A further difference between general X theory and Stabler's formalization of Internal Merge on the one hand and HPSG on the other is that in the latter case there is no restriction regarding the completeness (or valence 'saturation') of the filler daughter. Whether the filler daughter has to be a maximal projection (English) or not (German),

36See Bouma, Malouf & Sag (2001) for a traceless analysis of extraction in HPSG and Müller (2023a: Chapter 7) and Chapter 19 of this book for a general discussion of empty elements.

follows from restrictions that are enforced locally when the trace is combined with its head. This makes it possible to analyze sentences like (55) without remnant movement.37

(55) Gelesen read hat has das the Buch book keiner nobody \_ \_ .

In contrast, Stabler is forced to assume an analysis like the one in (56b) (see also G. Müller (1998) for a remnant movement analysis). In a first step, *das Buch* is moved out of the VP (56a) and in a second step, the emptied VP is fronted as in (56b).

(56) a. Hat [das Buch] [keiner [VP \_ gelesen]]. b. [VP \_ Gelesen] hat [das Buch] [keiner \_ ].

Haider (1993: 281), De Kuthy & Meurers (2001: Section 2) and Fanselow (2002) showed that this kind of remnant movement analysis is problematic for German. The only phenomenon that Fanselow identified as requiring a remnant movement analysis is the problem of multiple fronting (see Müller (2003a) for an extensive discussion of relevant data). Müller (2005b,c, 2023a) develops an alternative analysis of these multiple frontings which uses an empty verbal head in the *Vorfeld*, but does not assume that adjuncts or arguments like *das Buch* in (56b) are extracted from the *Vorfeld* constituent. Instead of the remnant movement analysis, the mechanism of argument composition from Categorial Grammar (Geach 1970, Hinrichs & Nakazawa 1994a) is used to ensure the proper realization of arguments in the sentence. Chomsky (2007: 20) already uses argument composition as part of his analysis of TPs and CPs. Hence both remnant movement and argument composition are assumed in recent Minimalist proposals. The HPSG alternative, however, would appear to need less theoretical apparatus and hence has to be preferred for reasons of parsimony.

Finally, it should be mentioned that all transformational accounts have problems with Across the Board extraction like (57a) and (57b) in which one element corresponds to several gaps.

	- b. The man who [Mary loves \_ ] and [Sally hates \_ ] computed my tax.

This problem was solved for GPSG by Gazdar (1981b) and the solution carries over to HPSG. The Minimalist community tried to address these problems by introducing operations like sideward movement (Nunes 2004) where constituents can be inserted into sister trees. So in the example in (57a), *bagels* is copied from the object position of *hates* into the object position of *like* and then these two copies are related to the fronted element. Kobele criticized such solutions since they overgenerate massively and need

37See also Müller & Ørsnes (2013b) for an analysis of object shift in Danish that can account for verb fronting without remnant movement. The analysis does not have any of the problems that remnant movement analyses have.

38Pollard & Sag (1994: 205).

complicated filters. What he suggests instead is the introduction of a GPSG-style slash mechanism into Minimalist theories (Kobele 2008).

Furthermore, movement paradoxes (Bresnan 2001: Chapter 2) can be avoided by not sharing all information between filler and gap, a solution that is not available for transformational accounts, which usually assume identity of filler and gap or – as under the Copy Theory of Movement – assume that a derivation contains multiple copies of one object only one of which is spelled out. See also Borsley (2012) for further puzzles for, and problems of, movement-based approaches.

A further difference between MG and HPSG is that the Head-Filler Schema is not the only schema for analyzing long-distance dependencies. As was noted in footnote 12 on page 148, there is dislocation to the right (extraposition) as well as fronting. Although these should certainly be analyzed as long-distance dependencies, they differ from other long-distance dependencies in various respects (see Section 13.1.5). For analyses of extraposition in the HPSG framework, see Keller (1995), Bouma (1996), and Müller (1999b).

Apart from the schema for long-distance dependencies, there are, of course, other schemata in HPSG which are not present in MG or Minimalism. These are schemata which describe constructions without heads or are necessary to capture the distributional properties of parts of constructions, which cannot be easily captured in lexical analyses (e.g., the distribution of *wh*- and relative pronouns). See Section 21.10.

Chomsky (2010) has compared a Merge-based analysis of auxiliary inversion to a HPSG analysis and critiqued that the HPSG analysis uses ten schemata rather than one (Merge). Ginzburg & Sag (2000) distinguish three types of constructions with moved auxiliaries: inverted sentences such as those with fronted adverbial and with *wh*-questions (58a,b), inverted exclamatives (58c) and polar interrogatives (58d):

	- b. Whose book *are you reading*?
	- c. Am I tired!
	- d. Did Kim leave?

Fillmore (1999) captures various different usage contexts in his Construction Grammar analysis of auxiliary inversion and shows that there are semantic and pragmatic differences between the various contexts. Every theory must be able to account for these. Furthermore, one does not necessarily require ten schemata. It is possible to determine this – as Categorial Grammar does – in the lexical entry for the auxiliary or on an empty head (see Chapter 21 for a more general discussion of lexical and phrasal analyses). Regardless of this, every theory has to somehow account for these ten differences. If one wishes to argue that this has nothing to do with syntax, then somehow this has to be modeled in the semantic component. This means that there is no reason to prefer one theory over another at this point.

### **4.6.5 Selection of atomic features vs. selection of complex categories**

Berwick & Epstein (1995) pointed out that Minimalist theories are very similar to Categorial Grammar and I have discussed the similarities between Minimalist theories and

HPSG in Müller (2013c) and in the previous subsections. However, I overlooked one crucial difference between the usual assumptions about selection in Minimalist proposals on the one hand and Categorial Grammar, Dependency Grammar, LFG, HPSG, TAG, and Construction Grammar on the other hand: what is selected in the former type of theory is a single feature, while the latter theories select for feature bundles. This seems to be a small difference, but the consequences are rather severe. Stabler's definition of External Merge that was given on page 165 removes the selection feature (=f) and the corresponding feature of the selected element (f). In some publications and in the introduction in this book, the selection features are called uninterpretable features and are marked with a *u*. The uninterpretable features have to be checked and then they are removed from the linguistic object as in Stabler's definition. The fact that they have been checked is represented by striking them out. It is said that all uninterpretable features have to be checked before a syntactic object is sent to the interfaces (semantics and pronunciation). If uninterpretable features are not checked, the derivation crashes. Adger (2003: Section 3.6) explicitly discusses the consequences of these assumptions: a selecting head checks a feature of the selected object. It is not possible to check features of elements that are contained in the object that a head combines with. Only features at the topmost node, the so-called root node, can be checked with external merge. The only way features inside complex objects can be checked is by means of movement. This means that a head may not combine with a partially saturated linguistic object, that is, with a linguistic object that has an unchecked selection feature. I will discuss this design decision with reference to an example provided by Adger (2003: 95). The noun *letters* selects for a P and Ps select for an N. The analysis of (59a) is depicted left in Figure 4.23.

	- b. \* letters to

Figure 4.23: The analysis of *letters to Peter* according to Adger (2003: 95)

The string in (59b) is ruled out since the uninterpretable N feature of the preposition *to* is not checked. So this integrates the constraint that all dependent elements have to be maximal into the core mechanism. This makes it impossible to analyze examples like (60) in the most straightforward way, namely as involving a complex preposition and a noun that is lacking a determiner:

(60) vom from.the Bus bus

In theories in which complex descriptions can be used to describe dependants, the dependent may be partly saturated. So, for instance, in HPSG, fused prepositions like *vom* 'from.the' can select an N, which is a nominal projection lacking a specifier:

### (61) N[spr ⟨ Det ⟩]

The description in (61) is an abbreviation for an internally structured set of feature-value pairs (see Section 9.1.1). The example here is given for the illustration of the differences only, since there may be ways of accounting for such cases in a single-feature-Merge system. For instance, one could assume a DP analysis and have the complex preposition select a complete NP (something of category N with no uninterpretable features). Alternatively, one can assume that there is indeed a full PP with all the structure that is usually assumed and the fusion of preposition and determiner happens during pronunciation. The first suggestion eliminates the option of assuming an NP analysis as it was suggested by Bruening (2009) in the Minimalist framework.

Apart from this illustrative example with a fused preposition, there are other cases in which one may want to combine unsaturated linguistic objects. I already discussed coordination examples above. Another example is the verbal complex in languages like German, Dutch, and Japanese. Of course there are analyses of these languages that do not assume a verbal complex (G. Müller 1998, Wurmbrand 2003a), but these are not without problems. Some of the problems were discussed in the previous section as well.

Summing up this brief subsection, it has to be said that the feature checking mechanism that is built into the conception of Merge is more restrictive than the selection that is used in Categorial Grammar, Lexical Functional Grammar, HPSG, Construction Grammar, and TAG. In my opinion, it is too restrictive.

### **4.6.6 Summary**

In sum, one can say that the computational mechanisms of the Minimalist Program (e.g., transderivational constraints and labeling) as well as the theory of feature-driven movement are problematic and the assumption of empty functional categories is sometimes ad hoc. If one does not wish to assume that these categories are shared by all languages, then proposing two mechanisms (Merge and Move) does not represent a simplification of grammar since every single functional category which must be stipulated constitutes a complication of the entire system.

The labeling mechanism is not yet worked out in detail, does not account for the phenomena it was claimed to provide accounts for, and hence should be replaced by the head/functor-based labeling that is used in Categorial Grammar and HPSG.

# **4.7 Summary and classification**

This section is similar to Section 3.6. I first comment on language acquisition and then on formalization.

### **4.7.1 Explaining language acquisition**

Chomsky (2008: 135) counts theories in the MP as Principle & Parameter analyses and identifies MP parameters as being in the lexicon. Also, see Hornstein (2013: 396). UG is defined as possibly containing non-language-specific components, which are genetically determined (Chomsky 2007: 7). UG consists of unbounded Merge and the condition that expressions derived by a grammar must fulfill the restrictions imposed by the phonological and conceptual-intentional interfaces. In addition, a specific repertoire of features is assumed to be part of UG (Chomsky 2007: 6–7). The exact nature of these features has not been explained in detail and, as a result, the power of UG is somewhat vague. However, there is a fortunate convergence between various linguistic camps as Chomsky does not assume that the swathes of functional projections which we encountered in Section 4.6.1 also form part of UG (however, authors like Cinque & Rizzi (2010) do assume that a hierarchy of functional projections is part of UG). Since there are still parameters, the same arguments used against GB approaches to language acquisition that were mentioned in Section 3.6.1 are still relevant for theories of language acquisition in the Minimalist Program. See Chapter 16 for an in-depth discussion of approaches to language acquisition and the Principles & Parameters model as well as input-based approaches.

Chomsky's main goal in the Minimalist Program is to simplify the theoretical assumptions regarding formal properties of language and the computational mechanisms that are used so much as to make it plausible that they or relevant parts of them are part of our genetic endowment. But if we recapitulate what was assumed in this chapter, it is difficult to believe that Minimalist theories achieve this goal. To derive a simple sentence with an intransitive verb, one needs several empty heads and movements. Features can be strong or weak, Agree operates nonlocally in trees across several phrase boundaries. And in order to make correct predictions, it has to be made sure that Agree can only see the closest possible element (13)–(14). This is a huge machinery in comparison to a Categorial Grammar that just combines adjacent things. Categorial Grammars can be acquired from input (see Section 13.8.3), while it is really hard to imagine how the fact that there are features that trigger movement when they are strong, but do not trigger it when they are weak, should be acquired from data alone.

### **4.7.2 Formalization**

Section 3.6.2 commented on the lack of formalization in transformational grammar up until the 1990s. The general attitude towards formalization did not change in the minimalist era and hence there are very few formalizations and implementations of Minimalist theories.

Stabler (2001) shows how it is possible to formalize and implement Kayne's theory of remnant movement. In Stabler's implementation39, there are no transderivational con-

39His system is available at: http://linguistics.ucla.edu/people/stabler/coding.html. 2020-07-16.

straints, no numerations40, he does not assume Agree (see Fong 2014: 132) etc. The following is also true of Stabler's implementation of Minimalist Grammars and GB systems: there are no large grammars. Stabler's grammars are small, meant as a proof of concept and purely syntactic. There is no morphology41, no treatment of multiple agreement (Stabler 2011b: Section 27.4.3) and above all no semantics. PF and LF processes are not modeled.42 The grammars and the computational system developed by Sandiway Fong are of similar size and faithfulness to the theory (Fong & Ginsburg 2012, Fong 2014): the grammar fragments are small, encode syntactic aspects such as labeling directly in the phrase structure (Fong & Ginsburg 2012: Section 4) and, therefore, fall behind X theory. Furthermore, they do not contain any morphology. Spell-Out is not implemented, so in the end it is not possible to parse or generate any utterances.43 Herring's (2016) dissertation is a promising beginning. Herring developed a system that can be used for grammar

'The man who claimed Maria laughed is standing next to the palm tree that was planted last year.'

41The test sentences have the form as in (i).

	- b. the king have -s eat -en
	- c. the king be -s eat -ing
	- d. the king -s will -s have been eat -ing the pie

42See Sauerland & Elbourne (2002) for suggestions of PF and LF-movement and the deletion of parts of copies (p. 285). The implementation of this would be far from trivial.

