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A Coalgebraic Approach to Dualities for Neighborhood Frames

Guram Bezhanishvili ; Nick Bezhanishvili ; Jim de Groot.

We develop a uniform coalgebraic approach to J\'onsson-Tarski and Thomason type dualities for various classes of neighborhood frames and neighborhood algebras. In the first part of the paper we construct an endofunctor on the category of complete and atomic Boolean algebras that is dual to the&nbsp;[&hellip;]

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Modal meet-implication logic

Jim de Groot ; Dirk Pattinson.

We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we obtain completeness and identify a common (modal) fragment of a&nbsp;[&hellip;]

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Coalgebraic Geometric Logic: Basic Theory

Nick Bezhanishvili ; Jim de Groot ; Yde Venema.

Using the theory of coalgebra, we introduce a uniform framework for adding modalities to the language of propositional geometric logic. Models for this logic are based on coalgebras for an endofunctor on some full subcategory of the category of topological spaces and continuous functions. We&nbsp;[&hellip;]

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