Coalgebraic logic
type: Item
instance of: scholarly article
title: Coalgebraic logic
zbMATH Open document ID: 0969.03026
DOI: 10.1016/S0168-0072(98)00042-6
author: Lawrence S. Moss
published in: Annals of Pure and Applied Logic
publication date: 1999-09-12T00:00:00Z
review text: A starting point of the paper is the characterization theorem for infinitary modal logic stating that two points in Kripke models satisfy the same infinitary modal formulas iff they are bisimilar; moreover, every bisimulation type is determined by a single formula [\textit{J. Barwise} and \textit{L. S. Moss}, Vicious circles (CSLI Lect. Notes 60), CSLI, Stanford (1996; Zbl 0865.03002)]. Coalgebraic logics are generalizations of infinitary modal logics. Such a logic is determined by a functor on sets with some properties; formulas are interpreted in coalgebras of that functor. Coalgebraic logics generalize modal logics as well as various logics of transition systems [\textit{J. J. M. M. Rutten}, ``A calculus of transition systems: towards universal coalgebra'', in: A. Ponse, M. de Rijke, Y. Venema (eds.), Modal logic and process algebra: a bisimulation perspective, CSLI Lect. Notes 53, 231-256 (1995; Zbl 0943.68508)]. The paper introduces a semantics for coalgebraic logics and proves soundness for the `minimal F-logic' (completeness remains an open problem). Moreover, it proves characterization results and a representation theorem stating that every final F-coalgebra can be extracted from an F-algebra with a complete semilattice ordering.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 68Q85
zbMATH DE Number: 1308102
zbMATH Keywords: infinitary modal logic
zbMATH Keywords: characterization theorem
zbMATH Keywords: bisimulation
zbMATH Keywords: functor on sets
zbMATH Keywords: coalgebra
zbMATH Keywords: greatest fixed point
zbMATH Keywords: transition system
reviewed by: Valentin Shehtman
MaRDI profile type: Publication
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full work available at URL: s0168-0072(98)00042-6
OpenAlex ID: W4213277014
description: scientific article; zbMATH DE number 1308102