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

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 all 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...

• Type: Conference
• Year: 2008
• Where: FOSSACS
• Authors: Dirk Pattinson, Lutz Schröder
• Keywords: Finite Model Property, FOSSACS 2008, Modal Logics, Monotone Modal Logic, Software Engineering