43The claim by Berwick, Pietroski, Yankama & Chomsky (2011: 1221) in reference to Fong's work is just plain wrong: *But since we have sometimes adverted to computational considerations, as with the ability to "check" features of a head/label, this raises a legitimate concern about whether our framework is computationally realizable. So it is worth noting that the copy conception of movement, along with the locally oriented "search and labeling" procedure described above, can be implemented computationally as an efficient parser; see Fong, 2011, for details.* If one has a piece of software which cannot parse a single sentence, then one cannot claim that it is efficient since one does not know whether the missing parts of the program could make it extremely inefficient. Furthermore, one cannot compare the software to other programs. As has already been discussed, labeling is not carried out by Fong as was described in Chomsky's work, but instead he uses a phrase structure grammar of the kind described in Chapter 2.

40There is a numeration lexicon in Veenstra (1998: Chapter 9). This lexicon consists of a set of numerations, which contain functional heads, which can be used in sentences of a certain kind. For example, Veenstra assumes numerations for sentences with bivalent verbs and subjects in initial position, for embeded sentences with monovalent verbs, for *wh*-questions with monovalent verbs, and for polar interrogatives with monovalent verbs. An element from this set of numerations corresponds to a particular configuration and a phrasal construction in the spirit of Construction Grammar. Veenstra's analysis is not a formalization of the concept of the numeration that one finds in Minimalist works. Normally, it is assumed that a numeration contains all the lexical entries which are needed for the derivation of a sentence. As (i) shows, complex sentences can consist of combinations of sentences with various different sentence types:

(i) Der the Mann, man der who behauptet claimed hat, has dass that Maria Maria gelacht laughed hat, has steht stands neben next.to der the Palme, palm.tree die which im in.the letzten last Jahr year gepflanzt planted wurde. aux

In (i), there are two relative clauses with verbs of differing valence, an embedded sentence with a monovalent verb and the matrix clause. Under a traditional understanding of numerations, Veenstra would have to assume an infinite numeration lexicon containing all possible combinations of sentence types.

development in the Minimalist Program. In the version described in his thesis the system could generate but was unable to parse sentences (p. 138, 143). PF phenomena were not modeled (p. 142–143) and the two example fragments are small and come without a semantics (p. 143).

The benchmark here has been set by implementations of grammars in constraintbased theories; for example, the HPSG grammars of German (Müller & Kasper 2000), English (Flickinger, Copestake & Sag 2000) and Japanese (Siegel 2000) that were developed in the 90s as part of Verb*mobil* (Wahlster 2000) for the analysis of spoken language or the LFG or CCG systems with large coverage. These grammars can analyze up to 83 % of utterances in spoken language (for Verb*mobil* from the domains of appointment scheduling and trip planning) or written language. Linguistic knowledge is used to generate and analyze linguistic structures. In one direction, one arrives at a semantic representation of a string of words and in the other one can create a string of words from a given semantic representation. A morphological analysis is indispensable for analyzing naturally occurring data from languages with elaborated morphological marking systems. In the remainder of this book, the grammars and computational systems developed in other theories will be discussed at the beginning of the respective chapters.

The reason for the lack of larger fragments inside of GB/MP could have to do with the fact that the basic assumptions of the Minimalist community change relatively quickly:

In Minimalism, the triggering head is often called a *probe*, the moving element is called a *goal*, and there are various proposals about the relations among the features that trigger syntactic effects. Chomsky (1995b: p. 229) begins with the assumption that features represent requirements which are checked and deleted when the requirement is met. The first assumption is modified almost immediately so that only a proper subset of the features, namely the 'formal', 'uninterpretable' features are deleted by checking operations in a successful derivation (Collins 1997; Chomsky 1995b: §4.5). Another idea is that certain features, in particular the features of certain functional categories, may be initially unvalued, becoming valued by entering into appropriate structural configurations with other elements (Chomsky 2008; Hiraiwa 2005). And some recent work adopts the view that features are never deleted (Chomsky 2007: p. 11). These issues remain unsolved. (Stabler 2011a: 397)

In order to fully develop a grammar fragment, one needs at least three years (compare the time span between the publication of *Barriers* (1986) and Stabler's implementation (1992)). Particularly large grammars require the knowledge of several researchers working in international cooperation over the space of years or even decades. This process is disrupted if fundamental assumptions are repeatedly changed at short intervals.

As far as large-scale coverage is concerned, the more recent work by John Torr is an exception to what was said above.44 Torr, Stanojevic, Steedman & Cohen (2019) state that their parser is the first one to take up the Sproat & Lappin Challenge to the Minimalist community (2005). The work of the authors is impressive and they really implemented

44It is not an exception as far as theory development is concerned. Torr's system is based on Chomsky (1995b), so he did not follow new trends but stayed within a certain setting.

a wide-coverage statistically trained parser based on Transformational Grammar, but what they did is different from standard Minimalism since they assume "around 45" versions of Move and Merge (p. 2488) in comparison to the two versions usually assumed in Minimalism (Move and Merge or Internal and External Merge).45 Torr & Stabler (2016) explain some of the schemata that are assumed: there are versions of Merge that combine a head with a complement and versions that combine a head with a specifier (see Müller (2013c) and Section <IP_ADDRESS> above for a comparison of Minimalist Grammars with HPSG. The respective variants of Merge correspond to HPSG's Specifier-Head Schema and the Head-Complement Schema, respectively). Torr & Stabler (2016: 4) assume four schemata for adjunction (HPSG has one such schema and use underspecification with respect to order, see Müller (2021a: Section 2)). They assume a special rule for rightward movement (p. 5) corresponding to Keller's (1995) and Müller's (1999b) Head-Extra Schema for extraposition. In addition the authors assume two schemata for head movement. HPSG assumes a lexical rule or a unary branching schema applying to words or coordinations of words (Müller 2023a, 2021a: Section 5.1)). Across the Board extraction (Ross 1967: Section <IP_ADDRESS>) is taken care of by four special schemata. See Abeillé & Chaves (2021) for an overview of treatments of coordination in HPSG. The treatment of Across the Board Extraction is non-standard Minimalism. For the analysis of examples like (62) in which one filler corresponds to two gaps in two conjuncts, the authors build on Kobele (2008) who uses a slash passing mechanism going back to Sag (1983) and Gazdar (1981b). While Kobele assumes the slash passing mechanism of GPSG, Torr & Stabler (2016) suggest an analyis of (62) with two instances of *who* in object positions, which are later unified into one when the second conjunct is merged into the main structure.

(62) Who did Jack say Mary likes \_ and Pete hates \_ ?

An interesting property of the analysis is that *who Pete hates* forms a discontinuous constituent: *who* is combined with *hates* despite its sentence-initial position. Information about this *wh*-element is passed up the tree in a GPSG-style way. The difference is that there is no trace, but the extracted element is identical in phonological material with the filler. Interestingly, there is an HPSG variant of nonlocal dependencies that is very similar to what Torr & Stabler (2016) suggest and together with a modified Filler-Head Schema the analyses are parallel: Hinrichs & Nakazawa (1994b) suggested that the linguistic objects that are involved in nonlocal dependencies are of type *sign* rather than *local*. This makes it possible to pass up information about a daughter including its phonological make up. If one assumes a version of HPSG permitting discontinuous constituents (Reape 1994, Kathol 2001, Müller 1995, 2004d and Section <IP_ADDRESS> of this book) and a Filler-Head Schema that requires that the phonology of the filler is identical to the phonology in the slash list and that does not insert the fronted element into the constituent order domain of the head (since it is in there already), we get an analysis of the type described in Torr & Stabler (2016). Figure 4.24 shows the analysis that was suggested by Torr &

45Torr explained in p.c. 2019 that these 45 rules can be folded into two Merge functions and two Move functions. But in the end this is just a clever way of hiding complexity. It is like Chomsky (2005: 12) revising the theory with Move and Merge into one with just one operation Merge but assuming two subcases of Internal and External Merge.

Stabler (2016) and Figure 4.25 the HPSG analog. Directional Minimalist Grammars use

### Figure 4.24: Derivation tree of *who Jack likes* in Directional Minimalist Grammar according to Torr & Stabler (2016)

the '=' sign to indicate the direction in which an argument is required. =d means that a DP is required to the left of a head and d= encodes the requirement of a DP to the right. This is like the '/' notation of Categorial Grammar (see Chapter 8). *likes* has the category d= =d v, which means that it is a verb requiring a d to its right (the object) and a d to its left (the subject). *who* is of category d and has a −wh feature, something that has to be checked for a derivation to be complete. *Jack* is the subject of *likes* and fulfills the =d requirement of *likes*. Items like [pres] and [int] are empty elements. [pres] has a +case feature and can make *Jack* move to its specifier. The movement consumes the −case feature and puts *Jack* to the front of the string. This looks like a unary projection in the derivation tree. The empty interrogative head [int] selects for a t to its right. The result is a C projection that has a +wh feature. In the final step *who*, which is −wh, moves to the left and the wh features are removed. The important thing is that the information about the phonology of *who* and its wh feature is percolated up in the tree until it is finally bound off in the last derivation step.

Figure 4.25 shows the HPSG analog. The information about the local properties of the *wh* word including its phonology are passed up in the tree until they are bound off in a filler-head configuration. The Filler-Head Schema binds off the nonlocal dependency and makes sure that the phonology of the filler is not realized twice (see Reape 1994, Müller 2021a: Section 6 on linearization domains and Abeillé & Chaves 2021: Section 7 on multi-dominance approaches in HPSG). An alternative to a binary branching Filler-Head Schema would be a unary branching rule that binds off the element in slash and adds

the stored phonology to the phonology of the daughter. This would then be completely parallel to the unary branching assumed in Torr's Directional Minimalist Grammar.

Concluding the discussion of Torr's work, it can be said that it is truly impressive but that it shows a convergence between Minimalism (or rather Minimalist Grammar) and HPSG. Tools from GPSG/HPSG were adopted and the outcome differs in crucial aspects from what is taught in Minimalist textbooks (just one or two instances of Merge vs. 45, transformations vs. GPSG-style percolation of features).

### **Further reading**

This chapter heavily draws on Adger (2003). Other textbooks on Minimalism are Radford (1997), Grewendorf (2002), and Hornstein, Nunes & Grohmann (2005).

Kuhn (2007) offers a comparison of modern derivational analyses with constraint-based LFG and HPSG approaches. Borsley (2012) contrasts analyses of long-distance dependencies in HPSG with movement-based analyses as in GB/ Minimalism. Borsley discusses four types of data which are problematic for movement-based approaches: extraction without fillers, extraction with multiple gaps, extractions where fillers and gaps do not match and extraction without gaps. Borsley & Müller (2021) is another comparison of Minimalism and HPSG. The authors discuss differences of approach and outlook of the two frameworks (formalization and exhaustivity), empirical quality of the work, differences in assumed syntactic structures, psycholinguistic issues and the assumptions made in the frameworks regarding language acquisition.

The discussion of labeling, abandonment of X theory and a comparison be-

tween Stabler's Minimalist Grammars and HPSG from Sections 4.6.2–4.6.4 can be found in Müller (2013c).

*Intonational Phrasing, Discontinuity, and the Scope of Negation* by Błaszczak & Gärtner (2005) is recommended for the more advanced reader. The authors compare analyses of negated quantifiers with wide scope in the framework of Minimalism (following Kayne) as well as Categorial Grammar (following Steedman).

Sternefeld (2006) is a good, detailed introduction to syntax (839 pages) which develops a Transformational Grammar analysis of German which (modulo transformations) almost matches what is assumed in HPSG (feature descriptions for arguments ordered in a valence list according to a hierarchy). Sternefeld's structures are minimal since he does not assume any functional projections if they cannot be motivated for the language under discussion. Sternefeld is critical regarding certain aspects which some other analyses take for granted. Sternefeld views his book explicitly as a textbook from which one can learn how to argue coherently when creating theories. For this reason, this book is not just recommended for students and PhD students.

Sternefeld & Richter (2012) discuss the situation in theoretical linguistics with particular focus on the theories described in this and the previous chapter. I can certainly understand the frustration of the authors with regard to the vagueness of analyses, argumentation style, empirical base of research, rhetorical clichés, immunization attempts and general respect for scientific standards: a recent example of this is the article *Problems of Projection* by Chomsky (2013).*a* I, however, do not share the general, pessimistic tone of this article. In my opinion, the patient's condition is critical, but he is not dead yet. As a reviewer of the Sternefeld and Richter paper pointed out, the situation in linguistics has changed so much that now having a dissertation from MIT does not necessarily guarantee you a position (footnote 16) later on. One could view a reorientation of certain scientists with regard to certain empirical questions, adequate handling of data (Fanselow 2004b; 2009: 137) and improved communication between theoretical camps as a way out of this crisis.

Since the 90s, it is possible to identify an increased empirical focus (especially in Germany), which manifests itself, for example, in the work of linguistic Collaborative Research Centers (SFBs) or the yearly *Linguistic Evidence* conference. As noted by the reviewer cited above, in the future, it will not be enough to focus on Chomsky's problems in determining the syntactic categories in sentences such as *He left* (see Section 4.6.2). Linguistic dissertations will have to have an empirical section, which shows that the author actually understands something about language. Furthermore, dissertations, and of course other publications, should give an indication that the author has not just considered theories from a particular framework but is also aware of the broad range of relevant descriptive and theoretical literature.

