An Algebraic Investigation of the Connexive Logic $$\textsf{C}$$

Studia Logica 112 (1):37-67 (2023)
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Abstract

In this paper we show that axiomatic extensions of H. Wansing’s connexive logic $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ ) are algebraizable (in the sense of J.W. Blok and D. Pigozzi) with respect to sub-varieties of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ )-algebras. We develop the structure theory of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ )-algebras, and we prove their representability in terms of twist-like constructions over implicative lattices (Heyting algebras). As a consequence, we further clarify the relationship between the aforementioned classes. Finally, taking advantage of the above machinery, we provide some preliminary remarks on the lattice of axiomatic extensions of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ ) as well as on some properties of their equivalent algebraic semantics.

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2023-06-22

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Citations of this work

Connexive Implications in Substructural Logics.Davide Fazio & Gavin St John - forthcoming - Review of Symbolic Logic:1-32.

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References found in this work

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Experiments on Aristotle’s Thesis.Niki Pfeifer - 2012 - The Monist 95 (2):223-240.
A semantical study of constructible falsity.Richmond H. Thomason - 1969 - Mathematical Logic Quarterly 15 (16-18):247-257.

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