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Article Dans Une Revue Journal of Logic and Computation Année : 2021

Internal Proof Calculi for Modal Logics with Separating Conjunction

Résumé

Modal separation logics are formalisms that combine modal operators to reason locally, with separating connectives that allow to perform global updates on the models. In this work, we design Hilbert-style proof systems for the modal separation logics MSL(* , Diff) and MSL(* , <>), where * is the separating conjunction, <> is the standard modal operator and Diff is the difference modality. The calculi only use the logical languages at hand (no external features such as labels) and can be divided in two main parts. First, normal forms for formulae are designed and the calculi allow to transform every formula into a formula in normal form. Second, another part of the calculi is dedicated to the axiomatisation for formulae in normal form, which may still require non-trivial developments but is more manageable.
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Dates et versions

hal-03185457 , version 1 (30-03-2021)

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Stéphane Demri, Raul Fervari, Alessio Mansutti. Internal Proof Calculi for Modal Logics with Separating Conjunction. Journal of Logic and Computation, 2021, 31 (3), pp.832-891. ⟨10.1093/logcom/exab016⟩. ⟨hal-03185457⟩
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