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Closure Algebras of Depth Two with Extremal Relations: Their Frames, Logics, and Structural Completeness
Ivo Düntsch and Wojciech Dzik
We consider varieties generated by finite closure algebras whose canonical relations have two levels, and whose restriction to a level is an “extremal” relation, i.e. the identity or the universal relation. The corresponding logics have frames of depth two, in which a level consists of a set of simple clusters or of one cluster with one or more elements.
Keywords: Closure algebras, modal logics of depth two, algebraic semantics, frame semantics