As I have shown in Section 4.6.4 and in Müller (2013c) and will also show in the following chapters and the discussion chapters in particular, there are most certainly similarities between the various analyses on the market and they do converge in certain respects. The way of getting out of the current crisis lies with the empirically-grounded and theoretically broad education and training of following generations.

In short, both teachers and students should read the medical record by Sternefeld and Richter. I implore the students not to abandon their studies straight after reading it, but rather to postpone this decision at least until after they have read the remaining chapters of this book.

*a*Vagueness: in this article, *perhaps* occurs 19 times, *may* 17 as well as various *if* s. Consistency: the assumptions made are inconsistent. See footnote 18 on page 156 of this book. Argumentation style: the term specifier is abolished and it is claimed that the problems associated with this term can no longer be formulated. Therefore, they are now not of this world. See footnote 28 on page 161 of this book. Immunization: Chomsky writes the following regarding the Empty Category Principle: *apparent exceptions do not call for abandoning the generalization as far as it reaches, but for seeking deeper reasons to explain where and why it holds* (p. 9). This claim is most certainly correct, but one wonders how much evidence one needs in a specific case in order to disregard a given analysis. In particular regarding the essay *Problems of Projection*, one has to wonder why this essay was even published only five years after *On phases*. The evidence against the original approach is overwhelming and several points are taken up by Chomsky (2013) himself. If Chomsky were to apply his own standards (for a quote of his from 1957, see page 6) as well as general scientific methods (Occam's Razor), the consequence would surely be a return to head-based analyses of labeling.

For detailed comments on this essay, see Sections 4.6.2 and 4.6.3.

# **5 Generalized Phrase Structure Grammar**

Generalized Phrase Structure Grammar (GPSG) was developed as an answer to Transformational Grammar at the end of the 1970s. The book by Gazdar, Klein, Pullum & Sag (1985) is the main publication in this framework. Hans Uszkoreit has developed a largish GPSG fragment for German (1987). Analyses in GPSG were so precise that it was possible to use them as the basis for computational implementations. The following is a possibly incomplete list of languages with implemented GPSG fragments:

As was discussed in Section 3.1.1, Chomsky (1957) argued that simple phrase structure grammars are not well-suited to describe relations between linguistic structures and claimed that one needs transformations to explain them. These assumptions remained unchallenged for two decades (with the exception of publications by Harman (1963) and Freidin (1975)) until alternative theories such as LFG and GPSG emerged, which addressed Chomsky's criticisms and developed non-transformational explanations of phenomena for which there were previously only transformational analyses or simply none at all. The analysis of local reordering of arguments, passives and long-distance dependencies are some of the most important phenomena that have been discussed in this framework. Following some introductory remarks on the representational format of GPSG in Section 5.1, I will present the GPSG analyses of these phenomena in some more detail.

# **5.1 General remarks on the representational format**

This section has five parts. The general assumptions regarding features and the representation of complex categories is explained in Section 5.1.1, the assumptions regarding the linearization of daughters in a phrase structure rule is explained in Section 5.1.2. Section 5.1.3 introduces metarules, Section 5.1.4 deals with semantics, and Section 5.1.5 with adjuncts.

## **5.1.1 Complex categories, the Head Feature Convention, and X rules**

In Section 2.2, we augmented our phrase structure grammars with features. GPSG goes one step further and describes categories as sets of feature-value pairs. The category in (1a) can be represented as in (1b):

	- b. { cat n, bar 2, per 3, num sg, case nom }

It is clear that (1b) corresponds to (1a). (1a) differs from (1b) with regard to the fact that the information about part of speech and the X level (in the symbol NP) are prominent, whereas in (1b) these are treated just like the information about case, number or person.

Lexical entries have a feature subcat. The value is a number which says something about the kind of grammatical rules in which the word can be used. (2) shows examples for grammatical rules and lists some verbs which can occur in these rules.1

These rules license VPs, that is, the combination of a verb with its complements, but not with its subject. The numbers following the category symbols (V or N) indicate the X projection level. For Uszkoreit, the maximum number of projections of a verbal projection is three rather than two as is often assumed.

The H on the right side of the rule stands for *head*. The *Head Feature Convention* (HFC) ensures that certain features of the mother node are also present on the node marked with H (for details see Gazdar, Klein, Pullum & Sag 1985: Section 5.4 and Uszkoreit 1987: 67):

### **Principle 1 (Head Feature Convention)**

The mother node and the head daughter must bear the same head features unless indicated otherwise.

In (2), examples for verbs which can be used in the rules are given in brackets. As with ordinary phrase structure grammars, one also requires corresponding lexical entries for verbs in GPSG. Two examples are provided in (3):

(3) V[5, vform *inf* ] → einzuschlafen V[6, vform *inf* ] → aufzuessen

The first rule states that *einzuschlafen* 'to fall asleep' has a subcat value of 5 and the second indicates that *aufzuessen* 'to finish eating' has a subcat value of 6. It follows, then, that *einzuschlafen* can only be used in the first rule (2) and *aufzuessen* can only be

1 The analyses discussed in the following are taken from Uszkoreit (1987).

used in the second. Furthermore, (3) contains information about the form of the verb (*inf* stands for infinitives with *zu* 'to').

If we analyze the sentence in (4) with the second rule in (2) and the second rule in (3), then we arrive at the structure in Figure 5.1.

(4) Karl Karl hat has versucht, tried [den the Kuchen cake aufzuessen]. to.eat.up 'Karl tried to finish eating the cake.'

Figure 5.1: Projection of head features in GPSG

The rules in (2) say nothing about the order of the daughters which is why the verb (H[6]) can also be in final position. This aspect will be discussed in more detail in Section 5.1.2. With regard to the HFC, it is important to bear in mind that information about the infinitive verb form is also present on the mother node. Unlike simple phrase structure rules such as those discussed in Chapter 2, this follows automatically from the Head Feature Convention in GPSG. In (3), the value of vform is given and the HFC ensures that the corresponding information is represented on the mother node when the rules in (2) are applied. For the phrase in (4), we arrive at the category V2[vform *inf* ] and this ensures that this phrase only occurs in the contexts it is supposed to:

	- b. \* [Den the Kuchen cake aufzuessen] to.eat.up darf is.allowed.to er he nicht. not Intended: 'He is not allowed to finish eating the cake.'
	- c. \* [Den the Kuchen cake aufessen] eat.up hat has er he nicht not gewagt. dared Intended: 'He did not dare to finish eating the cake.'
	- d. [Den the Kuchen cake aufessen] eat.up darf is.allowed.to er he nicht. not 'He is not allowed to finish eating the cake.'

*gewagt* 'dared' selects for a verb or verb phrase with an infinitive with *zu* 'to' but not a bare infinitive, while *darf* 'is allowed to' takes a bare infinitive.

This works in an analogous way for noun phrases: there are rules for nouns which do not take an argument as well as for nouns with certain arguments. Examples of rules for nouns which either require no argument or two PPs are given in (6) (Gazdar, Klein, Pullum & Sag 1985: 127):

The rule for the combination of N and a determiner is as follows:

$$(7)\quad \text{N2} \to \text{Det}, \text{H1}$$

N2 stands for NP, that is, for a projection of a noun phrase on bar level two, whereas H1 stands for a projection of the head daughter on the bar level one. The Head Feature Convention ensures that the head daughter is also a nominal projection, since all features on the head daughter apart from the X level are identified with those of the whole NP. When analyzing (8), the second rule in (6) licenses the N *Gesprächs mit Maria über Klaus*. The fact that *Gesprächs* 'conversation' is in the genitive is represented in the lexical item of *Gesprächs* and since *Gesprächs* is the head, it is also present at N, following the Head Feature Convention.

(8) des the.gen Gespräch-s conversation-gen mit with Maria Maria über about Klaus Klaus 'the conversation with Maria about Klaus'

For the combination of N with the determiner, we apply the rule in (7). The category of the head determines the word class of the element on the left-hand side of the rule, which is why the rule in (7) corresponds to the classical X rules that we encountered in (65c) on page 74. Since *Gesprächs mit Maria über Klaus* is the head daughter, the information about the genitive of N is also present at the NP node.

## **5.1.2 Local reordering**

The first phenomenon to be discussed is local reordering of arguments. As was already discussed in Section 3.5, arguments in the middle field can occur in an almost arbitrary order. (9) gives some examples:

	- b. [weil] because der the Mann man das the Buch book dem the Kind child gibt gives
	- c. [weil] because das the Buch book der the Mann man dem the Kind child gibt gives

In the phrase structure grammars in Chapter 2, we used features to ensure that verbs occur with the correct number of arguments. The following rule in (10) was used for the sentence in (9a):

(10) S → NP[nom] NP[dat] NP[acc] V\_nom\_dat\_acc

If one wishes to analyze the other orders in (9), then one requires an additional five rules, that is, six in total:

$$\begin{array}{ll} \text{(11)} \quad \text{S} \rightarrow \text{NP[nom] NP[data]} & \text{NP[acc]} \quad \text{V\\_nom\\_data\\_acc} \\ \text{S} \rightarrow \text{NP[nom] NP[acc]} & \text{NP[data]} \quad \text{V\\_nom\\_data\\_acc} \\ \text{S} \rightarrow \text{NP[acc]} & \text{NP[nom] NP[data]} \quad \text{V\\_nom\\_data\\_acc} \\ \text{S} \rightarrow \text{NP[acc]} & \text{NP[nom] NP[acc]} \quad \text{V\\_nom\\_data\\_acc} \\ \text{S} \rightarrow \text{NP[data]} & \text{NP[acc]} \quad \text{NP[nom]} \text{ V\\_nom\\_data\\_acc} \\ \end{array}$$

In addition, it is necessary to postulate another six rules for the orders with verb-initial order:

(12)  $\mathcal{S} \to \mathcal{V}\_{\rm non\\_data\\_acc\NP[nom] NP[data]}$   $\text{NP[acc]}$   $\mathcal{S} \to \mathcal{V}\_{\rm non\\_data\\_acc\NP[nom] NP[acc]}$   $\text{NP[data]}$   $\mathcal{S} \to \mathcal{V}\_{\rm non\\_data\\_acc\NP[acc]}$   $\text{NP[nom] NP[data]}$   $\mathcal{S} \to \mathcal{V}\_{\rm non\\_data\\_acc\NP[acc]}$   $\text{NP[data]}$   $\text{NP[nom]}$   $\mathcal{S} \to \mathcal{V}\_{\rm non\\_data\\_acc\NP[data]}$   $\text{NP[acc]}$   $\text{NP[nom]}$

Furthermore, one would also need parallel rules for transitive and intransitive verbs with all possible valences. Obviously, the commonalities of these rules and the generalizations regarding them are not captured. The point is that we have the same number of arguments, they can be realized in any order and the verb can be placed in initial or final position. As linguists, we find it desirable to capture this property of the German language and represent it beyond phrase structure rules. In Transformational Grammar, the relationship between the orders is captured by means of movement: the deep structure corresponds to verb-final order with a certain order of arguments and the surface order is derived by means of Move-. Since GPSG is a non-transformational theory, this kind of explanation is not possible. Instead, GPSG imposes restrictions on *immediate dominance* (ID), which differ from those which refer to *linear precedence* (LP): rules such as (13) are to be understood as dominance rules, which do not have anything to say about the order of the daughters (Pullum 1982).

(13) S → V, NP[nom], NP[dat], NP[acc]

The rule in (13) simply states that S dominates all other nodes. Due to the abandonment of ordering restrictions for the right-hand side of the rule, we only need one rule rather than twelve.

Nevertheless, without any kind of restrictions on the right-hand side of the rule, there would be far too much freedom. For example, the following order would be permissible:

(14) \* Dem the.dat Kind child der the.nom Mann man gibt gives ein the.acc Buch. book

Such orders are ruled out by so-called *Linear Precedence Rules* or LP-rules. LP-constraints are restrictions on local trees, that is, trees with a depth of one. It is, for example, possible to state something about the order of V, NP[nom], NP[acc] and NP[dat] in Figure 5.2 using linearization rules.

Figure 5.2: Example of a local tree

The following linearization rules serve to exclude orders such as those in (14):

(15) V[+mc] < X X < V[−mc]

mc stands for *main clause*. The LP-rules ensure that in main clauses (+mc), the verb precedes all other constituents and follows them in subordinate clauses (−mc). There is a restriction that says that all verbs with the mc-value '+' also have to be (+fin). This will rule out infinitive forms in initial position.

These LP rules do not permit orders with an occupied prefield or postfield in a local tree. This is intended. We will see how fronting can be accounted for in Section 5.4.

### **5.1.3 Metarules**

We have previously encountered linearization rules for sentences with subjects, however our rules have the form in (16), that is, they do not include subjects:

(16) V2 → H[7], N2[case dat] V2 → H[8], N2[case dat], N2[case acc]

These rules can be used to analyze the verb phrases *dem Mann das Buch zu geben* 'to give the man the book' and *das Buch dem Mann zu geben* 'to give the book to the man' as they appear in (17), but we cannot analyze sentences like (9), since the subject does not occur on the right-hand side of the rules in (16).

	- b. Er he verspricht, promises [das the.acc Buch book dem the.dat Mann man zu to geben]. give 'He promises to give the book to the man.'

