Modal logics in the vicinity of S1
type: Item
instance of: scholarly article
title: Modal logics in the vicinity of S1
zbMATH Open document ID: 0859.03011
author: Brian F. Chellas
author: Krister Segerberg
published in: Notre Dame Journal of Formal Logic
publication date: 1997-04-07T00:00:00Z
review text: The authors define prenormal logics and show that certain well-known nonnormal logics are Lewis versions of corresponding prenormal logics. Determination and decidability are shown. Cresswell logics are introduced and characterized. The formal apparatus consists in a combination of relational and neighborhood semantics. The paper is a far-reaching contribution to the ongoing discussion around \(S1\). A logic is called classical, if it permits replacement of logically equivalent formulas. A classical logic is called prenormal, if it provides the schema \[ \square \mathbb{T} \to\bigl(\square (A\to B) \to (\square A\to \square B) \bigr). \] A Lewis version of a logic is the smallest logic that extends that logic and contains \(\square \mathbb{T}\). A Cresswell logic is a prenormal logic closed under the Cresswell rules \[ A_0 \vee \cdots \vee A_{n-1}/(\square A_0 \& \cdots \& A_{n-1}) \to \square\mathbb{T}. \]
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 935222
zbMATH Keywords: Lewis systems
zbMATH Keywords: determination
zbMATH Keywords: prenormal logics
zbMATH Keywords: nonnormal logics
zbMATH Keywords: decidability
zbMATH Keywords: Cresswell logics
zbMATH Keywords: combination of relational and neighborhood semantics
zbMATH Keywords: Lewis version of a logic
reviewed by: Uwe Scheffler
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1040067312
OpenAlex ID: W2151163617
cites work: Q3867808
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DOI: 10.1305/NDJFL/1040067312
description: scientific article; zbMATH DE number 935222