Model constructions for moss' coalgebraic logic

Authors:
Jort Bergfeld;Yde Venema
Affiliations:
Artificial Intelligence and Cognitive Engineering, Rijksuniversiteit Groningen, Groningen, The Netherlands;Institute for Logic, Language and Computation, Universiteit van Amsterdam, Amsterdam, The Netherlands
Venue:
CALCO'11 Proceedings of the 4th international conference on Algebra and coalgebra in computer science
Year:
2011

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Abstract

We discuss two model constructions related to the coalgebraic logic introduced by Moss. Our starting point is the derivation system MT for this logic, given by Kupke, Kurz and Venema. Based on the one-step completeness of this system, we first construct a finite coalgebraic model for an arbitrary MT -consistent formula. This construction yields a simplified completeness proof for the logic MT with respect to the intended, coalgebraic semantics. Our second main result concerns a strong completeness result for MT, provided that the functor T satisfies some additional constraints. Our proof for this result is based on the construction, for an MT-consistent set of formulas A, of a coalgebraic model in which A is satisfiable.