A rule with the format of (18) does not make much sense for a GPSG analysis of German since it cannot derive all the orders in (9) as the subject can occur between the elements of the VP as in (9c).

(18) S → N2 V2

With the rule in (18), it is possible to analyze (9a) as in Figure 5.3 and it would also be possible to analyze (9b) with a different ordering of the NPs inside the VP. The remaining examples in (9) cannot be captured by the rule in (18), however. This has to do with the

Figure 5.3: VP analysis for German (not appropriate in the GPSG framework)

fact that only elements in the same local tree, that is, elements which occur on the righthand side of a rule, can be reordered. While we can reorder the parts of the VP and thereby derive (9b), it is not possible to place the subject at a lower position between the objects. Instead, a metarule can be used to analyze sentences where the subject occurs between other arguments of the verb. This rule relates phrase structure rules to other phrase structure rules. A metarule can be understood as a kind of instruction that creates another rule for each rule with a certain form and these newly created rules will in turn license local trees.

For the example at hand, we can formulate a metarule which says the following: if there is a rule with the form "V2 consists of something" in the grammar, then there also has to be another rule "V3 consists of whatever V2 consists + an NP in the nominative". In formal terms, this looks as follows:

(19) V2 → W ↦→ V3 → W, N2[case nom]

#### 5 Generalized Phrase Structure Grammar

W is a variable which stands for an arbitrary number of categories (W = *whatever*). The metarule creates the following rules in (20) from the rules in (16):

(20) V3 → H[7], N2[case dat], N2[case nom] V3 → H[8], N2[case dat], N2[case acc], N2[case nom]

Now, the subject and other arguments both occur in the right-hand side of the rule and can therefore be freely ordered as long as no LP rules are violated.

## **5.1.4 Semantics**

The semantics adopted by Gazdar, Klein, Pullum & Sag (1985: Chapter 9–10) goes back to Richard Montague (1974). Unlike a semantic theory which stipulates the combinatorial possibilities for each rule (see Section 2.3), GPSG uses more general rules. This is possible due to the fact that the expressions to be combined each have a semantic type. It is customary to distinguish between entities (*e*) and truth values (*t*). Entities refer to an object in the world (or in a possible world), whereas entire sentences are either true or false, that is, they have a truth value. It is possible to create more complex types from the types *e* and *t*. Generally, the following holds: if *a* and *b* are types, then ⟨ *a*, *b* ⟩ is also a type. Examples of complex types are ⟨ *e*, *t* ⟩ and ⟨ *e*, ⟨ *e*, *t* ⟩⟩. We can define the following combinatorial rule for this kind of typed expressions:

(21) If is of type ⟨ *b*, *a* ⟩ and of type *b*, then () is of type *a*.

This type of combination is also called *functional application*. With the rule in (21), it is possible that the type ⟨ *e*, ⟨ *e*, *t* ⟩⟩ corresponds to an expression which still has to be combined with two expressions of type *e* in order to result in an expression of *t*. The first combination step with *e* will yield ⟨ *e*, *t* ⟩ and the second step of combination with a further *e* will give us *t*. This is similar to what we saw with -expressions on page 62: *like*′ (x, y) has to combine with a y and an x. The result in this example was *like*′ (*max*′ , *lotte*′ ), that is, an expression that is either true or false in the relevant world.

In Gazdar et al. (1985), an additional type is assumed for worlds in which an expression is true or false. For reasons of simplicity, I will omit this here. The types that we need for sentences, NPs and N′ s, determiners and VPs are given in (22):

	- b. TYP(NP) = ⟨ ⟨ *e*, *t* ⟩, *t* ⟩
	- c. TYP(N′ ) = ⟨ *e*, *t* ⟩
	- d. TYP(Det) = TYP(N′ ), TYP(NP)
	- e. TYP(VP) = ⟨ *e*, *t* ⟩

A sentence is of type *t* since it is either true or false. A VP needs an expression of type *e* to yield a sentence of type *t*. The type of the NP may seem strange at first glance, however, it is possible to understand it if one considers the meaning of NPs with quantifiers. For sentences such as (23a), a representation such as (23b) is normally assumed:

	- b. ∀ *child*′ (x) → *laugh*′ (x)

The symbol ∀ stands for the universal quantifier. The formula can be read as follows. For every object, for which it is the case that it has the property of being a child, it is also the case that it is laughing. If we consider the contribution made by the NP, then we see that the universal quantifier, the restriction to children and the logical implication come from the NP:

#### (24) ∀ *child*′ (x) → P(x)

This means that an NP is something that must be combined with an expression which has exactly one open slot corresponding to the x in (24). This is formulated in (22b): an NP corresponds to a semantic expression which needs something of type ⟨ *e*, *t* ⟩ to form an expression which is either true or false (that is, of type *t*).

An N′ stands for a nominal expression of the kind x child(x). This means if there is a specific individual which one can insert in place of the x, then we arrive at an expression that is either true or false. For a given situation, it is the case that either John has the property of being a child or he does not. An N′ has the same type as a VP.

TYP(N′ ) and TYP(NP) in (22d) stand for the types given in (22c) and (22b), that is, a determiner is semantically something which has to be combined with the meaning of N′ to give the meaning of an NP.

Gazdar, Klein, Pullum & Sag (1985: 209) point out a redundancy in the semantic specification of grammars which follow the rule-to-rule hypothesis (see Section 2.3) since, instead of giving rule-by-rule instructions with regard to combinations, it suffices in many cases simply to say that the functor is applied to the argument. If we use types such as those in (22), it is also clear which constituent is the functor and which is the argument. In this way, a noun cannot be applied to a determiner, but rather only the reverse is possible. The combination in (25a) yields a well-formed result, whereas (25b) is ruled out.

(25) a. Det′ (N′ ) b. N′ (Det′ )

The general combinatorial principle is then as follows:

(26) Use functional application for the combination of the semantic contribution of the daughters to yield a well-formed expression corresponding to the type of the mother node.

The authors of the GPSG book assume that this principle can be applied to the vast majority of GPSG rules so that only a few special cases have to be dealt with by explicit rules.

### **5.1.5 Adjuncts**

For nominal structures in English, Gazdar et al. (1985: 126) assume the X analysis and, as we have seen in Section 2.4.1, this analysis is applicable to nominal structures in German. Nevertheless, there is a problem regarding the treatment of adjuncts in the verbal domain if one assumes flat branching structures, since adjuncts can freely occur between arguments:

	- b. [weil] because der the Mann man dem the Kind child *gestern* yesterday das the Buch book gab gave
	- c. [weil] because der the Mann man *gestern* yesterday dem the Kind child das the Buch book gab gave
	- d. [weil] because *gestern* yesterday der the Mann man dem the Kind child das the Buch book gab gave

For (27), one requires the following rule:

(28) V3 → H[8], N2[case dat], N2[case acc], N2[case nom], AdvP

Of course, adjuncts can also occur between the arguments of verbs from other valence classes:

(29) [weil] because (oft) often die the Frau woman (oft) often dem the Mann man (oft) often hilft helps 'because the woman often helps the man'

Furthermore, adjuncts can occur between the arguments of a VP:

(30) Der the Mann man hat has versucht, tried dem the Kind child heimlich secretly das the Buch book zu to geben. give 'The man tried to secretly give the book to the child.'

In order to analyze these sentences, we can use a metarule which adds an adjunct to the right-hand side of a V2 (Uszkoreit 1987: 146).

(31) V2 → W ↦→ V2 → W, AdvP

By means of the subject introducing metarule in (19), the V3-rule in (28) is derived from a V2-rule. Since there can be several adjuncts in one sentence, a metarule such as (31) must be allowed to apply multiple times. The recursive application of metarules is often ruled out in the literature due to reasons of generative capacity (see Chapter 17) (Thompson 1982; Uszkoreit 1987: 146). If one uses the Kleene star, then it is possible to formulate the adjunct metarule in such as way that it does not have to apply recursively (Uszkoreit 1987: 146):

$$\begin{array}{c} \text{(32)} \quad \text{V2} \rightarrow \text{W} \leftrightarrow\\ \text{V2} \rightarrow \text{W}, \text{AdvP\*} \end{array}$$

If one adopts the rule in (32), then it is not immediately clear how the semantic contribution of the adjuncts can be determined.2 For the rule in (31), one can combine the semantic contribution of the AdvP with the semantic contribution of the V2 in the input rule. This is of course also possible if the metarule is applied multiple times. If this metarule is applied to (33a), for example, the V2-node in (33a) contains the semantic contribution of the first adverb.

(33) a. V2 → V, NP, AdvP

b. V2 → V, NP, AdvP, AdvP

The V2-node in (33b) receives the semantic representation of the adverb applied to the V2-node in (33a).

Weisweber & Preuss (1992) have shown that it is possible to use metarules such as (31) if one does not use metarules to compute a set of phrase structure rules, but rather directly applies the metarules during the analysis of a sentence. Since sentences are always of finite length and the metarule introduces an additional AdvP to the righthand side of the newly licensed rule, the metarule can only be applied a finite number of times.

# **5.2 Passive as a metarule**

The German passive can be described in an entirely theory-neutral way as follows:3

This is true for all verb classes which can form the passive. It does not make a difference whether the verbs takes one, two or three arguments:

	- b. [weil] because noch still gearbeitet worked wurde aux 'because there was still working there'

2 In LFG, an adjunct is entered into a set in the functional structure (see Section 7.1.6). This also works with the use of the Kleene star notation. From the f-structure, it is possible to compute the semantic denotation with corresponding scope by making reference to the c-structure. In HPSG, Kasper (1994) has made a proposal which corresponds to the GPSG proposal with regard to flat branching structures and an arbitrary number of adjuncts. In HPSG, however, one can make use of so-called relational constraints. These are similar to small programs which can create relations between values inside complex structures. Using such relational constraints, it is then possible to compute the meaning of an unrestricted number of adjuncts in a flat branching structure.

3 This characterization does not hold for other languages. For instance, Icelandic allows for dative subjects. See Zaenen, Maling & Thráinsson (1985).

	- b. [weil] because an at Maria Maria gedacht thought wurde aux 'because Maria was thought of'
	- b. [weil] because der the.nom Weltmeister world.champion geschlagen beaten wurde aux 'because the world champion was beaten'
	- b. [weil] because ihm him.dat der the.nom Aufsatz essay gegeben given wurde aux 'because he was given the essay'

In a simple phrase structure grammar, we would have to list two separate rules for each pair of sentences making reference to the valence class of the verb in question. The characteristics of the passive discussed above would therefore not be explicitly stated in the set of rules. In GPSG, it is possible to explain the relation between active and passive rules using a metarule: for each active rule, a corresponding passive rule with suppressed subject is licensed. The link between active and passive clauses can therefore be captured in this way.

An important difference to Transformational Grammar/GB is that we are not creating a relation between two trees, but rather between active and passive rules. The two rules license two unrelated structures, that is, the structure of (38b) is not derived from the structure of (38a).

	- b. [weil] because der the.nom Weltmeister world.champion geschlagen beaten wurde aux 'because the world champion was beaten'

The generalization with regard to active/passive is captured nevertheless.

In what follows, I will discuss the analysis of the passive given in Gazdar, Klein, Pullum & Sag (1985) in some more detail. The authors suggest the following metarule for English (p. 59):4

(39) VP → W, NP ↦→ VP[pas] → W, (PP[*by*])

This rule states that verbs which take an object can occur in a passive VP without this object. Furthermore, a *by*-PP can be added. If we apply this metarule to the rules in (40), then this will yield the rules listed in (41):

It is possible to use the rules in (40) to analyze verb phrases in active sentences:

(42) a. [S The man [VP devoured the carcass]]. b. [S The man [VP handed the sword to Tracy]].

The combination of a VP with the subject is licensed by an additional rule (S → NP, VP).

With the rules in (41), one can analyze the VPs in the corresponding passive sentences in (43):

(43) a. [S The carcass was [VP[pas] devoured (by the man)]]. b. [S The sword was [VP[pas] handed to Tracy (by the man)]].

At first glance, this analysis may seem odd as an object is replaced inside the VP by a PP which would be the subject in an active clause. Although this analysis makes correct predictions with regard to the syntactic well-formedness of structures, it seems unclear how one can account for the semantic relations. It is possible, however, to use a lexical rule that licenses the passive participle and manipulates the semantics of the output lexical item in such a way that the *by*-PP is correctly integrated semantically (Gazdar et al. 1985: 219).

We arrive at a problem, however, if we try to apply this analysis to German since the impersonal passive cannot be derived by simply suppressing an object. The V2-rules for verbs such as *arbeiten* 'work' and *denken* 'think' as used for the analysis of (34a) and (35a) have the following form:

4 See Weisweber & Preuss (1992: 1114) for a parallel rule for German which refers to accusative case on the left-hand side of the metarule.

#### 5 Generalized Phrase Structure Grammar

There is no NP on the right-hand side of these rules which could be replaced by a *von*-PP. If the passive is to be analyzed as suppressing an NP argument in a rule, then it should follow from the existence of the impersonal passive that the passive metarule has to be applied to rules which license finite clauses, since information about whether there is a subject or not is only present in rules for finite clauses.5 In this kind of system, the rules for finite sentences (V3) are the basic rules and the rules for V2 would be derived from these.

