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.
This work was partially supported by the Austrian Science Fund (FWF) under grant P21698. The authors would like to thank Valentin Goranko, Robert Sochacki, and Urszula Wybraniec-Skardowska for valuable support during the preparation of this paper.
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Oetsch, J., Tompits, H. (2011). Gentzen-Type Refutation Systems for Three-Valued Logics with an Application to Disproving Strong Equivalence. In: Delgrande, J.P., Faber, W. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2011. Lecture Notes in Computer Science(), vol 6645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20895-9_28
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DOI: https://doi.org/10.1007/978-3-642-20895-9_28
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