Review of Symbolic Logic:1-16 (forthcoming)

Authors
Yale Weiss
CUNY Graduate Center
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.
Keywords Connexive logic  Semilattice semantics  Contra-classical logic
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DOI 10.1017/s1755020320000374
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References found in this work BETA

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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Semantics for Connexive Logics. I.Richard Routley - 1978 - Studia Logica 37 (4):393 - 412.
Meanings of Implication.John Corcoran - 1973 - Diálogos. Revista de Filosofía de la Universidad de Puerto Rico 9 (24):59-76.

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