It would only make sense to have a metarule which applies to V3 for German since English does not have V3 rules which contain both the subject and its object on the righthand side of the rule.6 For English, it is assumed that a sentence consists of a subject and a VP (see Gazdar et al. 1985: 139). This means that we arrive at two very different analyses for the passive in English and German, which do not capture the descriptive insight that the passive is the suppression of the subject and the subsequent promotion of the object in the same way. The central difference between German and English seems to be that English obligatorily requires a subject,7 which is why English does not have an impersonal passive. This is a property independent of passives, which affects the possibility of having a passive structure, however.

The problem with the GPSG analysis is the fact that valence is encoded in phrase structure rules and that subjects are not present in the rules for verb phrases. In the following chapters, we will encounter approaches from LFG, Categorial Grammar, HPSG, Construction Grammar, and Dependency Grammar which encode valence separately from phrase structure rules and therefore do not have a principled problem with impersonal passive.

See Jacobson (1987b: 394–396) for more problematic aspects of the passive analysis in GPSG and for the insight that a lexical representation of valence – as assumed in Categorial Grammar, GB, LFG and HPSG – allows for a lexical analysis of the phenomenon, which is however unformulable in GPSG for principled reasons having to do with the fundamental assumptions regarding valence representations.

# **5.3 Verb position**

Uszkoreit (1987) analyzed verb-initial and verb-final order as linearization variants of a flat tree. The details of this analysis have already been discussed in Section 5.1.2.

An alternative suggestion in a version of GPSG comes from Jacobs (1986: 110): Jacobs's analysis is a rendering of the verb movement analysis in GB. He assumes that there is an

5GPSG differs from GB in that infinitive verbal projections do not contain nodes for empty subjects. This is also true for all other theories discussed in this book with the exception of Tree-Adjoining Grammar.

6Gazdar et al. (1985: 62) suggest a metarule similar to our subject introduction metarule on page 189. The rule that is licensed by their metarule is used to analyze the position of auxiliaries in English and only licenses sequences of the form AUX NP VP. In such structures, subjects and objects are not in the same local tree either.

7Under certain conditions, the subject can also be omitted in English. For more on imperatives and other subject-less examples, see page 538.

empty verb in final position and links this to the verb in initial position using technical means which we will see in more detail in the following section.

# **5.4 Long-distance dependencies as the result of local dependencies**

One of the main innovations of GPSG is its treatment of long-distance dependencies as a sequence of local dependencies (Gazdar 1981b). This approach will be explained taking constituent fronting to the prefield in German as an example. Until now, we have only seen the GPSG analysis for verb-initial and verb-final position: the sequences in (45) are simply linearization variants.

	- b. Gibt gives der the.nom Mann man dem the.dat Kind child das the.acc Buch? book 'Does the man give the child the book?'

What we want is to derive the verb-second order in the examples in (46) from V1 order in (45b).

	- b. Dem the.dat Kind child gibt gives der the.nom Mann man das the.acc Buch. book 'The man gives the child the book.'

For this, the metarule in (47) has to be used. This metarule removes an arbitrary category X from the set of categories on the right-hand side of the rule and represents it on the left-hand side with a slash ('/'):8

(47) V3 → W, X ↦→ V3/X → W

This rule creates the rules in (49) from (48):

8An alternative to Uszkoreit's trace-less analysis (1987: 77), which is explained here, consists of using a trace for the extracted element as in GB.

The rule in (50) connects a sentence with verb-initial order with a constituent which is missing in the sentence:

$$\text{(50)}\quad \text{V3[+FN]}\rightarrow \text{X[+TOP], V3[+MC]/X}$$

In (50), X stands for an arbitrary category which is marked as missing in V3 by the '/'. X is referred to as a *filler*.

The interesting cases of values for X with regard to our examples are given in (51):

(51) V3[+fin] → N2[+top, case nom], V3[+mc]/N2[case nom] V3[+fin] → N2[+top, case dat], V3[+mc]/N2[case dat] V3[+fin] → N2[+top, case acc], V3[+mc]/N2[case acc]

(51) does not show actual rules. Instead, (51) shows examples for insertions of specific categories into the X-position, that is, different instantiations of the rule.

The following linearization rule ensures that a constituent marked by [+top] in (50) precedes the rest of the sentence:

(52) [+top] < X

top stands for *topicalized*. As was mentioned on page 107, the prefield is not restricted to topics. Focused elements and expletives can also occur in the prefield, which is why the feature name is not ideal. However, it is possible to replace it with something else, for instance *prefield*. This would not affect the analysis. X in (52) stands for an arbitrary category. This is a new X and it is independent from the one in (50).

Figure 5.4 shows the interaction of the rules for the analysis of (53).9

(53) Dem the.dat Kind child gibt gives er he.nom das the.acc Buch. book 'He gives the child the book.'

Figure 5.4: Analysis of fronting in GPSG

The metarule in (47) licenses a rule which adds a dative object into slash. This rule now licenses the subtree for *gibt er das Buch* 'gives he the book'. The linearization rule

9 The fin feature has been omitted on some of the nodes since it is redundant: +mc-verbs always require the fin value '+'.

V[+mc] < X orders the verb to the very left inside of the local tree for V3. In the next step, the constituent following the slash is bound off. Following the LP-rule [+top] < X, the bound constituent must be ordered to the left of the V3 node.

The analysis given in Figure 5.4 may seem too complex since the noun phrases in (53) all depend on the same verb. It is possible to invent a system of linearization rules which would allow one to analyze (53) with an entirely flat structure. One would nevertheless still need an analysis for sentences such as those in (37) on page 107 – repeated here as (54) for convenience:

	- c. Wen who glaubst believe du, you daß that ich I \_ gesehen seen habe?12 have 'Who do you think I saw?'
	- d. [Gegen against ihn] him falle fall es it den the Republikanern Republicans hingegen however schwerer, more.difficult [ [ Angriffe \_ ] attacks zu to lancieren].13 launch

'It is, however, more difficult for the Republicans to launch attacks against him.'

The sentences in (54) cannot be explained by local reordering as the elements in the prefield are not dependent on the highest verb, but instead originate in the lower clause. Since only elements from the same local tree can be reordered, the sentences in (54) cannot be analyzed without postulating some kind of additional mechanism for longdistance dependencies.14

Before I conclude this chapter, I will discuss yet another example of fronting, namely one of the more complex examples in (54). The analysis of (54c) consists of several

10taz, 04.05.2001, p. 20.

11Spiegel, 8/1999, p. 18.

12Scherpenisse (1986: 84).

13taz, 08.02.2008, p. 9.

14One could imagine analyses that assume the special mechanism for nonlocal dependencies only for sentences that really involve dependencies that are nonlocal. This was done in HPSG by Kathol (1995) and Wetta (2011) and by Groß & Osborne (2009) in Dependency Grammar. I discuss the Dependency Grammar analyses in detail in Section 11.7.1 and show that analyses that treat simple V2 sentences as ordering variants of non-V2 sentences have problems with the scope of fronted adjuncts, with coordination of simple sentences and sentences with nonlocal dependencies and with so-called multiple frontings.

steps: the introduction, percolation and finally binding off of information about the longdistance dependency. This is shown in Figure 5.5. Simplifying somewhat, I assume that

Figure 5.5: Analysis of long-distance dependencies in GPSG

*gesehen habe* 'have seen' behaves like a normal transitive verb.15 A phrase structure rule licensed by the metarule in (47) licenses the combination of *ich* 'I' and *gesehen habe* 'has seen' and represents the missing accusative object on the V3 node. The complementizer *dass* 'that' is combined with *ich gesehen habe* 'I have seen' and the information about the fact that an accusative NP is missing is percolated up the tree. This percolation is controlled by the so-called *Foot Feature Principle*, which states that all foot features of all the daughters are also present on the mother node. Since the slash feature is a foot feature, the categories following the '/' percolate up the tree if they are not bound off in the local tree. In the final step, the V3/N2[acc] is combined with the missing N2[acc]. The result is a complete finite declarative clause of the highest projection level.

# **5.5 Summary and classification**

This section is for advanced readers. It compares GPSG with theories introduced later in the book, in particular Categorial Grammar and HPSG. I suggest coming back here after reading at least Chapters 6, 8 and 9.

Some twenty years after Chomsky's criticism of phrase structure grammars, the first large grammar fragment in the GPSG framework appeared and offered analyses of phenomena which could not be described by simple phrase structure rules. Although works in GPSG essentially build on Harman's 1963 idea of a transformation-less grammar, they

15See Nerbonne (1986a) and Johnson (1986), for analyses of verbal complexes in GPSG.

also go far beyond this. A special achievement of GPSG is, in particular, the treatment of long-distance dependencies as worked out by Gazdar (1981b). By using the slash-mechanism, it was possible to explain the simultaneous extraction of elements from conjuncts (Across the Board Extraction, Ross 1967, Williams 1978: Section <IP_ADDRESS>). The following examples from Gazdar (1981b: 173) show that gaps in conjuncts must be identical, that is, a filler of a certain category must correspond to a gap in every conjunct:

(55) a. The kennel which Mary made and Fido sleeps in has been stolen.

(= S/NP & S/NP)

(= S/NP & S/PP)

GPSG can plausibly handle this with mechanisms for the transmission of information about gaps. In symmetric coordination, the slash elements in each conjunct have to be identical. On the one hand, a transformational approach is not straightforwardly possible since one normally assumes in such analyses that there is a tree and something is moved to another position in the tree thereby leaving a trace. However, in coordinate structures, the filler would correspond to two or more traces and it cannot be explained how the filler could originate in more than one place.

While the analysis of Across the Board extraction is a true highlight of GPSG, there are some problematic aspects that I want to address in the following: the interaction between valence and morphology, the representation of valence and partial verb phrase fronting, and the expressive power of the GPSG formalism.

# **5.5.1 Valence and morphology**

The encoding of valence in GPSG is problematic for several reasons. For example, morphological processes take into account the valence properties of words. Adjectival derivation with the suffix -*bar* '-able' is only productive with transitive verbs, that is, with verbs with an accusative object which can undergo passivization:

A rule for derivations with -*bar* '-able' must therefore make reference to valence information. This is not possible in GPSG grammars since every lexical entry is only assigned a

number which says something about the rules in which this entry can be used. For -*bar*derivations, one would have to list in the derivational rule all the numbers which correspond to rules with accusative objects, which of course does not adequately describe the phenomenon. Furthermore, the valence of the resulting adjective also depends on the valence of the verb. For example, a verb such as *vergleichen* 'compare' requires a *mit* (with)-PP and *vergleichbar* 'comparable' does too (Riehemann 1993: 7, 54; 1998: 68). In the following chapters, we will encounter models which assume that lexical entries contain information as to whether a verb selects for an accusative object or not. In such models, morphological rules which need to access the valence properties of linguistic objects can be adequately formulated.

The issue of interaction of valence and derivational morphology will be taken up in Section 21.2.2 again, where approaches in LFG and Construction Grammar are discussed that share assumptions about the encoding of valence with GPSG.

## **5.5.2 Valence and partial verb phrase fronting**

Nerbonne (1986a) and Johnson (1986) investigate fronting of partial VPs in the GPSG framework. (57) gives some examples: in (57a) the bare verb is fronted and its arguments are realized in the middle field, in (57b) one of the objects is fronted together with the verb, in (57c) the other object is fronted with the verb and in (57d) both objects are fronted with the verb.

	- b. [Ein a.acc Märchen fairy.tale erzählen] tell wird will er he.nom seiner his.acc Tochter daughter müssen. must
	- c. [Seiner his.dat Tochter daughter erzählen] tell wird will er he.nom das the.acc Märchen fairy.tale müssen. must
	- d. [Seiner his.dat Tochter daughter ein a.acc Märchen fairy.tale erzählen] tell wird will er he.nom müssen. must

The problem with sentences such as those in (57) is that the valence requirements of the verb *erzählen* 'to tell' are realized in various positions in the sentence. For fronted constituents, one requires a rule which allows a ditransitive to be realized without its arguments or with one or two objects. This means that the ditransitive verb *erzählen* 'to tell' should have the same valence numbers as *schalfen* 'to sleep', as *helfen* 'to help', as *kennen* 'to know' in addition to its normal ditransitive number. Furthermore, it has to be ensured that the arguments that are missing in the prefield are realized in the remainder of the clause. It is not legitimate to omit obligatory arguments or realize arguments with other properties like a different case, as the examples in (58) show:

	- b. \* Verschlungen devoured hat has er he.nom nicht. not
	- c. \* Verschlungen devoured hat has er he.nom ihm him.dat nicht. not

The obvious generalization is that the fronted and unfronted arguments must add up to the total set belonging to the verb. This is scarcely possible with the rule-based valence representation in GPSG. In theories such as Categorial Grammar (see Chapter 8), it is possible to formulate elegant analyses of (58) (Geach 1970). Nerbonne and Johnson both suggest analyses for sentences such as (58) which ultimately amount to changing the representation of valence information in the direction of Categorial Grammar.

Before I turn to the expressive power of the GPSG formalism, I want to note that the problems that we discussed in the previous subsections are both related to the representation of valence in GPSG. We already run into valence-related problems when discussing the passive in Section 5.2: since subjects and objects are introduced in phrase structure rules and since there are some languages in which subject and object are not in the same local tree, there seems to be no way to describe the passive as the suppression of the subject in GPSG.

