Categorial grammar and type theory
type: Item
instance of: scholarly article
title: Categorial grammar and type theory
zbMATH Open document ID: 0695.03016
DOI: 10.1007/BF00263539
published in: Journal of Philosophical Logic
publication date: 1990-01-01T00:00:00Z
review text: This is a survey of logical properties of categorial grammars. These are parsing devices for natural language driven by weak implicational logics lacking the usual structural rules of standard logic. There are various options, forming a Categorial Hierarchy similar to the Chomsky Hierarchy of rewrite grammars. It is shown how questions of recognizing power can be settled by proof-theoretic methods, combining general cut elimination with the use of special invariants. These calculi have a semantics through the formulas-as-types correspondence, and hence there is a matching hierarchy of fragments of lambda calculus. It is shown how various model-theoretic properties from linguistic and logical semantics (such as Boolean monotonicity) can be formulated here, with preservation theorems changing across-fragments. Finally, the resulting theory is related to more procedurally oriented dynamic logics, such as linear logic.
Mathematics Subject Classification ID: 03B65
Mathematics Subject Classification ID: 03B40
Mathematics Subject Classification ID: 68Q45
Mathematics Subject Classification ID: 03F05
zbMATH DE Number: 4137755
zbMATH Keywords: categorial derivation
zbMATH Keywords: lambda term semantics
zbMATH Keywords: survey of logical properties of categorial grammars
zbMATH Keywords: Categorial Hierarchy
zbMATH Keywords: recognizing power
zbMATH Keywords: formulas-as-types correspondence
zbMATH Keywords: dynamic logics
zbMATH Keywords: linear logic
author: Johan van Benthem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4137755