The central topic of this inquiry is a cross-linguistic contrast in the interaction of conjunction and negation. In Hungarian (Russian, Serbian, Italian, Japanese), in contrast to English (German), negated definite conjunctions are naturally and exclusively interpreted as `neither’. It is proposed that Hungarian-type languages conjunctions simply replicate the behavior of plurals, their closest semantic relatives. More puzzling is why English-type languages present a different range of interpretations. By teasing out finer distinctions in focus on connectives, syntactic structure, and context, the (...) paper tracks down missing readings and argues that it is eventually not necessary to postulate a radical cross-linguistic semantic difference. In the course of making that argument it is observed that negated conjunctions on the `neither’ reading carry the expectation that the predicate hold of both conjuncts. The paper investigates several hypotheses concerning the source of this expectation. (shrink)

Notice that this paper has not claimed that all natural languages are CFL's. What it has shown is that every published argument purporting to demonstrate the non-context-freeness of some natural language is invalid, either formally or empirically or both.18 Whether non-context-free characteristics can be found in the stringset of some natural language remains an open question, just as it was a quarter century ago.Whether the question is ultimately answered in the negative or the affirmative, there will be interesting further questions (...) to ask. If it turns out that natural languages are indeed always CFL's, it will be reasonable to ask whether this helps to explain why speakers apparently recognize so quickly whether a presented utterance corresponds to a grammatical sentence or not, and to associate structural and semantic details with it. It might also be reasonable to speculate about the explanation for the universally context-free character of the languages used by humans, and to wonder whether evolutionary biological factors are implicated in some way (Sampson (1979) could be read in this light). And naturally, it will be reasonable to pursue the program put forward by Gazdar (1981, in press) to see to what extent CFL-inducing grammatical devices can be exploited to yield insightful descriptions of natural languages that capture generalizations in revealing ways.If a human language that is not a CFL is proved to exist, on the other hand, a different question will be raised: give the non-context-free character of human languages in general, why has this property been so hard to demonstrate that it has taken over twenty-five years to bring it to light since the issue was first explicitly posed? If human languages do not have to be CFL's, why do so many (most?) of them come so close to having the property of context-freeness? And, since the CFL's certainly constitute a very broad class of mathematically natural and computationally tractable languages, what property of human beings or their communicative or cognitive needs is it that has caused some linguistic communities to reach beyond the boundaries of this class in the course of evolving a linguistic system?Either way, we shall be interested to see our initial question resolved, and further questions raised. One cautionary word should be said, however, about the implications (or lack of them) that the answer will have for grammatical studies. Chomsky has repeatedly stated that he does not see weak generative capacity as a theme of central importance in the theory of grammar, and we agree. It is very far from being the case that the recent resurgence of interest in exploring the potential of CF-PSG or equivalent systems will, or should, be halted dead in its tracks by the discovery (if it is ever forthcoming) that some natural language is not a CFL. In the area of parsing, for instance, it seems possible that natural languages are not only parsed on the basis of constituent structure such as a CF-PSG would assign, but are parsed as if they were finite state languages (see Langendoen (1975) and Church (1980) for discussion along these lines). That is, precisely those construction-types that figure in the various proofs that English is not an FSL appear to cause massive difficulty in the human processing system; the sentences crucial to the proofs are for the most part unprocessable unless they are extremely short (yet the arguments for English not being and FSL only go through if length is not an issue). This means that in practice properties of finite state grammars are still of great potential importance to linguistic theory despite the fact that they do not provide the framework for defining the total class of grammatical sentences. The same would almost certannly be true of CF-PSG's if they were shown to be inadequate in a similar sense. It is highly unlikely that the advances made so far in far in phrase structure description could be nullified by a discovery about weak generative capacity. Moreover, there are known to be numerous ways in which the power of CF-PSG's can be marginally enhanced to permit, for example, xx languages to be generated without allowing anything like the full class of recursively enumerable or even context-sensitive languages (see Hopcroft and Ullmann (1979), Chapter 14) for an introduction to this topic, noting especially Figure 14.7 on p. 393. The obvious thing to do if natural languages were ever shown not to be CFL's in the general case would be to start exploring such minimal enhancements of expressive power to determine exactly what natural languages call for in this regard and how it could be effectively but parsimoniously provided in a way that closely modelled human linguistic capacities.In the meantime, it seems reasonable to assume that the natural languages are a proper subset of the infinite-cardinality CFL's until such time as they are validly shown not to be. (shrink)

