Multi-valued calculi for logics based on non-determinism

Arnon Avron*, Beata Konikowska

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

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]).

Original languageEnglish
Pages (from-to)365-387
Number of pages23
JournalLogic Journal of the IGPL
Volume13
Issue number4
DOIs
StatePublished - Jul 2005

Funding

FundersFunder number
Israel Academy of Sciences and Humanities

    Keywords

    • Deduction systems
    • N-sequents
    • Nondeterministic matrices
    • R-S systems
    • Tableaux systems

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