Semantics for Pure Theories of Connexive Implication

Review of Symbolic Logic 15 (3):591-606 (2022)
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Abstract

In this article, I provide Urquhart-style semilattice semantics for three connexive logics in an implication-negation language (I call these “pure theories of connexive implication”). The systems semantically characterized include the implication-negation fragment of a connexive logic of Wansing, a relevant connexive logic recently developed proof-theoretically by Francez, and an intermediate system that is novel to this article. Simple proofs of soundness and completeness are given and the semantics is used to establish various facts about the systems (e.g., that two of the systems have the variable sharing property). I emphasize the intuitive content of the semantics and discuss how natural informational considerations underly each of the examined systems.

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Yale Weiss
CUNY Graduate Center

Citations of this work

A Variant of Material Connexive Logic.Alexander Belikov & Dmitry Zaitsev - 2022 - Bulletin of the Section of Logic 51 (2):227-242.

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References found in this work

Constructible falsity and inexact predicates.Ahmad Almukdad & David Nelson - 1984 - Journal of Symbolic Logic 49 (1):231-233.
Relevance Logic.Michael Dunn & Greg Restall - 2002 - In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer Academic Publishers.
Semantics for relevant logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
Connexive implication.Storrs Mccall - 1966 - Journal of Symbolic Logic 31 (3):415-433.

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