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Intuitionistic Modal Algebras.

Authors :
Celani, Sergio A.
Rivieccio, Umberto
Source :
Studia Logica; Jun2024, Vol. 112 Issue 3, p611-660, 50p
Publication Year :
2024

Abstract

Recent research on algebraic models of quasi-Nelson logic has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a nucleus. Among these various algebraic structures, for which we employ the umbrella term intuitionistic modal algebras, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their primitive operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of weak implicative semilattices, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana's strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00393215
Volume :
112
Issue :
3
Database :
Complementary Index
Journal :
Studia Logica
Publication Type :
Academic Journal
Accession number :
177559969
Full Text :
https://doi.org/10.1007/s11225-023-10065-2