Temporal reference in linear tense logic
type: Item
instance of: scholarly article
title: Temporal reference in linear tense logic
zbMATH Open document ID: 1202.03032
author: M. J. Cresswell
published in: Journal of Philosophical Logic
publication date: 2010-04-26T00:00:00Z
review text: This detailed paper presents a first-order theory, ET, within predicate linear tense logic (K4.\(3_t\)) which enables reference to individual times and in which `now' and `then' can be formalized. This theory contains a single short axiom in addition to those for first-order linear tense logic. That axiom is \(\exists x(\phi_N x\wedge G\sim\phi_N x)\), or simply \(\exists xNx\), where `\(Nx\)' abbreviates `\(\phi_Nx\wedge G\sim\phi_N x\)', for a single designated predicate \(\phi_N\). It is noteworthy that the reference to times does not require a special class of singular terms; all the work is done by regular individual variables and quantifiers and the predicate \(\phi_N\). The bulk of the paper establishes the expressive adequacy of ET and various properties of models in which the axiom is valid. This demonstrates that \(N\) itself possesses appropriate properties. This approach is then contrasted with other methods of extending the expressive capacity of predicate tense logic, and briefly generalized to other forms of modal and tense logics.
reviewed by: Louis F. Goble
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B44
zbMATH DE Number: 5701560
zbMATH Keywords: predicate tense logic
zbMATH Keywords: temporal reference
zbMATH Keywords: `now' and `then'
zbMATH Keywords: modal predicate logic
MaRDI profile type: Publication
full work available at URL: s10992-009-9122-x
OpenAlex ID: W1978121847
Wikidata QID: Q56852792
cites work: Modal logic with subjunctive conditionals and dispositional predicates
cites work: Nominal tense logic
cites work: Modal logic
cites work: Modality and Mellor's McTaggart
cites work: Physicalism, instrumentalism and the semantics of modal logic
cites work: Naming worlds in modal and temporal logic
cites work: Q3835817
cites work: Modal logic with names
cites work: Hierarchies of modal and temporal logics with reference pointers
cites work: Q4698331
cites work: Modal logic for other-world agnostics: Neutrality and Halldén incompleteness
cites work: Quantifiers as modal operators
cites work: To the memory of Arthur Prior Formal properties of ‘now’
cites work: Counterfactuals and comparative possibility
cites work: Multi-dimensional modal logic
cites work: `Now' and `then' in tense logic
cites work: Necessity and truth theories
cites work: Q3246315
cites work: Q5556395
cites work: Q5596205
cites work: Q3269129
cites work: Q5626600
cites work: Q4068699
cites work: Two-dimensional modal logic
DOI: 10.1007/S10992-009-9122-X
description: scientific article; zbMATH DE number 5701560