Beyond Rank 1: Algebraic Semantics and Finite Models for Coalgebraic Logics

Dirk Pattinson, Lutz Schröder

In: Roberto Amadio (Hrsg.). Foundations of Software Science and Computation Structures (FOSSACS 2008). International Conference on Foundations of Software Science and Computation Structures (FoSSaCS-2008) befindet sich the European Joint Conferences on Theory and Practice of Software (ETAPS 2008) March 29-April 6 Budapest Hungary Seiten 66-80 Lecture Notes in Computer Science (LNCS) 4962 Springer 2008.


Coalgebras provide a uniform framework for the semantics of a large class of (mostly non-normal) modal logics, including e.g. monotone modal logic, probabilistic and graded modal logic, and coalition logic, as well as the usual Kripke semantics of modal logic. In earlier work, the finite model property for coalgebraic logics has been established w.r.t. the class of emphall structures appropriate for a given logic at hand; the corresponding modal logics are characterised by being axiomatised in rank 1, i.e. without nested modalities. Here, we extend the range of coalgebraic techniques to cover logics that impose global properties on their models, formulated as frame conditions with possibly nested modalities on the logical side (in generalisation of frame conditions such as symmetry or transitivity in the context of Kripke frames). We show that the finite model property for such logics follows from the finite algebra property of the associated class of complex algebras, and then investigate sufficient conditions for the finite algebra property to hold. Example applications include extensions of coalition logic and logics of uncertainty and knowledge.

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Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence