Publicación: Intuitionistic modal algebras
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Fecha
2023-09-15
Autores
Celani, Sergio A.
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info:eu-repo/semantics/openAccess
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Springer Nature
Resumen
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.
Descripción
The registered version of this article, first published in Studia Logica, is available online at the publisher's website: Springer Nature, https://doi.org/10.1007/s11225-023-10065-2
La versión registrada de este artículo, publicado por primera vez en Studia Logica, está disponible en línea en el sitio web del editor: Springer Nature, https://doi.org/10.1007/s11225-023-10065-2
La versión registrada de este artículo, publicado por primera vez en Studia Logica, está disponible en línea en el sitio web del editor: Springer Nature, https://doi.org/10.1007/s11225-023-10065-2
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Palabras clave
intuitionistic modal algebras, nuclei, representation, topological duality, nuclear Heyting algebras, implicative semilattices, quasi-Nelson algebras, fragments, weak Heyting algebras
Citación
Celani, Sergio A., and Umberto Rivieccio. "Intuitionistic modal algebras." Studia Logica 112.3 (2024): 611-660. https://doi.org/10.1007/s11225-023-10065-2
Centro
Facultades y escuelas::Facultad de Filosofía
Departamento
Lógica, Historia y Filosofía de la Ciencia