On Polarity Frames: Applications to Substructural and Lattice-based Logics.
Tomoyuki Suzuki · ASEP · 2014
In this paper, on one hand, we address topology on polarities via general polarity frames by analogy of the relationship between topology on sets and general Kripke frames. Based on the topology on polarities, we provide the topological characterisation of descriptive polarity frames. On the other hand, we introduce disjoint unions and amalgamations of polarity frames with additional relations and constants. As applications of these constructions, we establish the Goldblatt-Thomason's theorem for (distributive) substructural logic and the amalgamation property for some lattice- based algebras.