Basic quantifier theory
type: Item
instance of: scholarly article
zbMATH Open document ID: 0966.03039
author: Jaap van der Does
author: Jan van Eijck
publication date: 2001-07-26T00:00:00Z
Mathematics Subject Classification ID: 03C80
Mathematics Subject Classification ID: 03B65
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 1574677
zbMATH Keywords: generalized quantifiers
zbMATH Keywords: quantification
zbMATH Keywords: linguistics
zbMATH Keywords: quantifier logics
zbMATH Keywords: tableau method
zbMATH Keywords: decidability
MaRDI profile type: Publication
title: Basic quantifier theory
review text: From the Preamble: According to \textit{P. Lindström} [``First-order predicate logic with generalized quantifiers'', Theoria 32, 186-195 (1966)] a quantifier is a functor which assigns to each non-empty domain a relation among relations which is closed under isomorphisms. A simple instance of this notion is given by the quantifier `more than half of the', which for each domain \(E\) gives the relation between sets \(A,B \subseteq E\) defined by: NEWLINE\[NEWLINE|\{a\in A: a\in B\}|> |\{a\in A: a\not\in B\}|.NEWLINE\]NEWLINE In the present collection of articles the authors investigate several aspects of such quantifiers, also of quantifiers with relational arguments. NEWLINENEWLINENEWLINEThis introduction presents some basic insights and techniques of quantification theory. After a brief history, we pay attention to application of the theory in linguistics, and then to its more logical features. The linguistic topics include: denotational constraints, behaviour in certain linguistic contexts, and polyadic forms of quantification. On the logical side, we discuss metaproperties of weak and of `real' quantifier logics. In particular, we concentrate on the tableau method for weak quantifier logics, and on decidability results.NEWLINENEWLINEFor the entire collection see [Zbl 0939.00021].
description: scientific article