number of elements that depend on one head to seven (Leiss 2003: 322) does not restrict the set of the sentences that are generated or licensed by a grammar to be finite. There are at most two dependents of each head in (2a). The extraposition of the relative clauses allows the hearer to group material into processable and reducible chunks, which reduces the cognitive burden during processing.

This means that the restriction to seven dependents does not cause a finitization of recursion ("Verendlichung von Rekursivität") as was claimed by Leiss (2003: 322). Leiss argued that Miller could not use his insights regarding short term memory, since he worked within Transformational Grammar rather than in Dependency Grammar. The discussion shows that dependency plays an important role, but that linear order is also important for processing.

### 15 The competence/performance distinction

our grammatical competence, that is, we possess the knowledge required to assign a structure to the sentence, although the processing of utterances such as (2b) exceeds language-independent abilities of our brain. In order to successfully process (2b), we would have to retain the first five noun phrases and corresponding hypotheses about the further progression of the sentence in our heads and could only begin to combine syntactic material when the verbs appear. Our brains become overwhelmed by this task. These problems do not arise when analyzing (2a) as it is possible to immediately begin to integrate the noun phrases into a larger unit.

Nevertheless, center self-embedding of relative clauses can also be constructed in such a way that our brains can handle them.

Therefore, one does not wish to include in the description of our grammatical knowledge that relative clauses are not allowed to be included inside each other as in (2b) as this would also rule out (3).

We can easily accept the fact that our brains are not able to process structures past a certain degree of complexity and also that corresponding utterances then become unacceptable. The contrast in the following examples is far more fascinating:2

	- b. \* The patient who the nurse who the clinic had hired met Jack.

Although (4a) is syntactically well-formed and (4b) is not, Gibson & Thomas (1999) were able to show that (4b) is rated better by speakers than (4a). It does not occur to some people that an entire VP is missing. There are a number of explanations for this fact, all of which in some way make the claim that previously heard words are forgotten as soon as new words are heard and a particular degree of complexity is exceeded (Frazier 1985: 178; Gibson & Thomas 1999).

Instead of developing grammatical theories that treat (2b) and (4a) as unacceptable and (3) and (4b) as acceptable, descriptions have been developed that equally allow (2b),

2 See Gibson & Thomas (1999: 227). Frazier (1985: 178) attributes the discovery of this kind of sentences to Janet Fodor.

15.1 The derivational theory of complexity

(3), and (4a) (competence models) and then additionally investigate the way utterances are processed in order to find out what kinds of structures our brains can handle and what kinds of structures it cannot. The result of this research is then a performance model (see Gibson (1998), for example). This does not rule out that there are languagespecific differences affecting language processing. For example, Vasishth, Suckow, Lewis & Kern (2010) have shown that the effects that arise in center self-embedding structures in German are different from those that arise in the corresponding English cases such as (4): due to the frequent occurrence of verb-final structures in German, speakers of German were able to better store predictions about the anticipated verbs into their working memory (p. 558).

Theories in the framework of Categorial Grammar, GB, LFG, GPSG and HPSG are theories about our linguistic competence.3 If we want to develop a grammatical theory that directly reflects our cognitive abilities, then there should also be a corresponding performance model to go with a particular competence model. In the following two sections, I will recount some arguments from Sag & Wasow (2011) in favor of constraintbased theories such as GPSG, LFG and HPSG.

### **15.1 The derivational theory of complexity**

The first point discussed by Sag & Wasow (2011) is the Derivational Theory of Complexity. In the early days of Transformational Grammar, it was assumed that transformations were cognitively real, that is, it is possible to measure the consumption of resources that transformations have. A sentence that requires more transformations than the analysis of another sentence should therefore also be more difficult for humans to process. The corresponding theory was dubbed the *Derivational Theory of Complexity* (DTC) and initial experiments seemed to confirm it (Miller & McKean 1964; Savin & Perchonock 1965; Clifton & Odom 1966), so that in 1968 Chomsky still assumed that the Derivational

3 For an approach where the parser is equated with UG, see Abney & Cole (1986: Section 3.4). For a performance-oriented variant of Minimalism, see Phillips (2003).

