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

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Logic Programming and Nonmonotonic Reasoning (LPNMR 2019)

Abstract

Sequent-type proof systems constitute an important and widely-used class of calculi well-suited for analysing proof search. In this paper, we introduce a sequent-type calculus for a variant of default logic employing Łukasiewicz’s three-valued logic as the underlying base logic. This version of default logic has been introduced by Radzikowska addressing some representational shortcomings of standard default logic. More specifically, our calculus axiomatises brave reasoning for this version of default logic, following the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a complementary calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

The first author was supported by the European Master’s Program in Computational Logic (EMCL).

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Notes

  1. 1.

    \({\mathsf {S}{{\textsf {\L }}}_3}\) has optimised rules for \(\,\supset \,\) compared to those of the calculus for \({\mathbf{\L }_\mathbf {3}}\) given by Malinowski [22]; also note that \({\mathsf {S}{{\textsf {\L }}}_3}\) does not require a cut rule.

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Correspondence to Sopo Pkhakadze .

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Pkhakadze, S., Tompits, H. (2019). A Sequent-Type Calculus for Three-Valued Default Logic, Or: Tweety Meets Quartum Non Datur. In: Balduccini, M., Lierler, Y., Woltran, S. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2019. Lecture Notes in Computer Science(), vol 11481. Springer, Cham. https://doi.org/10.1007/978-3-030-20528-7_13

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  • DOI: https://doi.org/10.1007/978-3-030-20528-7_13

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