Abstract
AbstractRecent 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.
Funder
H2020 Marie Skłodowska-Curie Actions
Ministerio de Ciencia e Innovación
Consejo Nacional de Investigaciones Científicas y Técnicas
Agencia Nacional de Promoción Científica y Tecnológica
Publisher
Springer Science and Business Media LLC
Subject
History and Philosophy of Science,Logic
Cited by
1 articles.
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