Evolution of Syntactic-Semantic Interface in Linguistics

1. The History of Formal Semantics: A History of Ideas and Controversies ______________________________Lecture 2: History of the Syntax-Semantics Interface Barbara H. Partee partee@linguist.umass.eduFall School for Formal Syntax and Formal Semantics HSE, Moscow, September 1-7, 2019

2. 1. Introduction • In this lecture I trace key developments in the history of the relation of semantics to syntax, focusing on the period from the beginnings of Chomskyan generative grammar in the 1950’s up until the mature period of formal semantics in the 1980’s. • A central theme is the challenge of developing a compositional semantic theory, and how that challenge has taken on different forms with respect to different syntactic and semantic theories. • The “syntax-semantics interface” is a relatively young topic in the history of linguistics. In early Western linguistics, there was little syntax and essentially no semantics other than some non-formal lexical semantics. • Formal syntax came first, with Noam Chomsky revolutionizing the field of linguistics with his work on syntax. HSE Lecture 2 51 total

3. Intro, cont’d. • Chomsky shared the field’s general skepticism about the possibility of semantics as a subject of scientific study. • But as semantics began to be developed in the context of generative grammar, the issue of the connection between syntax and semantics came to the fore very quickly and soon became a major area of research. • “Formal semantics” arose a little later, with the logician Richard Montague as the key figure in its origins, and linguists, logicians, and philosophers cooperated in its early development. • From both the syntactic and the semantic side, the emphasis was on the structure of sentences more than on the structure of words, and formal semantics has always been in large part “the semantics of syntax.” HSE Lecture 2 51 total

4. 2. Syntax-semantics before Syntactic Structures • Reviewing Lecture 1: Part of the Chomskyan revolution was to view linguistics as a branch of psychology (cognitive science) rather than philology or anthropology. • But semanticssuffered from a mixture of negative attitudes and neglect in American linguistics in the 20th century. • European linguists did study lexical semantics, which was important for philology and historical linguistics. But that did not involve syntax-semantics interface issues in any systematic way. • The great progress in semantics in logic and philosophy in the late 19th and early 20th centuries was unknown to most linguists. • So before Syntactic Structures (1957) there was no syntax-semantics interface to think about in generative linguistics, and the logicians’ descriptions of the syntax and semantics of their logical languages had no influence on linguistics. HSE Lecture 2 51 total

5. 3. Syntactic Structures and Chomsky’s early ambivalence • Chomsky was always ambivalent about semantics as a science and about its relation to syntax. This is evident in Syntactic Structures and also in his earlier The Logical Structure of Linguistic Theory (LSLT). In LSLT, Chomsky writes in the first chapter: • I will merely emphasize again that the “legitimacy of semantics” (whatever that might mean) has never, to my knowledge, been challenged, nor has there ever been any question of the importance of incorporating a study of reference, meaning, language use, and related topics within a full theory of language that will deal, in particular, with the highly significant relations between formal structure and semantic interpretation. … The [study of meaning] is unquestionably central to the general theory of language, and a major goal of the SS-LSLT approach is to advance it by showing how a sufficiently rich theory of linguistic form can provide structural descriptions that provide the basis for the fruitful investigation of semantic questions. [emphasis added - BHP] (Chomsky 1975b:21) HSE Lecture 2 51 total

6. Syntactic Structures and Chomsky’s ambivalence, cont’d. • And from the concluding paragraph of Syntactic Structures: • “More generally, it appears that the notion of “understanding a sentence” must be partially analyzed in grammatical terms. To understand a sentence it is necessary (though not, of course, sufficient) to reconstruct its representation on each level, including the transformational level where the kernel sentences underlying a given sentence can be thought of, in a sense, as the ‘elementary content elements’ out of which this sentence is constructed. • “In other words, one result of the formal study of grammatical structure is that a syntactic framework is brought to light which can support semantic analysis. Description of meaning can profitably refer to this underlying syntactic framework, although systematic semantic considerations are apparently not helpful in determining it in the first place. … continued on next slide -- HSE Lecture 2 51 total

7. Syntactic Structures and Chomsky’s ambivalence, cont’d. • “It is questionable that the grammatical devices available in language are used consistently enough so that meaning can be assigned to them directly. Nevertheless, we do find many important correlations … between syntactic structure and meaning ... These correlations could form part of the subject matter for a more general theory of language concerned with syntax and semantics and their points of connection.” (Chomsky 1957:107–108) • Much of Chomsky’s early emphasis on the “autonomy of syntax” is directed against earlier attempts to base syntax on semantics or reduce much of syntax to semantics, or to give semantic explanations for various syntactic phenomena and restrictions. • We might loosely paraphrase Chomsky’s attitude around the time of Syntactic Structures thus: “We don’t really understand anything about semantics, which is a subject not so far amenable to scientific investigation; but semantics is in principle important, and deep structure reveals semantically relevant structure that is obscured in surface structure.” HSE Lecture 2 51 total

