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An Algebraic Investigation of the Connexive Logic C Full article

Journal Studia Logica
ISSN: 0039-3215 , E-ISSN: 1572-8730
Output data Year: 2024, Volume: 112, Number: 1-2, Pages: 37–67 Pages count : 31 DOI: 10.1007/s11225-023-10057-2
Tags Connexive logic, Twist-products, Connexive modal logic, Nelson’s logic, Algebraic semantics.
Authors Fazio Davide 1 , Odintsov Sergei P. 2
Affiliations
1 Department of Communication Sciences University of Teramo
2 Sobolev Institute of Mathematics

Funding (1)

1 Sobolev Institute of Mathematics FWNF-2022-0012

Abstract: In this paper we show that axiomatic extensions of H. Wansing’s connexive logic ( ) are algebraizable (in the sense of J.W. Blok and D. Pigozzi) with respect to sub-varieties of ( )-algebras. We develop the structure theory of ( )-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 ( ) as well as on some properties of their equivalent algebraic semantics.
Cite: Fazio D. , Odintsov S.P.
An Algebraic Investigation of the Connexive Logic C
Studia Logica. 2024. V.112. N1-2. P.37–67. DOI: 10.1007/s11225-023-10057-2 WOS Scopus РИНЦ OpenAlex
Dates:
Published online: Jun 21, 2023
Published print: Apr 16, 2024
Identifiers:
Web of science: WOS:001019128000001
Scopus: 2-s2.0-85162952901
Elibrary: 61862957
OpenAlex: W4381487049
Citing:
DB Citing
Web of science 4
Scopus 5
OpenAlex 7
Elibrary 2
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