Semantics for Pure Theories of Connexive Implication
Review of Symbolic Logic 15 (3):591-606 (2022)
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.Author's Profile
DOI
10.1017/s1755020320000374
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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.
Did Aristotle Endorse Aristotle’s Thesis? A Case Study in Aristotle’s Metalogic.Yale Weiss - 2022 - Notre Dame Journal of Formal Logic 63 (4):551-579.
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.
On contra-classical variants of Nelson logic n4 and its classical extension.Hitoshi Omori & Heinrich Wansing - 2018 - Review of Symbolic Logic 11 (4):805-820.