8. Syntactic Structures and Chomsky’s ambivalence, cont’d. • The importance of deep structure for semantics is illustrated in Chomsky’s famous pair easy to pleasevs. eager to please. (1) a. John is easy to please < (for someone) to please John is easy
 b. John is eager to please < John is eager (for John) to please (someone) • But sometimes transformations change meaning: Chomsky (1957) noted that the following active-passive pair have different meanings, with the first quantifier having wider scope in each case: (2) a. Everyone in this room speaks two languages.
 b. Two languages are spoken by everyone in this room. • In later years, those judgments about (2) were questioned; it has been argued that one or both of (2a) and (2b) are ambiguous. Chomsky himself has a long footnote in Aspects(1965), noting that it is possible that both sentences are ambiguous, with unexplained factors making different readings preferred for (2a) and (2b). We return to the topic of quantifier scope further below. HSE Lecture 2 51 total

9. 4. From Syntactic Structures to Aspects: Katz, Fodor, Postal • At the beginning of the 1960’s, Jerrold Katz and Jerry Fodor, junior faculty at MIT, started developing proposals for how a semantic theory could be developed in a generative grammar framework. They were clearly concerned with what we now call compositionality, and which they called the Projection Problem. • Because such things as negation and question-formation were treated via transformations (T-NEG, T-Q) of affirmative declarative sentences, Katz and Fodor (1963) figured that the meaning must depend on the entire transformational history. The transformations are sketched in a very oversimplified way in (3a–b). (3) a. [Mary [has [visited Moscow]]] ⇒T-NEG [Mary [has not [visited Moscow]]] b. [Mary [has [visited Moscow]]] ⇒T-Q [has [Mary [visited Moscow]]] HSE Lecture 2 51 total

10. From Syntactic Structures to Aspects: Katz, Fodor, Postal, cont’d. Jerrold Katz (1932-2002) Jerry Fodor (1935-2017) HSE Lecture 2 51 total

11. From Syntactic Structures to Aspects: Katz, Fodor, Postal, cont’d. • Their idea for the syntax-semantics interface was to extend phrase-markers (trees) to T-markers (see (4) below) showing the transformational history of an expression, and computing the meaning on the basis of the whole T-marker. • (4) T-marker for (3a) = P-marker for the deep structure --- TNEG --- Taffix .... • = [Mary [has [visited Moscow]]] --- TNEG --- Taffix .... • Their T-markers, showing the whole syntactic derivation of a sentence, are analogous to Montague’s (later) derivation trees(Section 5 below). Both are examples of “tectogrammatical structures” (Section 13) • Their semantic rules operated first on the underlying Phrase-marker, bottom to top, to interpret that structure, and then a series of semantic rules corresponding to the transformational rules would apply, semantically transforming the result in appropriate ways. HSE Lecture 2 51 total

12. From Syntactic Structures to Aspects: Katz, Fodor, Postal, cont’d. • But as noted in Lecture 1, their semantics was very primitive. Katz and Fodor worked with “semantic features”, and their semantic representations had no real structure, just bundles of features – suitable at best for decompositions of one-place predicates. • Later they added some bits of structure to handle transitive verbs and their two arguments, but with no attention at all to things like quantifiers. • And what they were trying to capture was restricted to things that could be expressed in terms of ‘readings’ – how many, and same or different. Three main things to be captured were (i) ambiguity – having more than one reading; (ii) semantic anomaly – having no reading; (iii) synonymy – sharing a reading (synonymy on a reading), or the stronger version, having all the same readings. • And truth-conditions had no role in the semantics at all. In Lecture 1 I quoted David Lewis: “Semantics with no treatment of truth conditions is not semantics.” HSE Lecture 2 51 total

13. From Syntactic Structures to Aspects: Katz& Postal . Paul Postal (b. 1936) (Paul Schachter, foreground) at UCLA, 1969, by John Ohala • Then, as noted in Lecture 1, Katz and Postal (1964) made the innovation of putting such morphemes as Negand a Question morpheme into the Deep Structure, arguing that there was independent syntactic motivation for doing so, and then the meaning could be determined on the basis of Deep Structure alone. • This major change, accepted by Chomsky in Aspects (1965), rested on the claim that transformations are always meaning-preserving. HSE Lecture 2 51 total

