2021
DOI: 10.48550/arxiv.2104.09115
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Towards a Denotational Semantics for Proofs in Constructive Modal Logic

Abstract: In this paper we provide two new semantics for proofs in the constructive modal logics CK and CD.The first semantics is given by extending the syntax of combinatorial proofs for propositional intuitionistic logic, in which proofs are factorised in a linear fragment (arena net) and a parallel weakening-contraction fragment (skew fibration). In particular we provide an encoding of modal formulas by means of directed graphs (modal arenas), and an encoding of linear proofs as modal arenas equipped with vertex part… Show more

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