This book sets out the foundations, methodology, and practice of a formal framework for the description of language. The approach embraces the trends of lexicalism and compositional semantics in computational linguistics, and theoretical linguistics more broadly, by developing categorial grammar into a powerful and extendable logic of signs. Taking Montague Grammar as its point of departure, the book explains how integration of methods from philosophy (logical semantics), computer science (type theory), linguistics (categorial grammar) and meta-mathematics (mathematical logic ) provides a (...) categorial foundation with coverage including intensionality, quantification, featural polymorphism, domains and constraints. For the first time, the book systematises categorial thinking into a unified program which is at once both logically secured, and a practical tool for pure lexical grammar development with type-theoretic semantics. It should be of interest to all those active in computational linguistics and formal grammar and is suitable for use at advanced undergraduate, postgraduate, and research levels. (shrink)

If all dependent expressions were adjacent some variety of immediate constituent analysis would suffice for grammar, but syntactic and semantic mismatches are characteristic of natural language; indeed this is a, or the, central problem in grammar. Logical categorial grammar reduces grammar to logic: an expression is well-formed if and only if an associated sequent is a theorem of a categorial logic. The paradigmatic categorial logic is the Lambek calculus, but being a logic of concatenation the Lambek calculus can only capture (...) discontinuous dependencies when they are peripheral. In this paper we present the displacement calculus, which is a logic of intercalation as well as concatenation and which subsumes the Lambek calculus. On the empirical side, we apply the new calculus to discontinuous idioms, quantification, VP ellipsis, medial extraction, pied-piping, appositive relativisation, parentheticals, gapping, comparative subdeletion, cross-serial dependencies, reflexivization, anaphora, dative alternation, and particle shift. On the technical side, we prove that the calculus enjoys Cut-elimination. (shrink)

In sentences like Every teacher laughed we think of every teacher as a unary (=type (1)) quantifier - it expresses a property of one place predicate denotations. In variable binding terms, unary quantifiers bind one variable. Two applications of unary quantifiers, as in the interpretation of No student likes every teacher, determine a binary (= type (2)) quantifier; they express properties of two place predicate denotations. In variable binding terms they bind two variables. We call a binary quantifier Fregean (or (...) reducible) if it can in principle be expressed by the iterated application of unary quantifiers. In this paper we present two mathematical properties which distinguish non-Fregean quantifiers from Fregean ones. Our results extend those of van Benthem (1989) and Keenan (1987a). We use them to show that English presents a large variety of non-Fregean quantifi ers. Some are new here, others are familiar (though the proofs that they are non-Fregean are not). The main point of our empirical work is to inform us regarding the types of quantification natural language presents - in particular (van Benthem, 1989) that it goes beyond the usual (Fregean) analysis which treats it as mere iterated application of unary quantifiers. Secondarily, our results challenge linguistic approaches to "Logical Form" which constrain variable binding operators to "locally" bind just one occurrence of a variable, e.g., the Bijection Principle (BP) of Koopman and Sportiche (1983). The BP (correctly) blocks analyses like For which x, x's mother kissed x? for Who did his mother kiss? since For which x would locally bind two occurrences of x. But some of our irreducible binary quantifiers are naturally represented by operators which do locally bind two variables. This paper is organized as follows: Section 1 provides an explicit formulation of our questions of concern. Section 2 classifies the English constructions which we show to be non-Fregean. Section 3 presents the mathematical properties which test for non-Fregean quantification and applies these tests to the constructions in Section 2. Proofs of the mathema tical properties are given in the Appendix. (shrink)

We provide a semantic analysis of respective readings, including butnot limited to the interpretation of examples containing the adverbrespectively, which accounts for a number of facts that haveeither proven difficult for previous studies or heretofore goneunnoticed in the literature. The analysis introduces the new notionsof property sum and proposition sum which integrate smoothly with existing analyses of plurals and distributivity. The analysis also admits of a straightforward account of previouslyunacknowledged examples involving filler-gap dependencies that areproblematic for contemporary syntactic theories. Ramifications (...) anddirections for future research are discussed. (shrink)

This paper addresses a phenomenon in which certain word-parts can be omitted. The evidence shows that the full range of data cannot be captured by a sublexical analysis, since the phenomena can be observed both in phrasal and in lexical environments. It is argued that a form of deletion is involved, and that the phenomena—lexical or otherwise—are subject to the same phonological, semantic, and syntactic constraints. In the formalization that is proposed, all of the above constraints are cast in a (...) parallel and declarative fashion, in the framework of Head-Driven Phrase Structure Grammar (Pollard and Sag Head-driven phrase structure grammar, 1994), since the various levels of linguistic description are locally and simultaneously available. Building on recent accounts of ellipsis, this paper proposes a unified and general account of word-part ellipsis and phrasal ellipsis. (shrink)