In Construction Grammar, the question of whether a distinction between competence and performance would be justified at all is controversially discussed (see Section <IP_ADDRESS>.1). Fanselow, Schlesewsky, Cavar & Kliegl (1999) also suggest a model – albeit for different reasons – where grammatical properties considerably affect processing properties. The aforementioned authors work in the framework of Optimality Theory and show that the OT constraints that they assume can explain parsing preferences. OT is not a grammatical theory on its own but rather a meta theory. It is assumed that there is a component GEN that creates a set of candidates. A further component EVAL then chooses the most optimal candidate from this set of candidates. GEN contains a generative grammar of the kind that we have seen in this book. Normally, a GP/MP variant or also LFG is assumed as the base grammar. If one assumes a transformational theory, then one automatically has a problem with the Derivational Theory of Complexity that we will encounter in the following section. If one wishes to develop OT parsing models, then one has to make reference to representational variants of GB as the aforementioned authors seem to.

### 15 The competence/performance distinction

Theory of Complexity was in fact correct (Chomsky 1976a: 249–250).4 Some years later, however, most psycholinguists rejected the DTC. For discussion of several experiments that testify against the DTC, see Fodor, Bever & Garrett (1974: 320–328). One set of phenomena where the DTC makes incorrect predictions for respective analyses is that of elliptical constructions, for example (Fodor, Bever & Garrett 1974: 324): in elliptical constructions, particular parts of the utterance are left out or replaced by auxiliaries. In transformation-based approaches, it was assumed that (5b) is derived from (5a) by means of deletion of *swims* and (5c) is derived from (5b) by inserting *do*. 5

	- b. John swims faster than Bob.
	- c. John swims faster than Bob does.

The DTC predicts that (5b) should require more time to process than (5a), since the analysis of (5b) first requires to build up the structure in (5a) and then delete *swims*. This prediction was not confirmed.

Similarly, no difference could be identified for the pairs in (6) and (7) even though one of the sentences, given the relevant theoretical assumptions, requires more transformations for the derivation from a base structure (Fodor, Bever & Garrett 1974: 324).

	- b. John phoned the girl up.
	- b. The bus driver was fired after the wreck.

In (6), we are dealing with local reordering of the particle and the object. (7b) contains a passive clause that should be derived from an active clause under Transformational Grammar assumptions. If we compare this sentence with an equally long sentence with

4 In the Transformational Grammar literature, transformations were later viewed as a metaphor (Lohnstein 2014: 170, also in Chomsky 2001: Footnote 4), that is, it was no longer assumed to have psycholinguistic reality. In *Derivation by phase* and *On phases*, Chomsky refers once again to processing aspects such as computational and memory load (Chomsky 2001: 11, 12, 15; 2007: 3, 12; 2008: 138, 145, 146, 155). See also Marantz (2005: 440) and Richards (2015). Trinh (2011: 17) cites Chomsky (p.c.) with the following quote: "As speaking involves cognitive effort, Pronunciation Economy might be derived from the general principle of minimizing computation."

A structure building operation that begins with words and is followed by transformations/internal merge and further combinations, as recently assumed by theories in the Minimalist Program, is psycholinguistically implausible for sentence parsing. See Labelle (2007) and Section 15.2 for more on incremental processing.

Chomsky (2007: 6) (written later than *On phases*) seems to adopt a constraint-based view. He writes that "a Merge-based system involves parallel operations" and compares the analysis of an utterance with a proof and explicitly mentions the competence/performance distinction.

5 Similar analyses are assumed today in the Minimalist Program. For example, Trinh (2011: 63) assumes that VP ellipsis is deletion at Phonological Form (PF). This means that a complete structure is built which is then not pronounced. Since he talks about cognitive efforts and computation with respect to the activity of speaking (p. 17), it follows that he regards the structures he is assuming as congnitively real.

15.1 The derivational theory of complexity

an adjective, like (7a), the passive clause should be more difficult to process. This is, however, not the case.

