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Publication type: Article in Proceedings
Author: Dirk Pattinson, Lutz Schröder
Editor: Roberto Amadio
Title: Beyond Rank 1: Algebraic Semantics and Finite Models for Coalgebraic Logics
Book / Collection title: Foundations of Software Science and Computation Structures (FOSSACS 2008)
Volume: 4962
Page(s): 66 – 80
Series: Lecture Notes in Computer Science
Year published: 2008
Publisher: Springer
Abstract: 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.
Internet: http://dx.doi.org/10.1007/978-3-540-78499-9_6
PDF Version: http://www.informatik.uni-bremen.de/~lschrode/papers/fmp-fap.pdf
Keywords: Coalgebra modal logic frame conditions algebraic semantics quantitative uncertainty coalition logic
Status: Reviewed
Last updated: 18. 06. 2008

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