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Monotonic Distributive Semilattices

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Abstract

In the study of algebras related to non-classical logics, (distributive) semilattices are always present in the background. For example, the algebraic semantic of the {→, ∧, ⊤}-fragment of intuitionistic logic is the variety of implicative meet-semilattices (Chellas 1980; Hansen 2003). In this paper we introduce and study the class of distributive meet-semilattices endowed with a monotonic modal operator m. We study the representation theory of these algebras using the theory of canonical extensions and we give a topological duality for them. Also, we show how our new duality extends to some particular subclasses.

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Acknowledgments

This paper has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 689176, and the support of the grant PIP 11220150100412CO of CONICET (Argentina).

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Authors and Affiliations

  1. CONICET and Departamento de Matemáticas, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, 7000, Tandil, Argentina

    Sergio A. Celani & Ma. Paula Menchón

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  1. Sergio A. Celani
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  2. Ma. Paula Menchón
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Correspondence to Ma. Paula Menchón.

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Celani, S.A., Menchón, M.P. Monotonic Distributive Semilattices. Order 36, 463–486 (2019). https://doi.org/10.1007/s11083-018-9477-0

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  • DOI: https://doi.org/10.1007/s11083-018-9477-0

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