Journal ArticleDOI
The equivalence of Nonassociative Lambek Categorial Grammars and Context-Free Grammars
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This article is published in Mathematical Logic Quarterly.The article was published on 1988-01-01. It has received 45 citations till now. The article focuses on the topics: Equivalence (formal languages) & Indexed grammar.read more
Citations
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Book ChapterDOI
Categorial Type Logics
TL;DR: Categorial type logics developed out of the Syntactic Calculus proposed by Lambek fifty years ago, and complemented in the 1980'ies with a ‘proofs-as-programs’ interpretation associating derivations in a syntactic source calculus with terms of the simply typed linear lambda calculus expressing meaning composition.
Book ChapterDOI
Mathematical Linguistics and Proof Theory
TL;DR: This chapter discusses certain most characteristic links between proof theory and formal grammars and aims to persuade the reader of the generic unity of proof structures in appropriate deductive systems and syntactic and semantic structures generated by corresponding Grammars.
Book ChapterDOI
Lambek Grammars Based on Pregroups
TL;DR: This paper proves some new theorems on pre-groups and study grammars based on the calculus of free pregroups that are equivalent to context-free Grammars and discusses the relation of pregroups to the Lambek calculus.
Journal ArticleDOI
Type Grammars as Pregroups
TL;DR: This article presents an algebraic model of grammar in the form of a pregroup, which competes with an earlier model which was once proposed by me and is now being developed further by a small but dedicated group of researchers, and took the shape of a residuated monoid.
Journal ArticleDOI
Classical Non-Associative Lambek Calculus
TL;DR: Non-associative linear logic is introduced, which may be seen as the classical version of the non-associate Lambek calculus and its theory of proof-nets is defined, and proof search in it is polynomial.
References
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Journal ArticleDOI
The Mathematics of Sentence Structure
TL;DR: An effective rule (or algorithm) for distinguishing sentences from nonsentences is obtained, which works not only for the formal languages of interest to the mathematical logician, but also for natural languages such as English, or at least for fragments of such languages.
Book ChapterDOI
Generative Power of Categorial Grammars
TL;DR: The authors survey the generative capacity of categorial grammars and show that strong and weak generative capacities of various kinds of categorical grammar can be found in a large number of cases.
Book ChapterDOI
The Lambek Calculus
TL;DR: This paper presents one calculus of this kind, the so-called ‘Lambek Calculus’, and surveys its theoretical properties as a device in linguistic semantics, to provide a better understanding of the background theory of flexible categorial grammar, in tandem with its descriptive uses.
Journal ArticleDOI
The equivalence of two concepts of categorial grammar
Joel M. Cohen,Joel M. Cohen +1 more
TL;DR: It is proved that a set of strings of words forms a categorial language of one type if and only if it forms a category-based language of the other type.