@article{0be08b6dcedd4a1297961871b57097ce,
title = "Multi-valued calculi for logics based on non-determinism",
abstract = "Non-deterministic matrices (Nmatrices) 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 (the latter is new here). We use the Rasiowa-Sikorski (R-S) 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 (like the logic CAR from [18, 28]).",
keywords = "Deduction systems, N-sequents, Nondeterministic matrices, R-S systems, Tableaux systems",
author = "Arnon Avron and Beata Konikowska",
note = "Funding Information: This research was supported by THE ISRAEL SCIENCE FOUNDATION founded by The Israel Academy of Sciences and Humanities.",
year = "2005",
month = jul,
doi = "10.1093/jigpal/jzi030",
language = "אנגלית",
volume = "13",
pages = "365--387",
journal = "Logic Journal of the IGPL",
issn = "1367-0751",
publisher = "Oxford University Press",
number = "4",
}