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  1. (1 other version)Mixed computation: grammar up and down the Chomsky Hierarchy.Diego Gabriel Krivochen - 2021 - Evolutionary Linguistic Theory 2 (3):215-244.
    Proof-theoretic models of grammar are based on the view that an explicit characterization of a language comes in the form of the recursive enumeration of strings in that language. That recur-sive enumeration is carried out by a procedure which strongly generates a set of structural de-scriptions Σ and weakly generates a set of strings S; a grammar is thus a function that pairs an element of Σ with elements of S. Structural descriptions are obtained by means of Context-Free phrase structure (...)
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  2. Language, Lambdas, and Logic.Reinhard Muskens - 2003 - In R. Oehrle & J. Kruijff (eds.), resource sensitivity, binding, and anaphora. kluwer. 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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  3. (1 other version)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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  4. 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. 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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  5. 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. 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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