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SEMANTICS FOR PURE THEORIES OF CONNEXIVE IMPLICATION

Part of: General logic

Published online by Cambridge University Press:  21 October 2020

YALE WEISS
YALE WEISS*
Affiliation:
THE SAUL KRIPKE CENTER THE GRADUATE CENTER, CUNY 365 FIFTH AVE., ROOM 7118 NEW YORK, NY 10016, USAE-mail: yweiss@gradcenter.cuny.edu
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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.

Keywords

connexive logicsemilattice semanticscontra-classical logic

MSC classification

Primary: 03B53: Paraconsistent logics
Secondary: 03B60: Other nonclassical logic
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 3 , September 2022 , pp. 591 - 606
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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