14. From Syntactic Structures to Aspects: The Garden of Eden period • In Aspects, Chomsky tentatively accepted the Katz-Postal hypothesis, and redesigned the phrase-structure component so that all of the “kernel sentences” for a complex sentence were included in a single Deep Structure. • That Deep Structure was the input to semantics. • The brief period when Aspects held sway(roughly 1964-1967) was the only time in my memory when almost all generative grammarians believed that the form of syntactic theory was “finally understood”. • In that same “Garden of Eden” period, the syntax-semantics interface was believed to be relatively straightforward, thanks to the Katz-Postal hypothesis (even though conceptions of the nature of semantics were very primitive and entirely ‘representational’.) • The semantic rules, whatever they might be like, should simply apply bottom up to the nodes in the Deep Structure tree. HSE Lecture 2 51 total

15. 5. Expulsion from the Garden of Eden: The Linguistic Wars • But at least among working linguists, that very appealing view fell apart when the behavior of quantifiers was noticed. • The many differences between quantificational NPs and proper names (illustrated below) immediately created great conflicts between syntax and semantics, and in a sense kicked all of us generative grammarians out of our Garden of Eden. • A surprising historical accident is that the behavior of quantifiers with respect to transformational rules familiar from Syntactic Structures and Aspects was not really noticed until the Katz-Postal hypothesis had for most linguists reached the status of a necessary condition on writing rules. • I believe that this historical accident was one of the major causes of the “linguistic wars” between Generative Semantics and Interpretive Semantics, which I will describe below. • First I illustrate the problems raised by quantifiers. HSE Lecture 2 51 total

16. Expulsion from Garden of Eden & the Linguistic Wars, cont’d. • Here are some derivations that would have been given in the Aspects theory, where examples typically involved proper names like John and Mary, not quantifier phrases, as (6a-b). • We see that in the corresponding (c-d) examples with quantifier phrases, the transformations radically change the meaning (and it may change in different ways with different quantifiers). • I suspect that the Katz- Postal hypothesis would never have been suggested if such quantifier examples had been noticed earlier. (6)  a. John voted for himself. FROM:
 b. John voted for John.
 c. Every man voted for himself. FROM: d. Every man voted for every man. (7)  a. Mary wanted to win. FROM: b. Mary wanted Mary to win. c. Every candidate wanted to win. FROM: d. Every candidate wanted every candidate to win. 
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17. Expulsion from Garden of Eden & the Linguistic Wars, cont’d. (8) a. The pacifist who fought was inconsistent. FROM: b. The pacifist fought. The pacifist was inconsistent. c. All pacifists who fight are inconsistent. FROM: d. All pacifists fight. All pacifists are inconsistent. • Example (6) concerns the “Reflexivization Transformation”, originally operating on “identical NPs”. • Example (7) concerns the “Equi-NP Deletion Transformation”, originally posited for ‘control verbs’ like try, want, persuade. • Example (8) concerns relative clause formation, also originally formulated in terms of two identical NPs. • What all these examples revealed was that the syntactically simple notion of “identical NPs” was not a sound basis for accounting for the semantics of these constructions. • Clearly some big changes were needed – but the responses split the generative grammar community in two. HSE Lecture 2 51 total

18. Expulsion from Garden of Eden & the Linguistic Wars, cont’d. • The Generative Semantics response (Lakoff, Ross, McCawley, Postal, some Bach) was to make the deep structures “deeper”, and try to find a semantically sound level of underlying structure. • The underlying structures of the Generative semanticists became more and more abstract, often resembling first-order logic, and those structures plus the syntactic rules to get from there to surface structure often seemed “wild”. In one famous example, the underlying structure for “Floyd broke the glass” had 8 clauses. • (But What seemed “wild” then might not now: the shocking number of clauses in Ross’s deep structure for “Floyd broke the glass” is no more than the number of functional projections that now intervene between various pairs of “familiar” syntactic categories in respected generative analyses such as Cinque (1999).] • Interpretive semantics (Chomsky, Jackendoff) kept syntax close to classical transformational grammar, and worked on figuring out which parts of semantic interpretation should be based on deep structure, which on surface structure, which on something else, allowing for a more heterogeneous syntax-semantics relationship. HSE Lecture 2 51 total

