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Focused and Synthetic Nested Sequents

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Abstract

Focusing is a general technique for transforming a sequent proof system into one with a syntactic separation of non-deterministic choices without sacrificing completeness. This not only improves proof search, but also has the representational benefit of distilling sequent proofs into synthetic normal forms. We show how to apply the focusing technique to nested sequent calculi, a generalization of ordinary sequent calculi to tree-like instead of list-like structures. We thus improve the reach of focusing to the most commonly studied modal logics, the logics of the modal S5 cube. Among our key contributions is a focused cut-elimination theorem for focused nested sequents.
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Dates and versions

hal-01417618 , version 1 (15-12-2016)

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Kaustuv Chaudhuri, Sonia Marin, Lutz Strassburger. Focused and Synthetic Nested Sequents. FOSSACS 2016 - 19th International Conference Foundations of Software Science and Computation Structures, Apr 2016, Eindhoven, Netherlands. ⟨10.1007/978-3-662-49630-5_23⟩. ⟨hal-01417618⟩
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