## **5.5.3 Generative capacity**

In GPSG, the system of linearization, dominance and metarules is normally restricted by conditions we will not discuss here in such a way that one could create a phrase structure grammar of the kind we saw in Chapter 2 from the specification of a GPSG grammar. Such grammars are also called context-free grammars. In the mid-80s, it was shown that context-free grammars are not able to describe natural language in general, that is it could be shown that there are languages that need more powerful grammar formalisms than context-free grammars (Shieber 1985, Culy 1985; see Pullum (1986) for a historical overview). The so-called *generative capacity* of grammar formalisms is discussed in Chapter 17.

Following the emergence of constraint-based models such as HPSG (see Chapter 9) and unification-based variants of Categorial Grammar (see Chapter 8 and Uszkoreit 1986a), most authors previously working in GPSG turned to other frameworks. The GPSG analysis of long-distance dependencies and the distinction between immediate dominance and linear precedence are still used in HPSG and variants of Construction Grammar to this day. See also Section 12.2 for a Tree Adjoining Grammar variant that separates dominance from precedence.

#### 5 Generalized Phrase Structure Grammar

# **Comprehension questions**

## **Exercises**

	- (59) a. [dass] that der the.nom Mann man ihn him.acc liest reads 'that the man reads it'
		- b. [dass] that ihn him.acc der the.nom Mann man liest reads 'that the man reads it'
		- c. Der the.nom Mann man liest reads ihn. him.acc 'The man reads it.'

Include all arguments in a single rule without using the metarule for introducing subjects.

# **Further reading**

The main publication in GPSG is Gazdar, Klein, Pullum & Sag (1985). This book has been critically discussed by Jacobson (1987b). Some problematic analyses are contrasted with alternatives from Categorial Grammar and reference is made to the heavily Categorial Grammar influenced work of Pollard (1984), which counts as one of the predecessors of HPSG. Some of Jacobson's suggestions can be found in later works in HPSG.

Grammars of German can be found in Uszkoreit (1987) and Busemann (1992). Gazdar (1981b) developed an analysis of long-distance dependencies, which is still used today in theories such as HPSG.

A history of the genesis of GPSG can be found in Pullum (1989b).

# **6 Feature descriptions**

In the previous chapter, we talked about sets of feature-value pairs, which can be used to describe linguistic objects. In this chapter, we will introduce feature descriptions which play a role in theories such as LFG, HPSG, Construction Grammar, versions of Categorial Grammar and TAG (and even some formalizations of Minimalist theories (Veenstra 1998)). This chapter will therefore lay some of the groundwork for the chapters to follow.

Feature structures are complex entities which can model properties of a linguistic object. Linguists mostly work with feature descriptions which describe only parts of a given feature structure. The difference between models and descriptions will be explained in more detail in Section 6.7.

Alternative terms for feature structures are:

Other terms for feature description are the following:

In what follows, I will restrict the discussion to the absolutely necessary details in order to keep the formal part of the book as short as possible. I refer the interested reader to Shieber (1986), Pollard & Sag (1987: Chapter 2), Johnson (1988), Carpenter (1992), King (1994) and Richter (2004, 2021). Shieber's book is an accessible introduction to Unification Grammars. The works by King and Richter, which introduce important foundations for HPSG, would most probably not be accessible for those without a good grounding in mathematics. However, it is important to know that these works exist and that the corresponding linguistic theory is built on a solid foundation.

# **6.1 Feature descriptions**

When describing linguistic signs, we have to say something about their properties. For a noun, we can say that it has case, gender, number and person features. For a word such as *Mannes* 'man', we can say that these features have the values *genitive*, *masculine*, *singular* and *3*. If we were to write these as a list of feature-value pairs, we would arrive at the following feature description:

#### 6 Feature descriptions

(1) Feature-value pair for *Mannes*:

 case *genitive* gender *masculine* number *singular* person *3*

It is possible to describe a variety of different things using feature descriptions. For example, we can describe a person as in (2):

(2) firstname *max* lastname *meier* date-of-birth *10.10.1985*

People are related to other people – a fact that can also be expressed in feature-value pairs. For example, the fact that Max Meier has a father called Peter Meier can be captured by expanding (2) as follows:

The value of the father feature is another feature description containing the same features as (2).

In feature descriptions, a *path* is a sequence of features which immediately follow each other. The *value of a path* is the feature description at the end of the path. Therefore, the value of father|date-of-birth is *10.05.1960*.

One can think of many different features that could be included in representations such as (3). One may wonder how to integrate information about offspring into (3).

An obvious solution would be to add features for daughter and son:

This solution is not satisfactory as it is not immediately clear how one could describe a person with several daughters. Should one really introduce features such as daughter-1 or daughter-3?

(5) firstname *max* lastname *meier* date-of-birth *10.10.1985* father *…* mother *…* daughter-1 *…* daughter-2 *…* daughter-3 *…*

How many features do we want to assume? Where is the limit? What would the value of daughter-32 be?

For this case, it makes much more sense to use a list. Lists are indicated with angle brackets. Any number of elements can occur between these brackets. A special case is when no element occurs between the brackets. A list with no elements is also called *empty list*. In the following example, Max Meier has a daughter called Clara, who herself has no daughter.

Now, we are left with the question of sons. Should we add another list for sons? Do we want to differentiate between sons and daughters? It is certainly the case that the gender of the children is an important property, but these are properties of the objects themselves, since every person has a gender. The description in (7) therefore offers a more adequate representation.

At this point, one could ask why the parents are not included in a list as well. In fact, we find similar questions also in linguistic works: how is information best organized for the job at hand? One could argue for the representation of descriptions of the parents under separate features, by pointing out that with such a representation it is possible to make certain claims about a mother or father without having to necessarily search for the respective descriptions in a list.

If the order of the elements is irrelevant, then we could use sets rather than lists. Sets are written inside curly brackets.1

1 The definition of a set requires many technicalities. In this book, I would use sets only for collecting semantic information. This can be done equally well using lists, which is why I do not introduce sets here and instead use lists.

#### 6 Feature descriptions

# **6.2 Types**

In the previous section, we introduced feature descriptions consisting of feature-value pairs and showed that it makes sense to allow for complex values for features. In this section, feature descriptions will be augmented to include types. Feature descriptions which are assigned a type are also called *typed feature descriptions*. Types say something about which features can or must belong to a particular structure. The description previously discussed describes an object of the type *person*.

Types are written in *italics*.

The specification of a type determines which properties a modeled object has. It is then only possible for a theory to say something about these properties. Properties such as operating voltage are not relevant for objects of the type *person*. If we know the type of a given object, then we also know that this object must have certain properties even if we do not yet know their exact values. In this way, (9) is still a description of Max Meier even though it does not contain any information about Max's date of birth:

We know, however, that Max Meier must have been born on some day since this is a description of the type *person*. The question *What is Max' date of birth?* makes sense for a structure such as (9) in a way that the question *Which operating voltage does Max have?* does not. If we know that an object is of the type *person*, then we have the following basic structure:

>

In (10) and (9), the values of features such as firstname are in italics. These values are also types. They are different from types such as *person*, however, as no features belong to them. These kinds of types are called *atomic*.

Types are organized into hierarchies. It is possible to define the subtypes *woman* and *man* for *person*. These would determine the gender of a given object. (11) shows the feature description for the types *woman* and *man*.

At this point, we could ask ourselves if we really need the feature gender. The necessary information is already represented in the type *woman*. The question if specific information is represented by special features or whether it is stored in a type without a corresponding individual feature will surface again in the discussion of linguistic analyses. Both alternatives differ mostly in the fact that the information which is modeled by types is not immediately accessible for structure sharing, which is discussed in Section 6.4.

Type hierarchies play an important role in capturing linguistic generalizations, which is why type hierarchies and the inheritance of constraints and information will be explained with reference to a further example in what follows. One can think of type hierarchies as an effective way of organizing information. In an encyclopedia, the individual entries are linked in such a way that the entries for monkey and mouse will each contain a pointer to mammal. The description found under mammal does therefore not have to be repeated for the subordinate concepts. In the same way, if one wishes to

#### 6 Feature descriptions

Figure 6.1: Non-linguistic example of multiple inheritance

describe various electric appliances, one can use the hierarchy in Figure 6.1. The most general type *electrical device* is the highest in Figure 6.1. Electrical devices have certain properties, e.g., a power supply with a certain power consumption. All subtypes of *electrical device* "inherit" this property. In this way, *printing device* and *scanning device* also have a power supply with a specific power consumption. A *printing device* can produce information and a *scanning device* can read in information. A *photocopier* can both produce information and read it. Photocopiers have both the properties of scanning and printing devices. This is expressed by the connection between the two superordinate types and *photocopier* in Figure 6.1. If a type is at the same time the subtype of several superordinate types, then we speak of *multiple inheritance*. If devices can print, but not scan, they are of type *printer*. This type can have further more specific subtypes, which in turn may have particular properties, e.g., *laser printer*. New features can be added to subtypes, but it is also possible to make values of inherited features more specific. For example, the material that can be scanned with a *negative scanner* is far more restricted than that of the supertype *scanner*, since negative scanners can only scan negatives.

The objects that are modeled always have a maximally specific type. In the example above, this means that we can have objects of the type *laser printer* and *negative scanner* but not of the type *printing device*. This is due to the fact that *printing device* is not maximally specific since this type has two subtypes.

Type hierarchies with multiple inheritance are an important means for expressing linguistic generalizations (Flickinger, Pollard & Wasow 1985, Flickinger 1987, Sag 1997). Types of words or phrases which occur at the very top of these hierarchies correspond to constraints on linguistic objects, which are valid for linguistic objects in all languages. Subtypes of such general types can be specific to certain languages or language classes.

# **6.3 Disjunction**

Disjunctions can be used if one wishes to express the fact that a particular object can have various different properties. If one were to organize a class reunion twenty years after leaving school and could not recall the exact names of some former classmates, it would be possible to search the web for "Julia (Warbanow or Barbanow)". In feature descriptions, this "or" is expressed by a '∨'.

Some internet search engines do not allow for searches with 'or'. In these cases, one has to carry out two distinct search operations: one for "Julia Warbanow" and then another for "Julia Barbanow". This corresponds to the two following disjunctively connected descriptions:

Since we have type hierarchies as a means of expression, we can sometimes do without disjunctive specification of values and instead state the supertype: for *printer* ∨ *photocopier*, one can simply write *printing device* if one assumes the type hierarchy in Figure 6.1 on the preceding page.

# **6.4 Structure sharing**

Structure sharing is an important part of the formalism. It serves to express the notion that certain parts of a structure are identical. A linguistic example for the identity of values is agreement. In sentences such as (14), the number value of the noun phrase has to be identical to that of the verb:

	- b. Die the Männer men schlafen. sleep 'The men are sleeping.'
	- c. \* Der the Mann man schlafen. sleep Intended: 'The man are sleeping.'

The identity of values is indicated by boxes containing numbers. The boxes can also be viewed as variables.

When describing objects we can make claims about equal values or claims about identical values. A claim about the identity of values is stronger. Let us take the following feature description containing information about the children that Max's father and mother have as an example:

#### 6 Feature descriptions

Notice that under the paths father|children and mother|children, we find a list containing a description of a person with the first name Klaus. The question of whether the feature description is of one or two children of Peter and Anna cannot be answered. It is certainly possible that we are dealing with two different children from previous partnerships who both happen to be called Klaus.

By using structure sharing, it is possible to specify the identity of the two values as in (16). In (16), Klaus is a single child that belongs to both parents. Everything inside

the brackets which immediately follow 1 is equally present in both positions. One can think of 1 as a pointer or reference to a structure which has only been described once.

One question still remains open: what about Max? Max is also a child of his parents and should therefore also occur in a list of the children of his parents. There are two points in (16) where there are three dots. These ellipsis marks stand for information about the other children of Peter and Anna Meier. Our world knowledge tells us that both of them must have the same child namely Max Meier himself. In the following section, we will see how this can be expressed in formal terms.

# **6.5 Cyclic structures**

We have introduced structure sharing in order to be able to express the fact that Max's parents both have a son Klaus together. It would not be enough to list Max in the childlists of his parents separately. We want to capture the fact that it is the same Max which appears in each of these lists and, furthermore, we have to ensure that the child being described is identical to the entire object being described. Otherwise, the description would permit a situation where Max's parents could have a second child also called Max. The description given in (17) can capture all facts correctly.

Structures such as those described in (17) are called cyclic because one ends up going in a circle if one follows a particular path: e.g., the path father|children|…|father| children|… 2 can be potentially repeated an infinite number of times.

# **6.6 Unification**

Grammatical rules are written exactly like lexical entries in HPSG and Construction Grammar and are done so with the help of feature descriptions. For a word or a larger

2 The dots here stand for the path to 2 in the list which is the value of children. See Exercise 3.

#### 6 Feature descriptions

phrasal entity to be usable as daughter in a phrase licensed by some grammatical rule, the word or phrase must have properties which are compatible with the description of the daughters in the grammatical rule. If this kind of compatibility exists, then we can say that the respective items are *unifiable*. 3 If one unifies two descriptions, the result is a description which contains information from both descriptions but no additional information.

