Title: Beyond modalities: Sufficiency and mixed algebras
Authors: Ivo Düntsch , Dept of Computer Science , Brock University , St Catherines, Ontario, L2S 3A1, Canada
Ewa Orlowska, Institute of Telecommunications, Warsaw, Poland
Status: Preprint
Abstract: It is well known that modal operators are not sufficient to characterise all first order definable class of frames. In this paper, we explore logics (and their algebras) enhanced by sufficiency operators, and investigate a class of mixed algebras which corresponds to frames with a modal operator and a sufficiency operator [[R]]. We also give an example of a first order definable class of frames which cannot be defined by modal or sufficiency operators alone, but is definable in a mixed structure.

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