Some sahlqvist completeness results for coalgebraic logics

Authors:
Fredrik Dahlqvist;Dirk Pattinson
Affiliations:
Dept. of Computing, Imperial College London, UK;Dept. of Computing, Imperial College London, UK
Venue:
FOSSACS'13 Proceedings of the 16th international conference on Foundations of Software Science and Computation Structures
Year:
2013

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Abstract

This paper presents a first step towards completeness-via-canonicity results for coalgebraic modal logics. Specifically, we consider the relationship between classes of coalgebras for ω-accessible endofunctors and logics defined by Sahlqvist-like frame conditions. Our strategy is based on conjoining two well-known approaches: we represent accessible functors as (equational) quotients of polynomial functors and then use canonicity results for boolean algebras with operators to transport completeness to the coalgebraic setting.