Connexive Implications in Substructural Logics

Review of Symbolic Logic 17 (3):878-909 (2024)
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Abstract

This paper is devoted to the investigation of term-definable connexive implications in substructural logics with exchange and, on the semantical perspective, in sub-varieties of commutative residuated lattices (FL ${}_{\scriptsize\mbox{e}}$ -algebras). In particular, we inquire into sufficient and necessary conditions under which generalizations of the connexive implication-like operation defined in [6] for Heyting algebras still satisfy connexive theses. It will turn out that, in most cases, connexive principles are equivalent to the equational Glivenko property with respect to Boolean algebras. Furthermore, we provide some philosophical upshots like, e.g., a discussion on the relevance of the above operation in relationship with G. Polya’s logic of plausible inference, and some characterization results on weak and strong connexivity.

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References found in this work

Connexive logics. An overview and current trends.Hitoshi Omori & Heinrich Wansing - 2019 - Logic and Logical Philosophy 28 (3):371-387.
Experiments on Aristotle’s Thesis.Niki Pfeifer - 2012 - The Monist 95 (2):223-240.
Consistent Theories in Inconsistent Logics.Franci Mangraviti & Andrew Tedder - 2023 - Journal of Philosophical Logic 52 (04):1133-1148.
The Logic of Conditional Negation.John Cantwell - 2008 - Notre Dame Journal of Formal Logic 49 (3):245-260.

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