Gentzen-type refutation systems for three-valued logics with an application to disproving strong equivalence

Authors:
Johannes Oetsch;Hans Tompits
Affiliations:
Technische Universität Wien, Institut für Informationssysteme, Vienna, Austria;Technische Universität Wien, Institut für Informationssysteme, Vienna, Austria
Venue:
LPNMR'11 Proceedings of the 11th international conference on Logic programming and nonmonotonic reasoning
Year:
2011

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Abstract

While the purpose of conventional proof calculi is to axiomatise the set of valid sentences of a logic, refutation systems axiomatise the invalid sentences. Such systems are relevant not only for proof-theoretic reasons but also for realising deductive systems for nonmonotonic logics. We introduce Gentzen-type refutation systems for two basic three-valued logics and we discuss an application of one of these calculi for disproving strong equivalence between answer-set programs.