# 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

Sequent-Type Proof Systems for Three-Valued Default Logic

- Computer ScienceArXiv
- 2019

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.

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

- Computer ScienceLPNMR
- 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

- Computer Science
- 2019

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.

Refutation Systems: An Overview and Some Applications to Philosophical Logics

- Philosophy
- 2020

An overview with comprehensive references on the historical development of the theory of refutation systems is provided and some of their applications to philosophical logics are discussed.

On Axiomatic Rejection for the Description Logic ALC

- Computer ScienceKDPD
- 2013

This paper presents a sound and complete sequent-type rejection system which axiomatises concept non-subsumption for the description logic \(\mathcal {ALC}\).

Paraconsistency in classical logic

- PhilosophySynthese
- 2017

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.

Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

- Computer ScienceAxioms
- 2020

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.

Assessing Arguments with Schemes and Fallacies

- Philosophy, Computer ScienceLPNMR
- 2019

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.

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