I propose the first strictly compositional semantic account of same. New data, including especially NP-internal uses such as two men with the same name, suggests that same in its basic use is a quantificational element taking scope over nominals. Given type-lifting as a generally available mechanism, I show that this follows naturally from the fact that same is an adjective. Independently-motivated assumptions extend the analysis to standard examples such as Anna and Bill read the same book via a mechanism I (...) call PARASITIC SCOPE, in which the scope of same depends on the scope of some other scopetaking element in the sentence. Although I will initially discuss the analysis in terms of a familiar Quantifier Raising framework, I go on to implement the analysis within an innovative continuation-based Type-Logical Grammar. The empirical payoff for dealing in continuations is that a simple generalization of the basic analysis gives the first ever formal account of cases in which same distributes over objects other than NP denotations, as in the relevant interpretation of John hit and killed the same man. (shrink)

There is no doubt that the model presented here is incomplete. Many important categories, particularly negation and the adverbials, have been entirely ignored, and the treatment of Tense and the affixes is certainly inadequate. It also remains to be seen how the many constructions that have been ignored here are to be accommodated within the framework that has been outlined. However, the fact that a standard categorial lexicon, plus the four rule schemata, seems to come close to exhaustively specifying the (...) main clause constructions of English, and also seems to explain a number of major constraints on transformations, encourages us to compare the theory with certain alternatives, and to examine its broader implications. (shrink)

The book, which stepwise develops successively more powerful logical and grammatical systems, covers an unusually broad range of material.

This book takes concepts developed by researchers in theoretical computer science and adapts and applies them to the study of natural language meaning. Summarizing over a decade of research, Chris Barker and Chung-chieh Shan put forward the Continuation Hypothesis: that the meaning of a natural language expression can depend on its own continuation.

Chapter. 1. Logical. Form. as. a. Level. of. Linguistic. Representation. What is the relation of a sentence's syntactic form to its logical form? This issue has been of central concern in modern inquiry into the semantic properties of natural ...

This book surveys research in quantification starting with the foundational work in the 1970s. It paints a vivid picture of generalized quantifiers and Boolean semantics. It explains how the discovery of diverse scope behavior in the 1990s transformed the view of quantification, and how the study of the internal composition of quantifiers has become central in recent years. It presents different approaches to the same problems, and links modern logic and formal semantics to advances in generative syntax. A unique feature (...) of the book is that it systematically brings cross-linguistic data to bear on the theoretical issues, discussing French, German, Dutch, Hungarian, Russian, Japanese, Telugu (Dravidian), and Shupamem (Grassfield Bantu), and pointing to formal semantic literature involving quantification in around thirty languages. -- -/- 1. What this book is about and how to use it; 2. Generalized quantifiers and their elements: operators and their scopes; 3. Generalized quantifiers in non-nominal domains; 4. Some empirically significant properties of quantifiers and determiners; 5. Potential challenges for generalized quantifiers; 6. Scope is not uniform and not a primitive; 7. Existential scope versus distributive scope; 8. Distributivity and scope; 9. Bare numeral indefinites; 10. Modified numerals; 11. Clause-internal scopal diversity; 12. Towards a compositional semantics of quantifier words. (shrink)

One of the interests in the Gapping construction is the headache it causes for those trying to get constituency structure right. On the assumption that Gapping, like other processes of sentence grammar, respects constituency, it is very hard to deliver the right constituents in cases such as (1). (1) a. Some consider him honest and others consider him pleasant. b. The faculty brought scotch to the party and the students brought beer to the party. c. The girls occasionally ate peanuts (...) and the boys occasionally ate breath mints. (Understand the material in strikeouts to be Gapped.) Everything else tells us that the Gapped strings in (1) should not form a constituent which excludes the material left behind. Yet, the fact that only when the verb Gaps may the other material too suggests just the opposite. That is, if we deny that the verb forms a constituent with the other material, and let Gapping apply to each of the elided constituents independently, we would have no way to express this dependency. If we let Gapping only elide constituents that house the verb, on the other hand, it follows. (shrink)

This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable.

The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.

The ‘syntax’ and ‘combinatorics’ of my title are what Curry (1961) referred to as phenogrammatics and tectogrammatics respectively. Tectogrammatics is concerned with the abstract combinatorial structure of the grammar and directly informs semantics, while phenogrammatics deals with concrete operations on syntactic data structures such as trees or strings. In a series of previous papers (Muskens, 2001a; Muskens, 2001b; Muskens, 2003) I have argued for an architecture of the grammar in which finite sequences of lambda terms are the basic data structures, (...) pairs of terms syntax, semantics for example. These sequences then combine with the help of simple generalizations of the usual abstraction and application operations. This theory, which I call Lambda Grammars and which is closely related to the independently formulated theory of Abstract Categorial Grammars (de Groote, 2001; de Groote, 2002), in fact is an implementation of Curry’s ideas: the level of tectogrammar is encoded by the sequences of lambda-terms and their ways of combination, while the syntactic terms in those sequences constitute the phenogrammatical level. In de Groote’s formulation of the theory, tectogrammar is the level of abstract terms, while phenogrammar is the level of object terms. (shrink)