It is necessary to add two qualifications to Sag & Wasow's claims: if one has experimental data that show that the DTC makes incorrect predictions for a particular analysis, this does not necessarily mean that the DTC has been disproved. One could also try to find a different analysis for the phenomenon in question. For example, instead of a transformation that deletes material, one could assume empty elements for the analysis of elliptical structures that are inserted directly into the structure without deleting any material (see page 68 for the assumption of an empty nominal head in structures with noun ellipsis in German). Data such as (5) would then be irrelevant to the discussion.6 However, reordering such as (6b) and the passive in (7b) are the kinds of phenomena that are typically explained using transformations.

The second qualification pertains to analyses for which there is a representational variant: it is often said that transformations are simply metaphors (Jackendoff 2000: 22–23; 2007: 5, 20): for example, we have seen that extractions with a transformational grammar yield structures that are similar to those assumed in HPSG. Figure 15.1 shows cyclic movement in GB theory compared to the corresponding HPSG analysis.

Figure 15.1: Cyclic movement vs. feature percolation

In GB, an element is moved to the specifier position of CP (SpecCP) and can then be moved from there to the next higher SpecCP position.

(8) a. Chris*i* , we think [CP \_*i* Anna claims [CP \_*i* that David saw \_*i* ]]. (GB) b. Chris*i* , we think [CP/NP Anna claims [CP/NP that David saw \_*i* ]]. (HPSG)

In HPSG, the same effect is achieved by structure sharing. Information about a longdistance dependency is not located in the specifier node but rather in the mother node

6Culicover & Jackendoff (2005: Chapters 1 and 7) argue in favor of analyzing ellipsis as a semantic or pragmatic phenomenon rather than a syntactic one anyway.

### 15 The competence/performance distinction

of the projection itself. In Section 19.2, I will discuss various ways of eliminating empty elements from grammars. If we apply these techniques to structures such as the GB structure in Figure 15.1, then we arrive at structures where information about missing elements is integrated into the mother node (CP) and the position in SpecCP is unfilled. This roughly corresponds to the HPSG structure in Figure 15.1. 7 It follows from this that there are classes of phenomena that can be spoken about in terms of transformations without expecting empirical differences with regard to performance when compared to transformation-less approaches. However, it is important to note that we are dealing with an S-structure in the left-hand tree in Figure 15.1. As soon as one assumes that this is derived by moving constituents out of other structures, this equivalence of approaches disappears.

### **15.2 Incremental processing**

The next important point mentioned by Sag & Wasow (2011) is the fact that both comprehension and production of language take places incrementally. As soon as we hear or read even the beginning of a word, we begin to assign meaning and to create structure. In the same way, we sometimes start talking before we have finished planning the entire utterance. This is shown by interruptions and self-correction in spontaneous speech (Clark & Wasow 1998; Clark & Fox Tree 2002). When it comes to processing spoken speech, Tanenhaus et al. (1996) have shown that we access a word as soon as we have heard a part of it (see also Marslen-Wilson 1975). The authors of the study carried out an experiment where participants were instructed to pick up particular objects on a grid and reorganize them. Using eye-tracking measurements, Tanenhaus and colleagues could then show that the participants could identify the object in question earlier if the sound sequence at the beginning of the word was unambiguous than in cases where the initial sounds occurred in multiple words. An example for this is a configuration with a candle and candy: *candy* and *candle* both begin with *can* such that speakers could not yet decide upon hearing this sequence which lexical entry should be accessed. Therefore, there was a slight delay in accessing the lexical entry when compared to words where the objects in question did not contain the same segment at the start of the word (Tanenhaus et al. 1995: 1633).

If complex noun phrases were used in the instructions (*Touch the starred yellow square*), the participants' gaze fell on the object in question 250ms after it was unambiguously identifiable. This means that if there was only a single object with stars on it, then they looked at it after they heard *starred*. In cases where there were starred yellow blocks as well as squares, they looked at the square only after they had processed the word *square* (Tanenhaus et al. 1995: 1632). The planning and execution of a gaze lasts 200ms. From this, one can conclude that hearers combine words directly and as soon as enough information is available, they create sufficient structure in order to capture the (potential) meaning of an expression and react accordingly. This finding is incompatible with models that assume that one must have heard a complete noun phrase or even a complete

7 In Figure 15.1, additionally the unary branching of C′ to CP was omitted in the tree on the right so that C combines directly with VP/NP to form CP/NP.

### 15.2 Incremental processing