Dynamic squares
type: Item
instance of: scholarly article
title: Dynamic squares
zbMATH Open document ID: 0842.03016
DOI: 10.1007/BF01052600
author: Patrick Blackburn
author: Yde Venema
published in: Journal of Philosophical Logic
publication date: 1996-07-24T00:00:00Z
review text: The authors provide various propositional logics for the dynamic implication studied by Kamp, Groenendijk, Stokhof, and others to analyse some natural language phenomena. The underlying idea in these theories, which analyses sentence meanings as active entities transforming state spaces like computer programs, is abstracted in the framework of two-dimensional propositional modal logic so that the dynamic implication is characterized as a binary modal operator by a sort of two-dimensional Kripke models, which are called square models. The binary modality thus characterized, is then reinterpreted in the context of Boolean modal logic of Gargov et al. and axiomatised in Hilbert style on classical propositional logic. The Boolean-connective-free fragment of such logics is also examined and formulated in a tableau system featuring Fitting's prefixed formula method.
reviewed by: Osamu Sonobe
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B65
Mathematics Subject Classification ID: 03B70
zbMATH DE Number: 819340
zbMATH Keywords: dynamic logic
zbMATH Keywords: discourse representation theory
zbMATH Keywords: dynamic implication
zbMATH Keywords: two-dimensional propositional modal logic
zbMATH Keywords: two-dimensional Kripke models
zbMATH Keywords: Boolean modal logic
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01052600
OpenAlex ID: W4245235266
description: scientific article; zbMATH DE number 819340