Maehara-style Modal Nested Calculi

Lutz Straßburger 1, 2 Roman Kuznets 3
2 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : We develop multi-conclusion nested sequent calculi for the fifteen logics of the intuitionistic modal cube between IK and IS5. The proof of cut-free completeness for all logics is provided both syntactically via a Maehara-style translation and semantically by constructing an infinite birelational countermodel from a failed proof search. Interestingly, the Maehara-style translation for proving soundness syntactically fails due to the hierarchical structure of nested sequents. Consequently, we only provide the semantic proof of soundness. The countermodel construction used to prove completeness required a completely novel approach to deal with two independent sources of non-termination in the proof search present in the case of transitive and Euclidean logics.
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Lutz Straßburger, Roman Kuznets. Maehara-style Modal Nested Calculi. [Research Report] RR-9123, Inria Saclay. 2017. 〈hal-01644750〉

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