Gentzen-Type Refutation Systems for Three-Valued Logics with an Application to Disproving Strong Equivalence

@inproceedings{Oetsch2011GentzenTypeRS,
  title={Gentzen-Type Refutation Systems for Three-Valued Logics with an Application to Disproving Strong Equivalence},
  author={Johannes Oetsch and Hans Tompits},
  booktitle={LPNMR},
  year={2011}
}
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. 

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