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International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 2019: Logic Programming and Nonmonotonic Reasoning pp 163–177Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11481))

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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Authors and Affiliations

  1. Institute of Logic and Computation, Knowledge-Based Systems Group E192-03, Technische Universität Wien, Favoritenstraße 9-11, 1040, Vienna, Austria

    Sopo Pkhakadze & Hans Tompits

Authors
  1. Sopo Pkhakadze
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  2. Hans Tompits
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Correspondence to Sopo Pkhakadze .

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Editors and Affiliations

  1. Saint Joseph's University, Philadelphia, PA, USA

    Marcello Balduccini

  2. University of Nebraska at Omaha, Omaha, USA

    Yuliya Lierler

  3. TU Wien, Vienna, Austria

    Stefan Woltran

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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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