An Algebraic Investigation of the Connexive Logic C Full article
| Journal |
Studia Logica
ISSN: 0039-3215 , E-ISSN: 1572-8730 |
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| 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 |
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| Affiliations |
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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
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 |