# 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.

## 8 Citations

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- 2019

This paper introduces a sequent-type calculus for a variant of default logic employing Łukasiewicz’s three-valued logic as the underlying base logic, and axiomatises brave reasoning for this version ofdefault logic.

### A Sequent-Type Calculus for Three-Valued Default Logic, Or: Tweety Meets Quartum Non Datur

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This paper introduces a sequent-type calculus for a variant of default logic employing Lukasiewicz’s three-valued logic as the underlying base logic and axiomatises brave reasoning for this version ofdefault logic.

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Any decidable logic with a syntactically incomplete proof theory allows for a paraconsistent characterization of its set of theorems, and this has important bearing on the very nature of paraconsistency as standardly characterized.

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- Computer ScienceAxioms
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This paper introduces sequent-type calculi for two variants of default logic, viz., for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default Logic, due to Gelfond, Lifschitz, Przymusinski, and Truszczynski, which are introduced to address certain representational shortcomings of standard default logic.

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It is shown that classical inference obtains when arguments are based on classical schemes (e.g. Hilbert axioms) and the notion of validity in the context of logic-based arguments along different aspects is clarified.

### Sequent-Type Proof Systems for Three-Valued Default Logic

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This master's thesis introduces sequent-type calculi for a variant of default logic employing Lukasiewicz's three-valued logic as the underlying base logic, addressing some representational shortcomings of standard default logic.

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