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Arnon Avron, Beata Konikowska
Proof Systems for Logics
Based on Non-deterministic Multiple-valued Structures
976
Abstract
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 develop general deductive proof systems employing
the $n$-sequent formalism and the R-S decomposition methodology for logics
based on those structures. Later we show how these systems can be used to
obtain
cut-free ordinary Gentzen calculi for some well-known paraconsistent logics.
Keywords: formal logics, non-deterministic matrices, deduction systems.
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