Sequent-systems and groupoid models. II
type: Item
instance of: scholarly article
title: Sequent-systems and groupoid models. II
zbMATH Open document ID: 0688.03012
DOI: 10.1007/BF00370633
published in: Studia Logica
publication date: 1989-01-01T00:00:00Z
review text: This is the sequel to part I [ibid. 47, 353-385 (1988; Zbl 0671.03018)]. Generalizing relevant model structures (of Urquhart, Fine, Routley, Meyer and Maksimova) the author introduces groupoid frames. Such a frame is a quadruple \(<W,\cdot,\cap,1>\) in which \(<W,\cdot >\) is a groupoid, \(<W,\cap >\) is a semilattice, \(1\in W\), and \(\cdot\) is two-side distributive w.r.t. \(\cap\). The minimal system L introduced in part I is shown to be complete w.r.t. the class of all groupoid frames. Correspondence and completeness results are sketched also for some extensions of L. In particular, Johansson logic is determined by those groupoid frames in which \(<W,\cdot,1>\) is a commutative monoid and \(1\leq x\), \(x\cdot x\leq x\) for any x. Semantics of this type for disjunctionless fragments of extensions of L is presented as well. Also semantics for some extensions of the negationless fragment of the relevant system R is discussed.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 03C90
Mathematics Subject Classification ID: 03F05
zbMATH DE Number: 4127176
zbMATH Keywords: Kripke frame
zbMATH Keywords: correspondence
zbMATH Keywords: relevant logic
zbMATH Keywords: groupoid frames
zbMATH Keywords: completeness
zbMATH Keywords: Johansson logic
author: Kosta Došen
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00370633
OpenAlex ID: W2003452157
description: scientific article; zbMATH DE number 4127176