19. Expulsion from Garden of Eden & the Linguistic Wars, cont’d. HSE Lecture 2 51 total

20. Expulsion from Garden of Eden & the Linguistic Wars, cont’d. • The impact of philosophy and logic on semantics in linguistic work of the 50's and 60's was limited; many linguists knew some first-order logic, aspects of which began to be borrowed into linguists’ “semantic representations,” and there was gradually increasing awareness of the work of some philosophers of language. • Generative semanticists in the late 1960’s and early 1970’s in particular started giving serious attention to issues of “logical form” in relation to grammar, and to propose ever more abstract underlying representations intended to serve simultaneously as unambiguous semantic representations and as input to the transformational mapping from meaning to surface form (Bach, Fillmore, Lakoff, McCawley, Karttunen). • Structures of “logical form” (or LF) that entered the work of Chomsky and his followers starting with the work of Robert May in many cases have clear antecedents in the work of the Generative Semanticists, although the architecture is different. HSE Lecture 2 51 total

21. My own experience of the Linguistic Wars • The seeds of the linguistic wars were being planted near the end of my graduate student career at MIT (I finished in June 1965), even before Aspects was published. (But the publication dates of all those important works are always a couple of years (or more) later than the peak of the discussion surrounding them.) • Lakoff and Ross were already starting doing Generative Semantics work in 1964-65; my dissertation included a section arguing against their idea that transitive open should be derived from an underlying structure like CAUSE (BECOME (open)), on the grounds that you can say A change in air pressure caused the door to openbut not A change in air pressure opened the door. • I was a syntactician, interested in logical structure, but afraid that all the semantic work I knew of seemed to be built on sand. One of my early papers, ‘On the requirement that transformations preserve meaning’, chronicled problems I saw on both sides of the debates. I didn’t myself see any good resolution. So I was very glad to discover a very different third possibility. HSE Lecture 2 51 total

22. 5. ThenMontaguesuggested a different Garden of Eden. • Richard Montague (1930-1971) was a logician and philosopher whose seminal works on language founded the theory known after his death as Montague grammar, one of the main starting points for the field of formal semantics. • The Fregean principle of compositionality was central to Montague’s theory and remains central in formal semantics. I repeat it here for emphasis. (9) The Principle of Compositionality: The meaning of any complex expression is a function of the meanings of its parts and of the way they are syntactically combined. • Bach (1989) summed up Chomsky’s and Montague’s innovations thus: Chomsky’s Thesis was that English can be described as a formal system; Montague's Thesis was that English can be described as an interpreted formal system. HSE Lecture 2 51 total

23. Montague, cont‘d. • So what did the syntax-semantics interface look like in Montague’s work, in particular in the fragment of English in “The proper treatment of quantification in ordinary English”? • Syntactic rules build up expressions from their parts; and for each syntactic rule there is a semantic rule that specifies how the meanings of the parts are to be combined to get the meaning of the whole. • Syntax is an algebra of ‘forms’, semantics is an algebra of ‘meanings’, and there is a homomorphism mapping the syntactic algebra into the semantic algebra. • The crucial syntactic structure for semantics is the “derivation tree”, showing what parts have been combined at each step, by what syntactic rule. • The semantic interpretation rules apply in steps according to that derivation tree, interpreting the output of each syntactic ‘combining’ step as a corresponding semantic function applied to the meanings of the parts that were combined. HSE Lecture 2 51 total

24. Montague, cont‘d. • One important distinction: A syntactic rulemay involve more than one syntactic “operation”. One syntactic rule in PTQ forms a sentence from an NP and a VP. That rule involves both concatenation and subject-verb agreement. • English uses the syntactic operation of “subject - Aux inversion” in a number of rules – the formation of yes-no questions, of Wh-questions, exclamatives, conditionals, with fronted negative adverbs, etc.., as illustrated in (10a-e) below. (10) a. Was Arthur ever in trouble? b. When was Arthur in trouble? c. Was Arthur ever in trouble!! d. Were Arthur ever in trouble, his father would know about it. e. Never before had Arthur been in such trouble. • That operation can be thought of as a “Macro” used in English syntactic rules. It has no semantic interpretation of its own. Compositionality cares about the rules, not the operations. HSE Lecture 2 51 total

25. Montagueandthe syntax-semantics interface • Montague was not a syntactician. He had some interesting syntactic insights, but had no independent interest in syntax. For him, syntax was a necessary basis for semantic structure: syntax should provide the relevant “part – whole” structure for compositionality to work. • It was left to others, mostly linguists, to explore what kinds of syntactic components would be good candidates for the needed “syntactic algebra”, simultaneously providing the necessary basis for semantic interpretation and satisfying linguists’ criteria for explanatory adequacy in syntax. • One key insight that linguists got from Montague (and from David Lewis and Terry Parsons), which traces back to Frege: Function-argument structure provides some of the basic semantic glue, the basis for HOW meanings combine. Example: former (senator) : former denotes a function that applies to a property P and forms a new property which is true of an individual x if P was true of x in the past. HSE Lecture 2 51 total

