A splitting logic in NExt(KTB)
type: Item
instance of: scholarly article
title: A splitting logic in NExt(KTB)
zbMATH Open document ID: 1130.03016
author: Yutaka Miyazaki
published in: Studia Logica
publication date: 2007-09-10T00:00:00Z
review text: The author initially relates subdirectly irreducible modal algebras (s.i. algebras) with general frames for modal logics. The author shows that every descriptive KTB frame which is connected corresponds to an s.i. KTB algebra. Thus, connected KTB frames can be regarded as building blocks of KTB logics. Next, the author shows that the normal modal logic of a Kripke frame of two reflexive points joint with a symmetric relation splits the lattice of all normal extensions of the logic KTB and, with this, that there exists a unique largest logic in the class of all normal extensions of KTB.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 5189071
zbMATH Keywords: possible worlds frames
zbMATH Keywords: modal algebras
zbMATH Keywords: KTB frame
zbMATH Keywords: KTB algebra
zbMATH Keywords: KTB logics
zbMATH Keywords: normal modal logic
zbMATH Keywords: Kripke frame
zbMATH Keywords: normal extensions
MaRDI profile type: Publication
full work available at URL: s11225-007-9039-8
OpenAlex ID: W2052832447
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DOI: 10.1007/S11225-007-9039-8
description: scientific article; zbMATH DE number 5189071