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  1. Categorial Grammar — A Basis for a Natural Language Calculus?Hans Karlgren - 1978 - Studia Logica 37 (1):65-78.
  2. The Logic of Unification in Grammar.Robert T. Kasper & William C. Rounds - 1990 - Linguistics and Philosophy 13 (1):35 - 58.
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  3. Phrase Structure Grammar, Head‐Driven.Robert D. Levine - 2003 - In L. Nadel (ed.), Encyclopedia of Cognitive Science. Nature Publishing Group.
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  4. Head-Driven Phrase Structure Grammar: Linguistic Approach, Formal Foundations, and Computational Realization.Robert D. Levine & W. Detmar Meurers - 2006 - In Keith Brown (ed.), Encyclopedia of Language and Linguistics. Elsevier.
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  5. Language, Lambdas, and Logic.Reinhard Muskens - 2003 - In R. Oehrle & J. Kruijff (eds.), Resource Sensitivity, Binding, and Anaphora (Studies in Linguistics and Philosophy 80). Dordrecht: Kluwer Academic Publishers. pp. 23--54.
    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.
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  6. Categorial Grammar and Lexical-Functional Grammar.Reinhard Muskens - 2001 - In Miriam Butt & Tracey Holloway King (eds.), Proceedings of the LFG01 Conference, University of Hong Kong. Stanford, CA: CSLI Publications. pp. 259-279.
    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.
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  7. Talking About Trees and Truth-Conditions.Reinhard Muskens - 2001 - Journal of Logic, Language and Information 10 (4):417-455.
    We present Logical Description Grammar (LDG), a model ofgrammar and the syntax-semantics interface based on descriptions inelementary logic. A description may simultaneously describe the syntacticstructure and the semantics of a natural language expression, i.e., thedescribing logic talks about the trees and about the truth-conditionsof the language described. Logical Description Grammars offer a naturalway of dealing with underspecification in natural language syntax andsemantics. If a logical description (up to isomorphism) has exactly onetree plus truth-conditions as a model, it completely specifies thatgrammatical (...)
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  8. Description Theory, LTAGs and Underspecified Semantics.Reinhard Muskens & Emiel Krahmer - 1998 - In Anne Abeillé, Tilman Becker, Giorgio Satta & K. Vijay-Shanker (eds.), Fourth International Workshop on Tree Adjoining Grammars and Related Frameworks. Philadelphia, PA: Institute for Research in Cognitive Science. pp. 112-115.
    An attractive way to model the relation between an underspecified syntactic representation and its completions is to let the underspecified representation correspond to a logical description and the completions to the models of that description. This approach, which underlies the Description Theory of Marcus et al. 1983 has been integrated in Vijay-Shanker 1992 with a pure unification approach to Lexicalized Tree-Adjoining Grammars (Joshi et al. 1975, Schabes 1990). We generalize Description Theory by integrating semantic information, that is, we propose to (...)
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