26. Montagueandthe syntax-semantics interface, cont‘d. • As both David Lewis and Montague pointed out, categorial grammar, invented by the Polish logician Ajdukiewicz, is designed to expressly capture function-argument structure in the syntax. • Instead of a phrase-structure rule like S → NP VP, in a categorial grammar, the category VP might be represented as S\NP, something that combines with an NP on its left to make an S. • And semantically, an expression of category S\NP would be interpreted as a function that applies to the meaning of an NP to make a sentence meaning. • So a pure categorial grammar would automatically have a compositional semantics, and the syntax-semantics interface would be almost trivially simple. [More in Lecture 4.] • In fact, the whole grammar would be encoded in the lexical categories. A transitive verb would be an (S\NP)/NP, interpreted as a function that applies to the meaning of its object to make a function that applies to the subject to give a sentence meaning. HSE Lecture 2 51 total

27. Montagueandthe syntax-semantics interface, cont‘d. • Of course, natural languages are not quite that simple; pure categorial grammars have the same shortcomings as other context-free phrase structure grammars. • David Lewis in ‘General semantics’ (1970) suggested having a categorial grammar for the Base component of a transformational grammar, if transformations can be meaning-preserving. Montague provided categorial-grammar style syntactic categories, but did not limit his syntactic rules to simple concatenation, building something like transformational power into the bottom-up construction rules. • Emmon Bach (early 1980s) advocated “extended categorial grammars” with enough extra power to handle various sorts of discontinuous constituents and word order alternations while keeping the basic function-argument architecture of categorial grammars. • Other ideas of Montague’s and his colleagues entered linguistics as attempts were made to combine their ideas with Chomsky’s. HSE Lecture 2 51 total

28. 6. Towards a synthesisofMontagueand Chomsky • Montague’s work was first introduced to linguists by Partee and Thomason in the early 1970’s. Partee’s goal was to find a way to combine Montague’s semantics (MG) with Chomskian transformational grammar (TG). • In Lecture 1 I described the obstacle faced by the existence of deletion transformations, like the “Equi-NP Deletion” used in the derivation of control sentences like Mary was eager to win. • In a compositional semantics, there is no analog of “deleting” the meaning of one of the constituent parts of a construction. • The resolution came with the awareness that deletion was the wrong way to think about those control sentences in the first place, as witnessed by the semantic problems raised by quantifiers, illustrated earlier. The meaning of Everyone wanted to windoes not contain “two instances” of the meaning of everyone, only one. • The formation of an infinitival phrase involves something like lambda abstraction, “the property of being an x such that x wins”, represented in current generative syntax by PRO win. HSE Lecture 2 51 total

29. Towardsa synthesisofMontagueandChomsky, cont‘d. • One of the central questions dividing generative semantics and interpretive semantics had been “Do transformations ever change meaning?”. • The Katz-Postal hypothesis had posited the answer “No”, and Chomsky had accepted that answer, tentatively, in Chomsky (1965). • But as the generative semanticists took that “No” answer farther, Chomsky and the interpretive semanticists rejected it, and were left without a clear picture of the nature of the syntax-semantics interface. • Montague gave a different kind of answer. For him, the syntactic Rules which combine parts into larger wholes might compose phrase-structure-like operations and transformation-like operations together. • Partee, Bach, Parsons, Dowty, others worked in the 70’s on finding ways to modify both MG and TG to make them fit together. But then new developments in non-transformational grammar came along. HSE Lecture 2 51 total

30. Towardsa synthesisofMontagueandChomsky, cont‘d. Terry Parsons (b. 1939), Barbara Partee (b. 1940), Emmon Bach (1929-2014) at the 1974 LSA Linguistic Institute at UMass Amherst. HSE Lecture 2 51 total

31. 8. GPSG andthepossibilityofeliminatingtransformations • One interesting possibility raised in Montague’s work, a new idea for generative linguists at the time, was that for sentences like Mary/everyone was eager to win, there doesn’t have to be an embedded full sentence in the syntax at all. An embedded VP is enough, and the “identity” between the subject of be eagerand the subject of wincan be part of the semantics of predicates like eager. • Control can be considered a lexical semantic property of verbs (Chierchia, 1983). Lexical semantics can include the information that, for instance, X promises Y to leave entails that X promises Y that X will leave; or that X tries to winentails that X acts with the goal of bringing about a state of affairs in which X wins. • Similarly for the relation between active and passive sentences: as (Dowty, 1978) argued, all “governed transformations”, that is, transformations whose conditions of application depend on the presence of a lexical item of an appropriate sort (“transitive verb”, approximately, in the case of passive), could be and arguably should be replaced by lexical rules. HSE Lecture 2 51 total

