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November 2020 Four-Valued Logics of Truth, Nonfalsity, Exact Truth, and Material Equivalence
Adam Přenosil
Notre Dame J. Formal Logic 61(4): 601-621 (November 2020). DOI: 10.1215/00294527-2020-0025

Abstract

The four-valued semantics of Belnap–Dunn logic, consisting of the truth values True, False, Neither, and Both, gives rise to several nonclassical logics depending on which feature of propositions we wish to preserve: truth, nonfalsity, or exact truth (truth and nonfalsity). Interpreting equality of truth values in this semantics as material equivalence of propositions, we can moreover see the equational consequence relation of this four-element algebra as a logic of material equivalence. In this paper, we axiomatize all combinations of these four-valued logics, for example, the logic of truth and exact truth or the logic of truth and material equivalence. These combined systems are consequence relations which allow us to express implications involving more than one of these features of propositions.

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Adam Přenosil. "Four-Valued Logics of Truth, Nonfalsity, Exact Truth, and Material Equivalence." Notre Dame J. Formal Logic 61 (4) 601 - 621, November 2020. https://doi.org/10.1215/00294527-2020-0025

Information

Received: 2 February 2019; Accepted: 3 August 2020; Published: November 2020
First available in Project Euclid: 29 December 2020

Digital Object Identifier: 10.1215/00294527-2020-0025

Subjects:
Primary: 03B50
Secondary: 03B53, 03G27

Rights: Copyright © 2020 University of Notre Dame

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Vol.61 • No. 4 • November 2020
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