Modal languages and bounded fragments of predicate logic
type: Item
instance of: scholarly article
title: Modal languages and bounded fragments of predicate logic
zbMATH Open document ID: 0919.03013
DOI: 10.1023/A:1004275029985
author: Johan van Benthem
author: Hajnal Andréka
author: István Németi
published in: Journal of Philosophical Logic
publication date: 1998-11-18T00:00:00Z
review text: The aim of the paper is to find natural fragments of first-order logic which have the ``nice'' properties of basic modal logic: decidability, the finite model property, interpolation, etc. First, the authors show that the finite-variable fragments are not suitable in this sense. Then they define the guarded fragment, in which only bounded quantification of the form \(\exists\overline y(R\overline x\overline y \& \phi(\overline x,\overline y))\) is allowed, and prove that it enjoys the nice properties mentioned above.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B20
zbMATH DE Number: 1206975
zbMATH Keywords: fragments of first-order logic
zbMATH Keywords: modal logic
zbMATH Keywords: decidability
zbMATH Keywords: finite model property
zbMATH Keywords: interpolation
zbMATH Keywords: guarded fragment
zbMATH Keywords: bounded quantification
reviewed by: Michael Zakharyaschev
MaRDI profile type: Publication
cites work: On a decidable generalized quantifier logic corresponding to a decidable fragment of first-order logic
cites work: Correspondence and Completeness for Generalized Quantifiers
cites work: Representations of distributive lattice-ordered semigroups with binary relations
cites work: Q4860647
cites work: Expressibility of properties of relations
cites work: On universal algebraic constructions of logics
cites work: Q4075450
cites work: Q4717366
cites work: Modal reduction principles
cites work: Q4342096
cites work: Q3781066
cites work: Language in action
cites work: Q3122692
cites work: Logic of transition systems
cites work: Model theory
cites work: Natural deduction and arbitrary objects
cites work: Q3674621
cites work: Q4108293
cites work: Q3478385
cites work: Algebraic laws for nondeterminism and concurrency
cites work: Finite \(H\)-dimension does not imply expressive completeness
cites work: Q4833774
cites work: Properties of independently axiomatizable bimodal logics
cites work: The metatheory of the classical propositional calculus is not axiomatizable
cites work: Nonfinitizability of classes of representable cylindric algebras
cites work: Cylindric-relativised set algebras have strong amalgamation
cites work: Q4273476
cites work: Algebraization of quantifier logics, an introductory overview
cites work: Semantics-Based Translation Methods for Modal Logics
cites work: Amalgamation, congruence-extension, and interpolation properties in algebras
cites work: Q4273484
cites work: Q4011731
cites work: Der Interpolationssatz der intuitionistischen Prädikatenlogik
cites work: Q4040000
cites work: A Modal Logic for Chopping Intervals
cites work: Q4873977
cites work: Cylindric modal logic
cites work: Multi-dimensional modal logic
full work available at URL: a:1004275029985
OpenAlex ID: W1991981864
Recommended article: THE BOUNDED FRAGMENT AND HYBRID LOGIC WITH POLYADIC MODALITIES
Recommended article: Q4394917
Recommended article: Q3220557
Recommended article: Modal Foundations for Predicate Logic
Recommended article: Q4250037
Recommended article: The monodic fragment of propositional term modal logic
Recommended article: Some theorems on the expressive limitations of modal languages
Recommended article: Modal logic over finite structures
Recommended article: Q5483012
Recommended article: Q4580320
description: scientific article; zbMATH DE number 1206975