32. GPSG andthepossibilityofeliminatingtransformations, cont‘d. • That is, instead of a transformation mapping (14a) into (14b), there should be a lexical rule as in (15): (14) a. Archaeologists have discovered a new fossil skeleton. b. A new fossil skeleton has been discovered by archaeologists. (15) (simplified): If V is a transitive verb with syntactic frame NP1___ NP2 and with meaning α, then V+ed is a (passive) verb with syntactic frame NP2be ___ ( by NP1), whose meaning is the “inverse” of α. David Dowty HSE Lecture 2 51 total

33. GPSG andthepossibilityofeliminatingtransformations, cont‘d. • So when it was noticed that many arguments for “syntactic relatedness” that motivated transformations were implicitly semantic, this led to the renewed interest in the possibility of English as a context‑free language first raised by Gil Harman in 1963. • Dowty’s reformulation of governed transformations as lexical rules was an important step towards non-transformational grammars. • Such an approach was developed in Generalized Phrase Structure Grammar (GPSG), first by Gazdar in 1982 and then in subsequent work by Gazdar, Pullum, Klein, and Sag. • A later variant, Head-Driven Phrase Structure Grammar (HPSG), incorporating some ideas from Bach’s work on extended categorial grammars and other new ideas, was developed by Pollard and Sag. • Both GPSG and HPSG have MG-like compositional semantic rules. • Bresnan and Kaplan’s Lexical Functional Grammar (LFG), another thriving alternative approach, is also non-transformational and fully compositional. HSE Lecture 2 51 total

34. GPSG andthepossibilityofeliminatingtransformations, cont‘d. Gerald Gazdar (b. 1950), Ewan Klein (b. 1949), Geoffrey Pullum (b. 1945), Ivan Sag (1949-2013) HSE Lecture 2 51 total

35. GPSG andthepossibilityofeliminatingtransformations, cont‘d. • Non-transformational grammars, also called monostratal, have long been preferred for computational linguistic applications. (Only recently have computationally tractable versions of Chomskyan Minimalist grammars been developed.) • Among linguists, there was for several decades a de facto correlation between doing formal semantics and preferring one of the monostratal syntactic theories. Compositionality was more straightforward with such theories, the syntactic theories were ‘cleaner’ and much easier to formalize, and there was enthusiasm for seeing how much could be explained within the semantics. • This preference was never absolute, however, and especially since the 90’s, with Heim and Kratzer among the leaders, many contemporary linguists combine contemporary Chomskyan syntax with formal semantics. (Section 11 below.) HSE Lecture 2 51 total

36. 9. Quantifier scope ambiguity: a perennial problem for the syntax-semantics interface • In both transformational and non-transformational syntactic theories, the problem of quantifier scope ambiguity has remained a difficult one: it is in fact a difficult problem for every theory of the syntax-semantics interface. • The basic problem is that if one accepts the principle of compositionality, then an ambiguous sentence like (16) must have two different syntactic structures, even though there may be no independent syntactic evidence of ambiguity. (16) Every student read one book. • One can hardly count the number of different solutions that have been proposed to the problem of quantifier scope ambiguity. • In an remarkable 1976 paper, Cooper and Parsonscompared how Generative Semantics, interpretive semantics, and Montague grammar handled quantifier scope ambiguities and provided an algorithm for converting among them. HSE Lecture 2 51 total

37. Quantifier scope ambiguity, cont’d. • Here we give a thumbnail sketch of six different approaches to quantifier scope ambiguity from the 60’s to the 80’s, before the introduction of choice functions and various non-quantificational analyses of indefinites. There are many more approaches by now. • (i) Generative semantics (Lakoff, McCawley et al): Underlying structures similar to first-order logic structure, plus a transformation of Quantifier Lowering. The (imagined) need to constrain derivations so that scope corresponded to surface c-command led to “Transderivational Constraints”. • (ii) Interpretive semantics (Chomsky, 1971, Jackendoff, 1972) proposed a separate mechanism for quantifier scope; see Cooper and Parsons 1976 for a reformulation as an indexing mechanism. • (iii) Montague’s “Rule-by-rule” approach, with a rule of Quantifying In. Different derivational order of quantifying in different quantifiers can result in different scopes for the same surface structure. Compositionality is homomorphism between syntactic and semantic derivations. HSE Lecture 2 51 total

