Arrow logic and infinite counting
type: Item
instance of: scholarly article
title: Arrow logic and infinite counting
zbMATH Open document ID: 0963.03032
DOI: 10.1023/A:1005215730377
author: Agnes Kurucz
published in: Studia Logica
publication date: 2001-06-18T00:00:00Z
review text: Arrow logic is a propositional modal logic with three modal operators, dyadic, monadic, and constant, which correspond, respectively, to composition, inverse, and identity of arrows. It is a broadly applicable modal formalism covering various areas from dynamic semantics of natural language to transition systems in computer science. The weakly associative arrow logic, one of the fundamental ones among them, has been proved to be finitely axiomatizable by Maddux and decidable by Nemeti. It is also known by Andreka, Hodkinson and Nemeti that weakly associative relational algebras, which constitute the algebraic counterparts of the logic, have the finite base property. In this paper, the author introduces to the logic various kinds of additional modalities modeling infinite counting features of natural language such as ``much more'', ``of good quantity'', and ``many times'', and proves that the logics thus enriched are also finitely axiomatizable and decidable. The finite axiomatizability results are consequences of (in fact, equivalent to) the finite base property of weakly associative relational algebras. Nevertheless, interestingly enough, it is also shown that their algebras do not enjoy the property.
reviewed by: Osamu Sonobe
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03G15
zbMATH DE Number: 1513063
zbMATH Keywords: arrow logic
zbMATH Keywords: weakly associative relation algebra
zbMATH Keywords: graded modality
zbMATH Keywords: finite axiomatizability
zbMATH Keywords: decidability
zbMATH Keywords: finite base property
MaRDI profile type: Publication
full work available at URL: a:1005215730377
OpenAlex ID: W1592072016
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description: scientific article; zbMATH DE number 1513063