Issue Theoret. Informatics Appl. Volume 35, Number 1, January-February 2001 Coalgebraic Methods in Computer Science Page(s) 31 - 59 DOI 10.1051/ita:2001108

DOI: 10.1051/ita:2001108


Theoret. Informatics Appl. 35, 31-59 (2001)

Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study

Bart Jacobs

Department of Computer Science, University of Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands; (bart@cs.kun.nl) URL: http://www.cs.kun.nl/$^\sim$bart

(Accepted March 9, 2001.)

Abstract
This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean Algebras with Operators, combining standard (categorical) models of modal logic and of many-sorted predicate logic. In this setting we will see Lindenbaum MBAO models as initial objects, and canonical coalgebraic models of maximally consistent sets of formulas as final objects. They will be used to (re)prove completeness results, and Hennessey-Milner style characterisation results for the modal logic, first established by Rößiger.

AMS Subject: 03G05, 03G30, 06E25

Key words: Modal logic -- coalgebra -- Boolean algebra with operators.


© EDP Sciences 2001

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