38. Quantifier scope ambiguity, cont’d. • (iv) Cooper storage (Cooper, 1975). Cooper proposed that the semantics should compositionally derive a set of interpretations for each syntactic structure. Working up the syntactic tree, when you reach a quantifier phrase, you can optionally “store” it, then “retrieve it” from storage when you hit a suitable higher node, like an S or a VP. (Scope islands represent points in the derivation where the store must be empty.) Cooper storage was also used in GPSG– their only exception to surface compositionality. • (v) Quantifier Raising (May, 1977). May’s Quantifier Raising rule is a syntactic rule, roughly the inverse of the Generative Semantics rule of Quantifier Lowering. Quantifier Raising (QR) produces a derived syntactic structure dubbed LF (for “logical form”); that’s the syntactic level that gets compositionally interpreted. • (vi) Type-shifting (Hendriks, 1988). On Hendriks’s approach, there is no ‘movement’; alternative readings are derived via type-shifting of verbs and other functors so as to change relative ‘function-argument command’ relations. (Type-shifting is in Lecture 4) HSE Lecture 2 51 total

39. 10. “Logical Form” or “LF” in later generative grammar • Generative semantics lost favor for a complex of reasons; but not because of any great success of “interpretive semantics”. • I will not discuss the waning of the Linguistic Wars here -- see books by Newmeyerand Randy Harris -- but I will state as my own opinion that some of the semantics that was developed under the label of “Logical Form” or “LF” in the Chomskyan school (first within the Revised Extended Standard Theory, continuing in later theories) amounted to an adaptation or rediscovery of various ideas from Generative Semantics but “upside down”: LF was not viewed by Chomskyans as a “deep structure”, but as a derived syntactic level. So where Generative Semantics had “Quantifier Lowering”, May (1977) invented “Quantifier Raising” in LF. • Chomsky himself has remained quite skeptical of whether “real semantics” belongs in linguistics; he seems to have some respect for it, but he also seems inclined to draw a line at some syntactic level such as LF: something which may have a close relation to semantics, but is still syntactic in form. HSE Lecture 2 51 total

40. 11. Later synthesis: Heim, Kratzer doing formal semantics on (improved) LF • Both Generative Semantics and Logical Form in Chomskyan theories included structures that were hard to make clear semantic sense of. Many of us tended to dismiss those approaches as just “semantic representations” unsuitable for “real semantics”. • But Irene Heim in her 1982 dissertation made some simple but fundamental changes that made it possible to give a compositional formal semantic interpretation of sentences represented at a suitably designed level of “Logical Form”. • I have always recommended Heim’s dissertation as possibly the finest dissertation ever written. When I interviewed her for my history project, I commented that she was the first of Emmon’s or my PhD students to write a semantics dissertation using Chomskyan syntax. Her response was interesting. HSE Lecture 2 51 total

41. Synthesis: Heim & Kratzer’s formal semantics with LF, cont’d. • Heim: “Right. So that was at a point -- this was a couple of years then after the Pisa lectures, and a revolution, and you know, that was something ... So there had been a perception that if you’re serious and precise about semantics, you had to do a particular kind of syntax. So either you were a syntactician who really didn’t know what a quantifier was, or you were a semanticist and you had to do categorial syntax or GPSG or whatever it was, right. And it just didn’t seem that the connections were that logical between these choices, and that was a point I wanted to make in my dissertation. • Her Chapter II has rules of construal for building generative grammar Logical Forms, revised so that they could be semantically interpreted in the way that she wanted. That chapter was immensely influential, and also changed Chomsky’s attitude towards semantics. HSE Lecture 2 51 total

42. Synthesis: Heim & Kratzer’s formal semantics with LF, cont’d. • Kai von Fintel, when he was featured linguist on the LSA site with a “spotlight” interview in September 2015, was asked to name his favorite linguistics article or study. Without hesitation he replied “Irene Heim’s dissertation. It was a defining moment in the development of modern natural language semantics at the confluence of work deriving from formal logic and the generative linguistic framework." • Irene clearly accomplished in 1983 what I had tried and failed to do in my early attempts to synthesize MG and TG, and research at what soon came to be called the syntax-semantics interface developed by leaps and bounds. • The influence of this new direction, incorporating Chomskyan approaches to syntax with formal semantics, was soon apparent in the establishment of a new conference (SALT), a new journal (Natural Language Semantics, with founding editors Heim and Kratzer), and a new textbook (Heim & Kratzer). HSE Lecture 2 51 total

43. Synthesis: Heim & Kratzer’s formal semantics with LF, cont’d. Irene Heim, b.1954 Angelika Kratzer, b. 1948 HSE Lecture 2 51 total

