Positive (Modal) Logic Beyond Distributivity

04/28/2022

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by   Nick Bezhanishvili, et al.

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We present a duality for non-necessarily-distributive (modal) lattices and use this to study non-necessarily-distributive positive (modal) logic. Our duality is similar to Priestley duality and as such allows us to use similar tools and techniques to study logic. As a result, we prove Sahlqvist correspondence and canonicity for both the propositional logic as well as a modal extension.