Multi-valued Calculi for Logics Based on Non-determinism

Logic Journal of the IGPL 13 (4):365-387 (2005)
Non-deterministic matrices are multiple-valued structures in which the value assigned by a valuation to a complex formula can be chosen non-deterministically out of a certain nonempty set of options. We consider two different types of semantics which are based on Nmatrices: the dynamic one and the static one . We use the Rasiowa-Sikorski decomposition methodology to get sound and complete proof systems employing finite sets of mv-signed formulas for all propositional logics based on such structures with either of the above types of semantics. Later we demonstrate how these systems can be converted into cut-free ordinary Gentzen calculi which are also sound and complete for the corresponding non-deterministic semantics. As a by-product, we get new semantic characterizations for some well-known logics
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DOI 10.1093/jigpal/jzi030
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Sara Negri (2011). Proof Theory for Modal Logic. Philosophy Compass 6 (8):523-538.

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