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Four-Valued Paradefinite Logics

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Abstract

Paradefinite (‘beyond the definite’) logics are logics that can be used for handling contradictory or partial information. As such, paradefinite logics should be both paraconsistent and paracomplete. In this paper we consider the simplest semantic framework for introducing paradefinite logics. It consists of the four-valued matrices that expand the minimal matrix which is characteristic for first degree entailments: Dunn–Belnap matrix. We survey and study the expressive power and proof theory of the most important logics that can be developed in this framework.

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Authors and Affiliations

  1. School of Computer Science, The Academic College of Tel-Aviv, Tel Aviv, Israel

    Ofer Arieli

  2. School of Computer Science, Tel-Aviv University, Tel Aviv, Israel

    Arnon Avron

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  1. Ofer Arieli
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  2. Arnon Avron
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Correspondence to Ofer Arieli.

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Arieli, O., Avron, A. Four-Valued Paradefinite Logics. Stud Logica 105, 1087–1122 (2017). https://doi.org/10.1007/s11225-017-9721-4

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