Contents 1 Introduction: grammatical reasoning 1 2 Linguistic inference: the Lambek systems 5 2.1 Modelinggrammaticalcomposition ............................ 5 2.2 Gentzen calculus, cut elimination and decidability . . . . . . . . . . . . . . . . . . . . 9 2.3 Discussion: options for resource management . . . . . . . . . . . . . . . . . . . . . . 13 3 The syntax-semantics interface: proofs and readings 16 3.1 Term assignment for categorial deductions . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Natural language interpretation: the deductive view . . . . . . . . . . . . . . . . . . . 21 4 Grammatical composition: multimodal systems 26 4.1 Mixedinference:themodesofcomposition........................ 26 4.2 Grammaticalcomposition:unaryoperations ....................... 30 4.2.1 Unary connectives: logic and structure . . . . . . . . . . . . . . . . . . . . . . . 31 4.2.2 Applications: imposing constraints, structural relaxation

Abstract: This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods. 1 1

tem of rewrite rules or "productions" like (2), which have their origin in early work in recursion theory by Post, among others. (1) Dexter likes Warren. (2) S ! NP VP VP ! TV NP TV ! flikes;sees; : : :g Categorial Grammar (CG), together with its close cousin Dependency Grammar (which also originated in the 1950s, in work by Tesniere) stems from an alternative approach to context-free grammar pioneered by Bar-Hillel 1953 and Lambek 1958, with earlier antecedents in Ajdukiewicz 1935 and still earlier work by Husserl and Russell in category theory and the theory of types. Categorial Grammars capture the same information by associating a functional type or category with all grammatical entities. For example, all transitive verbs are associated via the lexicon with a category that can be written as follows: (3) likes := (SnNP)=NP The no

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The canonical linguistic process is the cycle of the speech-circuit [Saussure, 1915]. A speaker expresses a psychological idea by means of a physiological articulation. The signal is transmitted through the medium by a physical process incident on a hearer who from the consequent physiological impression recovers the psychological idea. The hearer may then reply, swapping the roles of speaker and hearer, and so the circuit cycles. For communication to be successful speakers and hearers must have shared associations between forms (signifiers) andmeanings(signifieds). De Saussure called such a pairing of signifier and signified a sign. Therelationisone-to-many (ambiguity) and many-to-one (paraphrase). Let us call a stable totality of such associations a language. It would be arbitrary to propose that there is a longest expression (where would we propose to cut off IknowthatyouknowthatIknow that you know...?) therefore language is an infinite abstraction over the finite number of acts of communication that can ever occur. The program of formal syntax [Chomsky, 1957] is to define the set of all and only

this paper, we will study the possibilities for applying lexical rules to the analysis of English syntax, and in particular the structure of the verb phrase. We will develop a lexicon whose empirical coverage extends to the full range of verb subcategories, complex adverbial phrases, auxiliaries, the passive construction, yes/no questions and the particularly troublesome case of predicatives. The effect of a lexical rule, in our system, will be to produce new lexical entries from old lexical entries. The similarity between our system and the metarule system of generalized phrase-structure grammar (GPSG, as presented in Gazdar, et al. 1985) is not coincidental. Our lexical rules serve much the same purpose as metarules in GPSG, which were restricted to lexical phrase structure rules. The similarity is in a large part due to the fact that with the universal phrase-structure schemes being fixed, the role of a lexical category assignment in effect determines phrase-structure in much the same way as a lexical category entry and lexical phrase-structure rule determines lexical phrase-structure in GPSG. Our lexical rules will also bear a relationship to the lexical rules found in lexical-functional grammar (LFG, see Bresnan 1982), as LFG rules are driven by the grammatical role assigned to arguments. Many of our analyses were first applied to either LFG or GPSG, as these were the first serious linguistic theories based on a notion of unification. In the process of explaining the basic principles behind categorial grammar and developing our lexical rule system, we will establish a categorial grammar lexicon with coverage of English syntactic constructions comparable to that achieved within published accounts of the GPSG or LFG frameworks. Language, at its most abstract level, i...

ABSTRACT: We demonstrate ways to enhance the coverage of a symbolic NLP system through data-intensive and machine learning techniques, while preserving the advantages of using a principled symbolic grammar formalism. We automatically acquire a large syntactic CCG lexicon from the Penn Treebank and combine it with semantic and morphological infor-mation from another hand-built lexicon using decision tree and maximum entropy classifiers. We also integrate statistical preprocessing methods in our system.

In this paper, we argue that the grammatical scopings of quantifiers should be treated by deductive methods. In support of this position, we offer a logical treatment of almost all previously proposed substantive constraints on quantifier scoping, including those imposed by coordinate structure, control verbs, unbounded dependency constructions, anaphoric dependency and nested dependent quantifiers. These are correctly captured by a handful of linguistically motivated and logically natural inference schemes for quantification, coordination and unbounded dependency, combined with the previously motivated function introduction and elimination schemes of categorial logic. In addition, we argue that phrase-structure and transformational accounts of similar phenomena at best provide an approximation of the logical approach.

This paper addresses a number of empirical problems surrounding the analysis of `extraction' from French nominal phrases. The lexically based analysis that we present expresses a fundamental generalization in this domain, namely, the correlation between the potential for extraction from NPs and the possibility of `pied piping'. As observed by Godard (1992), this generalization is left unexplained by existing accounts of extraction. We will also sketch how our treatment of extraction and pied piping fits into a broader analysis of the core syntactic phenomena of modern French. Our lexical treatment of cliticization, itself a consequence of the strict lexicalism that we embrace, allows us to unify the analysis of unbounded extraction phenomena with that of cliticization, in the process explaining their common properties. We are able to derive the facts in question through the interaction of independently motivated constraints on representations. The relevant generalizations are naturally cast as constraints in the framework of Head-Driven Phrase Structure Grammar (HPSG), whose relevant constructs we explain in section 3 below.

Even though residuation is at the core of Categorial Grammar [11], it is not always immediate to realize how standard logic systems like Multi-modal Categorial Type Logics (MCTL) [17] actually embody this property. In this paper we focus on the basic system NL [12] and its extension with unary modalities NL(3) [16], and we spell things out by means of Display Calculi (DC) [3, 10]. The use of structural operators in DC permits a sharp distinction between the core properties we want to impose on the logic system and the way these properties are projected into the logic operators. We will show how we can obtain Lambek residuated triple n, = and of binary operators, and how the operators 3 and 2 introduced by Moortgat in [16] are indeed their unary counterpart.