Generalizing Functional Completeness in Belnap-Dunn Logic

Studia Logica 103 (5):883-917 (2015)
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Abstract

One of the problems we face in many-valued logic is the difficulty of capturing the intuitive meaning of the connectives introduced through truth tables. At the same time, however, some logics have nice ways to capture the intended meaning of connectives easily, such as four-valued logic studied by Belnap and Dunn. Inspired by Dunn’s discovery, we first describe a mechanical procedure, in expansions of Belnap-Dunn logic, to obtain truth conditions in terms of the behavior of the Truth and the False, which gives us intuitive readings of connectives, out of truth tables. Then, we revisit the notion of functional completeness, which is one of the key notions in many-valued logic, in view of Dunn’s idea. More concretely, we introduce a generalized notion of functional completeness which naturally arises in the spirit of Dunn’s idea, and prove some fundamental results corresponding to the classical results proved by Post and Słupecki

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Citations of this work

Connexive logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
Connexive Negation.Luis Estrada-González & Ricardo Arturo Nicolás-Francisco - 2023 - Studia Logica (Special Issue: Frontiers of Conn):1-29.

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References found in this work

Reasoning with logical bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.
A Calculus for Antinomies.F. G. Asenjo - 1966 - Notre Dame Journal of Formal Logic 16 (1):103-105.
The value of the four values.Ofer Arieli & Arnon Avron - 1998 - Artificial Intelligence 102 (1):97-141.

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