The way unification works can be demonstrated with feature descriptions describing people. One can imagine that Bettina Kant goes to the private detective Max Müller and wants to find a specific person. Normally, those who go to a detective's office only come with a partial description of the person they are looking for, e.g., the gender, hair color or date of birth. Perhaps even the registration number of the car belonging to the person is known.

It is then expected of the detective that he or she provides information fitting the description. If we are looking for a blond female named Meier (18a), then we do not want to get descriptions of a male red-head (18b). The descriptions in (18) are incompatible and cannot be unified:

The description in (19) would be a possible result for a search for a blond, female individual called Meier:

3 The term *unification* should be used with care. It is only appropriate if certain assumptions with regard to the formal basis of linguistic theories are made. Informally, the term is often used in formalisms where unification is not technically defined. In HPSG, it mostly means that the constraints of two descriptions lead to a single description. What one wants to say here, intuitively, is that the objects described have to satisfy the constraints of both descriptions at the same time (*constraint satisfaction*). Since the term *unification* is so broadly-used, it will also be used in this section. The term will not play a role in the remaining discussions of theories with the exception of explicitly unification-based approaches. In contrast, the concept of constraint satisfaction presented here is very important for the comprehension of the following chapters.

Katharina Meier could also have other properties unknown to the detective. The important thing is that the properties known to the detective match those that the client is looking for. Furthermore, it is important that the detective uses reliable information and does not make up any information about the sought object. The unification of the search in (18a) and the information accessible to the detective in (19) is in fact (19) and not (20), for example:

(20) contains information about children, which is neither contained in (18a) nor in (19). It could indeed be the case that Katharina Meier has no children, but there are perhaps several people called Katharina Meier with otherwise identical properties. With this invented information, we might exclude one or more possible candidates.

It is possible that our detective Max Müller does not have any information about hair color in his files. His files could contain the following information:

These data are compatible with the search criteria. If we were to unify the descriptions in (18a) and (21), we would get (19). If we assume that the detective has done a good job, then Bettina Kant now knows that the person she is looking for has the properties of her original search plus the newly discovered properties.

# **6.7 Phenomena, models and formal theories**

In the previous sections, we introduced feature descriptions with types. These feature descriptions describe typed feature structures, which are models of observable linguistic structures. In the definitions of types, one determines which properties of linguistic objects should be described. The type hierarchy together with type definitions is also referred to as a *signature*. As a grammarian, one typically uses types in feature descriptions. These descriptions contain constraints which must hold for linguistic objects. If no constraints are given, all values that are compatible with the specification in the signature are possible values. For example, one can omit the case description of a linguistic object such as *Frau* 'woman' since *Frau* can – as shown in (22) – appear in all four cases:

In a given model, there are only fully specified representations, that is, the model contains four forms of *Frau*, each with a different case. For masculine nouns such as *Mann* 'man', one would have to say something about case in the description since the genitivesingular form *Mann-es* differs from other singular forms, which can be seen by adding *Mann* into the examples in (22). (23) shows the feature descriptions for *Frau* 'woman' and *Mann* 'man':

(23) a. Frau 'woman': - gender *fem* b. Mann 'man': gender *mas* case *nominative* ∨ *dative* ∨ *accusative*

Unlike (23b), (23a) does not contain a case feature since we do not need to say anything special about case in the description of *Frau*. Since all nominal objects require a case feature, it becomes clear that the structures for *Frau* must actually also have a case feature. The value of the case feature is of the type *case*. *case* is a general type which subsumes the subtypes *nominative*, *genitive*, *dative* and *accusative*. Concrete linguistic objects always have exactly one of these maximally specified types as their case value. The feature structures belonging to (23) are given in Figure 6.2 and Figure 6.3.

Figure 6.2: Feature structures for the description of *Frau* 'woman' in (23a)

In these representations, each node has a certain type (*noun*, *fem*, *nominative*, …) and the types in feature structures are always maximally specific, that is, they do not have any further subtypes. There is always an entry node (*noun* in the example above) and 6.7 Phenomena, models and formal theories

Figure 6.3: Feature structures for the description of *Mann* 'man' in (23b)

the other nodes are connected with arrows that are annotated with the feature labels (gender, case).

If we return to the example with people from the previous sections, we can capture the difference between a model and a description as follows: if we have a model of people that includes first name, last name, date of birth, gender and hair color, then it follows that every object we model also has a birthday. We can, however, decide to omit these details from our descriptions if they do not play a role for stating constraints or formulating searches.

The connection between linguistic phenomena, the model and the formal theory is shown in Figure 6.4, which is adapted from Pollard & Sag (1994: 7). The model is designed

Figure 6.4: Phenomenon, model and formal theory according to Netter (1998: 26)

to model linguistic phenomena. Furthermore, it must be licensed by our theory. The theory determines the model and makes predictions with regard to possible phenomena.

#### 6 Feature descriptions

# **Comprehension questions**

# **Exercises**

4. (Additional exercise) The relation *append* will play a role in Chapter 9. This relation serves to combine two lists to form a third. Relational constraints such as *append* do in fact constitute an expansion of the formalism. Using relational constraints, it is possible to relate any number of feature values to other values, that is, one can write programs which compute a particular value depending on other values. This poses the question as to whether one needs such powerful descriptive tools in a linguistic theory and, if we do allow them, what kind of complexity we afford them. A theory which can do without relational constraints should be preferred over one that uses relational constraints (see Müller 2007a: Chapter 20 for a comparison of theories).

For the concatenation of lists, there is a possible implementation in feature structures without recourse to relational constraints. Find out how this can be done. Give your sources and document how you went about finding the solution.

## **Further reading**

This chapter was designed to give the reader an easy-to-follow introduction to typed feature descriptions. The mathematical properties of the structures, type hierarchies and the combinatorial possibilities of such structures could not be discussed in detail here, but knowledge of at least part of these properties is important for work in computational linguistics and in developing one's own analyses. For more information, I refer the interested reader to the following publications: Shieber (1986) is a short introduction to the theory of Unification Grammar. It offers a relatively general overview followed by the discussion of important grammar types such as DCG, LFG, GPSG, HPSG, PATR-II. Johnson (1988) describes the formalism of untyped feature structures in a mathematically precise way. Carpenter (1992) enters into details about the mathematical aspects of typed feature structures. The formalism developed by King (1999) for HPSG-grammars forms the basis for the formalism by Richter (2004), which currently counts as the standard formalism for HPSG. See also Richter (2021) for an overview of the formal properties of HPSG grammars.

This chapter introduced typed feature structures/descriptions. Frameworks like LFG do not use types and type hierarchies, but they use macros instead. The formal underpinnings of LFG, including assumptions regarding models, differ slightly from those presented here. Przepiórkowski (2023) discusses both LFG and HPSG assumptions about the model theoretic foundations of the respective frameworks and points out commonalities and differences.

# **7 Lexical Functional Grammar**

Lexical Functional Grammar (LFG) was developed in the 80s by Joan Bresnan and Ron Kaplan (Bresnan & Kaplan 1982). LFG forms part of so-called West-Coast linguistics: unlike MIT, where Chomsky works and teaches, the institutes of researchers such as Joan Bresnan and Ron Kaplan are on the west coast of the USA (Joan Bresnan in Stanford and Ron Kaplan at Xerox in Palo Alto and now at the language technology firm Nuance Communications in the Bay Area in California).

Bresnan & Kaplan (1982) view LFG explicitly as a psycholinguistically plausible alternative to transformation-based approaches. For a discussion of the requirements regarding the psycholinguistic plausibility of linguistics theories, see Chapter 15.

The more in-depth works on German are Berman (1996, 2003a) and Cook (2001).

LFG has well-designed formal foundations (Kaplan & Bresnan 1982, Kaplan 1989), and hence first implementations were available rather quickly (Frey & Reyle 1983b,a, Yasukawa 1984, Block & Hunze 1986, Eisele & Dörre 1986, Wada & Asher 1986, Delmonte 1990, Her, Higinbotham & Pentheroudakis 1991, Kohl 1992, Kohl, Gardent, Plainfossé, Reape & Momma 1992, Kaplan & Maxwell III 1996, Mayo 1997, 1999, Boullier & Sagot 2005a,b, Clément 2009, Clément & Kinyon 2001).

The following is a list of languages with implemented LFG fragments, probably incomplete:

#### 7 Lexical Functional Grammar

Many of theses grammars were developed in the ParGram consortium1 (Butt, King, Niño & Segond 1999, Butt, Dyvik, King, Masuichi & Rohrer 2002). Apart from these grammars there is a small fragment of Northern Sotho, which is currently being expanded (Faaß 2010).

Many of the LFG systems combine linguistically motivated grammars with a statistical component. Such a component can help to find preferred readings of a sentence first, it can increase the efficiency of processing and make the complete processing robust (for instance Kaplan et al. 2004, Riezler et al. 2002). Josef van Genabith's group in Dublin is working on the induction of LFG grammars from corpora (e.g., Johnson et al. 1999, O'Donovan et al. 2005, Cahill et al. 2005, Chrupala & van Genabith 2006, Guo et al. 2007, Cahill et al. 2008, Schluter & van Genabith 2009).

1 http://pargram.w.uib.no/research-groups/. 2022-11-24.

Some of the systems can be tested online:

# **7.1 General remarks on the representational format**

LFG assumes multiple levels of representation.2 The most important are c-structure and f-structure. c-structure is the constituent structure and it is licensed by a phrase structure grammar. This phrase structure grammar uses X structures for languages for which this is appropriate. f-structure stands for functional structure. Functional structure contains information about the predicates involved and about the grammatical functions (subject, object, …) which occur in a constituent. Mappings mediate between these representational levels.

### **7.1.1 Functional structure**

In LFG, grammatical functions such as subject and object play a very important role. Unlike in most other theories discussed in this book, they are primitives of the theory. A sentence such as (1a) will be assigned a functional structure as in (1b):

(1) a. David devoured a sandwich.

b. pred 'DEVOUR⟨SUBJ, OBJ⟩' subj pred 'DAVID' obj spec A pred 'SANDWICH'

All lexical items that have a meaning (e.g., nouns, verbs, adjectives) contribute a pred feature with a corresponding value. The grammatical functions governed by a head (government = subcategorization) are determined in the specification of pred.3 Corresponding functions are called *governable grammatical functions*. Examples of these are shown in Table 7.1 on the next page (Dalrymple 2006). The PRED specification corresponds to the theta grid in GB theory. The valence of a head is specified by the pred value.

The non-governable grammatical functions are given in Table 7.2 on the following page. Topic and focus are information-structural terms. There are a number of works on their exact definition, which differ to varying degrees (Kruijff-Korbayová & Steedman

2 The English examples and their analyses discussed in this section are taken from Dalrymple (2001) and Dalrymple (2006).

3 In the structure in (1b), the SUBJ and OBJ in the list following *devour* are identical to the values of SUBJ and OBJ in the structure. For reasons of presentation, this will not be explicitly indicated in this structure and following structures.

Table 7.1: Governable grammatical functions

Table 7.2: Non-governable grammatical functions

2003: 253–254), but broadly speaking, one can say that the focus of an utterance constitutes new information and that the topic is old or given information. Bresnan (2001: 97) uses the following question tests in order to determine topic and focus:

f-structures are characterized using functional descriptions, for example, one can refer to a value of the feature tense in the functional structure using the following expression:

(4) ( TENSE)

It is possible to say something about the value which this feature should have in the feature description. The following descriptions express the fact that in the structure , the feature TENSE must have the value PAST.

(5) ( TENSE) = PAST

The value of a feature may also be a specific f-structure. The expression in (6) ensures that the subj feature in is the f-structure :

(6) ( SUBJ) =

For the analysis of (7a), we get the constraints in (7b):

	- b. ( PRED) = 'SNEEZE⟨SUBJ⟩' ( TENSE) = PAST ( SUBJ) = ( PRED) = 'DAVID'

The description in (7b) describes the following structure:

(8) : pred 'SNEEZE⟨SUBJ⟩' tense PAST subj : h pred 'DAVID'i

But (7b) also describes many other structures which contain further features. We are only interested in minimal structures that contain the information provided in the description.

(9) shows how a node in the c-structure can be connected to the f-structure for the entire sentence:

The function from the NP-node to the f-structure corresponding to the NP is depicted with an arrow marked .

A phrase and its head always correspond to the same f-structure:

(10) V′ V sneezed pred 'SNEEZE⟨SUBJ⟩' tense PAST

In LFG grammars of English, the CP/IP system is assumed as in GB theory (see Section 3.1.5). IP, I′ and I (and also VP) are mapped onto the same f-structure.

(11) a. David is yawning.

f-structures have to fulfill two well-formedness conditions: they have to be both *complete* and *coherent*. Both these conditions will be discussed in the following sections.

# **7.1.2 Completeness**

Every head adds a constraint of the pred value of the corresponding f-structure. In determining completeness, one has to check that the elements required in the pred value are actually realized. In (12b), obj is missing a value, which is why (12a) is ruled out by the theory.

(12) a. \* David devoured. b. pred 'DEVOUR⟨SUBJ,OBJ⟩' subj pred 'DAVID'

# **7.1.3 Coherence**

The Coherence Condition requires that all argument functions in a given f-structure have to be selected in the value of the local pred attribute. (13a) is ruled out because comp does not appear under the arguments of *devour*.

(13) a. \* David devoured a sandwich that Peter sleeps.