44. Synthesis: Heim & Kratzer’s formal semantics with LF, cont’d. • The architecture of the syntax-semantics interface on the model of the Heim and Kratzer textbook is that there are syntactic rules that derive a Logical Form for each sentence, and then the compositional semantic interpretation rules operate directly on that structure. • To a classical Montague grammarian, the unattractive feature of that approach is that it gives up on being able to compositionally interpret the independently motivated syntactic structure of sentences. • The attractive feature is that there is a rather close match between the structure represented by a Montagovian “derivation tree” and the structure of a Heim & Kratzer LF tree. • The formal semantics community remains congenial while pursuing different approaches. There are quite a few different conceptions of the nature of the syntax-semantics interface under active development, with open lines of communication and sharing of ideas. HSE Lecture 2 51 total

45. 12. Alternative conceptions of syntax and semantics and their interface • The two kinds of approaches involving formal semantics are the non-transformational theories mentioned earlier, and the now flourishing work combining Chomskyan syntax, with a level of LF, and formal semantics initiated by Heim and Kratzer. • The contemporary architectures that are probably closest to the vision of what Montague’s ideas might make possible are various kinds of “Surface Compositionality” (Barker and Jacobson, 2007, Jacobson, 1999), employing syntactic theories that generate surface structures directly, and interpreting them compositionally. Polly Jacobson HSE Lecture 2 51 total

46. 13. Tectogrammatical Structure • One promising way of bringing different particular theories closer together is through approaches that invoke a “tectogrammatical” structure. • Tectogrammatical structure is used in Prague school linguistics, and also bears resemblance to David Lewis’s ‘structured meanings’. • The distinction between tectogrammatical and phenogrammatical structure comes from Haskell Curry (1961). • Tectogrammatical structure is analogous to Montague’s derivation trees; it reflects how a sentence is built up, abstracting away from language-particular realization. Haskell Curry 1900 - 1982 HSE Lecture 2 51 total

47. Tectogrammatical Structure, cont’d. • David Dowty (1982) advocated linguistic recognition of the tectogrammatical - phenogrammatical distinction, using a modified version of Montague’s analysis trees, eliminating the language-particular expressions at the nodes. • Montague’s distinction between syntactic rules (such as transitive verb-plus-object combination)and syntactic operations (such as concatenation and assignment of accusative case)corresponds to the tecto-/pheno- distinction. • Dowty suggested that the rules, and hence the tectogrammatical structures, may well be universal. What varies are the morpho-syntactic operations that are used in the rules. HSE Lecture 2 51 total

48. Tectogrammatical Structure, cont’d. • Reinhard Muskens (2010) offers a version which gives a core tectogrammatical structure for each sentence, and then with explicit mapping rules maps that common structure homomorphically both onto a morphosyntactic structure (and a terminal string) and a semantic interpretation. • This structure in effect shows the common algebraic structure of semantics and syntax for a language, and is compatible with many different theories of what meanings are and of morpho-syntactic structure. • As in Montague: syntax is an algebra, semantics is an algebra, and there should be a homomorphism between them. This is the same idea in cleaner and clearer form. Reinhard Muskens b. 1953 HSE Lecture 2 51 total

49. 14. Concluding remarks • Formal semantics is still a relatively young field. It has a small, but growing, presence in fieldwork and in language typology, and in psycholinguistics and theories of on-line language processing. But it has already had enough impact to convince linguists that it is important to study syntax and semantics together. • In recent decades, which I mostly have not discussed here, work at the syntax-semantics interface has been greatly enriched by the fact that it has become much more common for linguists who want to work on either syntax or semantics to feel some obligation to pay attention to both. • Syntax remains formally autonomous on many current approaches, but the goal of compositionality is now a widely shared goal, and it is understood that both syntactic and semantic evidence can be important for the finding the best syntactic or semantic analysis of any phenomenon, and essential for figuring out the best division of labor between syntax and semantics and the nature of the interface between them. HSE Lecture 2 51 total

50. Selected references More material and fuller references can be found in several papers, versions of which are downloadable from my site, http://people.umass.edu/partee/ . • Partee, Barbara H. 2011. Formal semantics: Origins, issues, early impact. In Formal Semantics and Pragmatics. Discourse, Context, and Models., eds. Partee, Glanzberg and Skilters, 1-52. http://thebalticyearbook.org/journals/baltic/article/view/1580/1228 . • Partee, Barbara H. 2014. A brief history of the syntax-semantics interface in Western formal linguistics. Semantics-Syntax Interface 1.1:1-20. https://semanticsarchive.net/Archive/zJjODVlN/ . • Partee, Barbara H. In press. A note on varieties of syntax in the history of formal semantics. In Making Worlds Accessible, eds. Rajesh Bhatt, IlariaFrana and Paula Menéndez-Benito. Amherst, MA: Linguistics Dept, UMass Amherst. https://semanticsarchive.net/Archive/TgzMDIyO/ . HSE Lecture 2 51 total