Book ChapterDOI
Mathematical Linguistics and Proof Theory
Wojciech Buszkowski
- pp 683-736
TLDR
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.Abstract:
Publisher Summary In the traditional sense of the term, “mathematical linguistics” is a branch of applied algebra mainly concerned with formal languages, formal grammars, and automata—the latter being purely computational devices that generate formal languages. A natural link between proof theory and semantics has been established by the constructive approaches in logic as the so–called “formulas-as-types” interpretation: typed lambda terms can be interpreted as formal proofs in natural deduction systems. This chapter discusses certain most characteristic links between proof theory and formal grammars. It 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. The chapter discusses some algebra connected with syntactic structures determined by proofs in the deductive part of grammars. The algebraic models of deductive systems underlying grammars are considered in the chapter. The algebraic models of logical systems are a traditional domain of metalogic. Substructural logics relevant to the theory of grammar give rise to special algebraic structures residuated algebras.read more
Citations
More filters
Journal ArticleDOI
On the dynamics
TL;DR: A linear time algorithm for computing, given the component tree of a function, the dynamics of all its maxima, and a link between the dynamics, minimum spanning trees, and component trees is established.
Book
Mathematics of Language
TL;DR: This book develops the mathematical foundations of present day linguistics from a mathematical point of view starting with ideas already contained in Montague's work and equips the reader with all the background necessary to understand and evaluate theories as diverse as Montague Grammar, Categorial grammar, HPSG and GB.
Journal ArticleDOI
Lambek calculus is NP-complete
TL;DR: It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NP-complete.
Book
The mathematics of language
Marcus Kracht,Hans-Jörg Tiede +1 more
TL;DR: In this paper, the authors study language and linguistic theories from a mathematical point of view, starting with ideas already contained in Montague's work, and develop the mathematical foundations of present day linguistics.
BookDOI
The Logic of Categorial Grammars
Richard Moot,Christian Retoré +1 more
TL;DR: A method for harvesting invention fowl which includes the steps of horizontally extending beneath the fowl, in a confined area, a plurality of lifting fingers.
References
More filters
Book ChapterDOI
The Proper Treatment of Quantification in Ordinary English
TL;DR: The aim of this paper is to present in a rigorous way the syntax and semantics of a certain fragment of acertain dialect of English.
Journal ArticleDOI
Fiftieth volume of theoretical computer science
TL;DR: This contribution was made possible only by the miraculous fact that the first members of the Editorial Board were sharing the same conviction about the necessity of Theoretical Computer Science.
Book
Introduction to higher order categorical logic
Joachim Lambek,Philip J. Scott +1 more
TL;DR: In this article, Cartesian closed categories and Calculus are used to represent Numerical functions in various categories and to describe the relation between categories. But they do not specify the topology of the categories.