The constraints on completeness and coherence together ensure that all and only those arguments required in the PRED specification are actually realized. Both of those constraints taken together correspond to the Theta-Criterion in GB theory (see page 92).4

4 For the differences between predicate-argument structures in LFG and the deep structure oriented Theta Criterion, see Bresnan & Kaplan (1982: xxvi–xxviii).

### **7.1.4 Restrictions on the c-structure/f-structure relation**

Symbols in c-structures are assigned restrictions for f-structures. The following symbols are used: '↑ ' refers to the f-structure of the immediately dominating node and '↓' refers to the f-structure of the c-structure node bearing the annotation. A common annotation is '↑ = ↓'. This constraint states that the f-structure of the mother node is identical to that of the annotated category:

$$\begin{array}{ll} \text{(14)} \quad \text{V}' \rightarrow & \text{V} \\ & \uparrow = \downarrow \\ \text{f-structure of the mother} = \text{own f-structure} \end{array}$$

The annotation '↑ = ↓' is below the head of a structure.

Phrases which are licensed by the annotated c-structure in (14) can be visualized as follows:

$$
\stackrel{\text{(15)}}{\underset{\text{v}}{\rightleftharpoons}}
\stackrel{\text{v}}{\underset{\text{v}}{\bigtriangleup}}
$$

(16) shows a V′ rule with an object:

$$\begin{array}{ccccc} \text{(16)} & \text{V}' & \rightarrow & \text{V} & \text{NP} \\ & & \uparrow = \downarrow & \text{(\uparrow OBI)} = \downarrow \end{array}$$

The annotation on the NP signals that the obj value in the f-structure of the mother (↑ OBJ) is identical to the f-structure of the NP node, that is, to everything that is contributed from the material below the NP node (↓). This is shown in the figure in (17):

In the equation (↑ OBJ) = ↓, the arrows '↑ ' and '↓' correspond to feature structures. '↑ ' and '↓' stand for the and in equations such as (6).

(18) is an example with an intransitive verb and (19) is the corresponding visualization:

$$\begin{array}{ll} \text{(18)} \quad sneezed \quad \text{V} & \text{(\uparrow \text{ PRED})} = \text{'SNEZE} \text{(SUBJ)'}\\ & \text{(\uparrow \text{ TENSE})} = \text{PAST} \end{array}$$

(19) V sneezed pred 'SNEEZE⟨SUBJ⟩' tense PAST

### **7.1.5 Semantics**

Following Dalrymple (2006: 90–92), *glue semantics* is the dominant approach to semantic interpretation in LFG (Dalrymple, Lamping & Saraswat 1993; Dalrymple 2001: Chapter 8). There are, however, other variants where Kamp's discourse representation structures (Kamp & Reyle 1993) are used (Frey & Reyle 1983b,a).

In the following, glue semantics will be presented in more detail.5 Under a glue-based approach, it is assumed that f-structure is the level of syntactic representation which is crucial for the semantic interpretation of a phrase, that is, unlike in GB theory, it is not the position of arguments in the tree which plays a role in the composition of meaning, but rather functional relations such as SUBJ and OBJ. Glue semantics assumes that each substructure of the f-structure corresponds to a semantic resource connected to a meaning and, furthermore, that the meaning of a given f-structure comes from the sum of these parts. The way the meaning is assembled is regulated by certain instructions for the combination of semantic resources. These instructions are given as a set of logic premises written in linear logic as *glue language*. The computation of the meaning of an utterance corresponds to a logical conclusion.

This conclusion is reached on the basis of logical premises contributed by the words in an expression or possibly even by a syntactic construction itself. The requirements on how the meaning of the parts can be combined to yield the full meaning are expressed in linear logic, a resource-based logic. Linear logic is different from classic logic in that it does not allow that premises of conclusions are not used at all or more than once in a derivation. Hence, in linear logic, premises are resources which have to be used. This corresponds directly to the use of words in an expression: words contribute to the entire meaning exactly once. It is not possible to ignore them or to use their meaning more than once. A sentence such as *Peter knocked twice.* does not mean the same as *Peter knocked*. The meaning of *twice* must be included in the full meaning of the sentence. Similarly, the sentence cannot mean the same as *Peter knocked twice twice.*, since the semantic contribution of a given word cannot be used twice.

The syntactic structure for the sentence in (20a) together with its semantic representation is given in (20b):

(20) a. David yawned.

The semantic structure of this sentence is connected to the f-structure via the correspondence function (depicted here as a dashed line). The semantic representation is derived from the lexical information for the verb *yawned*, which is given in (21).

(21) .*yawn*′ () : (↑ SUBJ) −◦ ↑

This formula is referred to as the *meaning constructor*. Its job is to combine the meaning of *yawned* – a one place predicate .*yawn*′ () – with the formula (↑ SUBJ) −◦ ↑ in

5 The following discussion heavily draws from the corresponding section of Dalrymple (2006). (It is a translation of my translation of the original material into German.)

linear logic. Here, the connective −◦ is the *linear implication* symbol of linear logic. The symbol contains the meaning that *if* a semantic resource (↑ SUBJ) for the meaning of the subject is available, *then* a semantic resource for ↑ must be created which will stand for the entire meaning of the sentence. Unlike the implication operator of classic logic, the linear implication must consume and produce semantic resources: the formula (↑ SUBJ) −◦ ↑ states that if a semantic resource (↑ SUBJ) is found, it is consumed and the semantic resource ↑ is produced.

Furthermore, it is assumed that a proper name such as *David* contributes its own semantic structure as a semantic resource. In an utterance such as *David yawned*, this resource is consumed by the verb *yawned*, which requires a resource for its SUBJ in order to produce the resource for the entire sentence. This corresponds to the intuition that a verb in any given sentence requires the meaning of its arguments in order for the entire sentence to be understood.

The f-structure of *David yawned* with the instantiated meaning construction contributed by *David* and *yawned* is given in (22):

(22) : " pred 'YAWN⟨SUBJ⟩' subj : - pred 'DAVID' # **[David]** *david*′ : **[yawn]** .*yawn* ′ () : −◦

The left side of the meaning constructor marked by **[David]** is the meaning of the proper name *David*, *david*′ to be precise. The left-hand side of the meaning constructor **[yawn]** is the meaning of the intransitive verb – a one-place predicate .*yawn*′ ().

Furthermore, one must still postulate further rules to determine the exact relation between the right-hand side (the glue) of the meaning constructors in (22) and the lefthand side (the meaning). For simple, non-implicational meaning constructors such as **[David]** in (22), the meaning on the left is the same as the meaning of the semantic structure on the right. Meaning constructors such as **[yawn]** have a -expression on the left, which has to be combined with another expression via functional application (see Section 2.3). The linear implication on the right-hand side must be applied in parallel. This combined process is shown in (23).

$$\begin{array}{c} \text{(23)} \\ \qquad \qquad \begin{array}{c} \text{x} : f\_{\sigma} \\ \text{P} : f\_{\sigma} \multimap g\_{\sigma} \end{array} \\ \hline \begin{array}{c} \text{(23)} : g\_{\sigma} \end{array} \end{array}$$

The right-hand side of the rule corresponds to a logical conclusion following the *modus ponens* rule. With these correspondences between expressions in linear logic and the meanings themselves, we can proceed as shown in (24), which is based on Dalrymple (2006: 92). After combining the respective meanings of *yawned* and *David* and then carrying out -reduction, we arrive at the desired result of *yawn*′ (*david*′ ) as the meaning of *David yawned*.

Glue analyses of quantification, modification and other phenomena have been investigated in a volume on glue semantics (Dalrymple 1999). Particularly problematic for these approaches are cases where there appear to be too many or too few resources for the production of utterances. These kinds of cases have been discussed by Asudeh (2004).

## **7.1.6 Adjuncts**

Adjuncts are not selected by their head. The grammatical function adj is a non-governable grammatical function. Unlike arguments, where every grammatical function can only be realized once, a sentence can contain multiple adjuncts. The value of adj in the f-structure is therefore not a simple structure as with the other grammatical functions, but rather a set. For example, the f-structure for the sentence in (25a) contains an adj set with two elements: one for *yesterday* and one for *at noon*.

(25) a. David devoured a sandwich at noon yesterday.

$$\begin{array}{|c|c|c|}
\hline
\text{ } & \text{'DEVOUR (SUBJ, OBJ)'} \\
\text{'SUBJ} & \text{'PRED 'DAVI'} \\
\text{b.} & \begin{bmatrix} \text{spEC} & \text{A} \\ \text{PRED} & \text{'SAND} \text{WICH'} \end{bmatrix} \\
\text{ADJ} & \left\{ \begin{bmatrix} \text{PRED 'YESTERDAY'} \end{bmatrix}, \begin{bmatrix} \text{PRED 'AT\{OBJ\}'} \\ \text{OBJ} \end{bmatrix} \begin{bmatrix} \text{PRED 'AT\{OBJ\}'} \end{bmatrix} \right\} \\
\hline
\end{array}$$

The annotation on the c-structure rule for adjuncts requires that the f-structure of the adjuncts be part of the adj set of the mother's f-structure:

$$\begin{array}{ccccc} \text{(26)} & \text{V}' & \rightarrow & \text{V}' & \text{PP} \\ & & \uparrow = \downarrow & \downarrow \in \text{(\uparrow ADJ)} \end{array}$$

The representation of adjuncts in a set is not sufficient to characterize the meaning of an utterance containing scope-bearing adjuncts (as for instance the negation in sentences like (31) on page 104). In order to determine scopal relations, one has to refer to the linear order of the adjuncts, that is, the c-structure. For linearization restrictions in LFG, see Zaenen & Kaplan (1995).

# **7.2 Passive**

Bresnan & Mchombo (1995) argue that one should view words as "atoms" of which syntactic structure is comprised (*lexical integrity*6 ). Syntactic rules cannot create new words or make reference to the internal structure of words. Every terminal node (each "leaf" of the tree) is a word. It follows from this that analyses such as the GB analysis of Pollock (1989) in Figure 7.1 on the next page for the French example in (27) are ruled out (the figure is taken from Kuhn 2007: 617):

(27) Marie Marie ne neg parlerait speak.cond.3sg pas neg 'Marie would not speak.'

In Pollock's analysis, the various morphemes are in specific positions in the tree and are combined only after certain movements have been carried out.

The assumption of lexical integrity is made by all theories discussed in this book with the exception of GB and Minimalism. However, formally, this is not a must as it is also possible to connect morphemes to complex syntactic structures in theories such as Categorial Grammar, GPSG, HPSG, CxG, DG and TAG (Müller 2018b: Section 4). As far as I know, this kind of analysis has never been proposed.

Bresnan noticed that, as well as passivized verbs, there are passivized adjectives which show the same morphological idiosyncrasies as the corresponding participles (Bresnan 1982b: 21; Bresnan 2001: 31). Some examples are given in (28):

	- b. a recently given talk (give given)
	- c. my broken heart (break broken)
	- d. an uninhabited island (inhabit inhabited)
	- e. split wood (split split)

If one assumes lexical integrity, then adjectives have to be derived in the lexicon. If the verbal passive were not a lexical process, but rather a phrase-structural one, then the form identity would remain unexplained.

In LFG, grammatical functions are primitives, that is, they are not derived from a position in the tree (e.g., Subject = SpecIP). Words (fully inflected word-forms) determine the

6 See Anderson (1992: 84) for more on lexical integrity.

Figure 7.1: Pollock's analysis of *Marie ne parlerait pas* 'Marie would not speak.' according to Kuhn (2007: 617)

grammatical function of their arguments. Furthermore, there is a hierarchy of grammatical functions. During participle formation in morphology, the highest verbal argument is suppressed. The next highest argument moves up and is not realized as the object but rather as the subject. This was explicitly encoded in earlier work (Bresnan 1982b: 8):

(29) Passivization rule: (SUBJ) ↦→ ∅/(OBL) (OBJ) ↦→ (SUBJ)

The first rule states that the subject is either not realized (∅) or it is realized as an oblique element (the *by*-PP in English). The second rule states that if there is an accusative object, this becomes the subject.

In later work, the assignment of grammatical functions was taken over by Lexical Mapping Theory (Bresnan & Kanerva 1989). It is assumed that thematic roles are ordered in a universally valid hierarchy (Bresnan & Kanerva 1989; Bresnan 2001: 307): agent > beneficiary > experiencer/goal > instrument > patient/theme > locative. Patient-like roles are marked as unrestricted ([−r]) in a corresponding representation, the so-called a-structure. Secondary patient-like roles are marked as *objective* ([+o]) and all other roles are marked as non-objective ([−o]). For the transitive verb *schlagen* 'to beat', we have the following:

(30) Agent Patient a-structure *schlagen* 'beat' ⟨ x y ⟩ [−o] [−r]

The mapping of a-structure to f-structure is governed by the following restrictions:

	- b. The argument roles are connected to grammatical functions as shown in the following table. Non-specified values for o and r are to be understood as '+':
		- [−r] [+r] [−o] SUBJ OBL
		- [+o] OBJ OBJ
	- c. Function-Argument Biuniqueness: Every a-structure role must be associated to exactly one function and vice versa.

For the argument structure in (30), the principle in (31a) ensures that the agent x receives the grammatical function SUBJ. (31b) adds an o-feature with the value '+' so that the patient y is associated with OBJ: