, Volume 36, Issue 3, pp 463–486 | Cite as

Monotonic Distributive Semilattices

  • Sergio A. Celani
  • Ma. Paula MenchónEmail author


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.


Distributive meet semilattices Monotonic modal logics DS-spaces Modal operators 


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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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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.CONICET and Departamento de Matemáticas, Facultad de Ciencias ExactasUniversidad Nacional del CentroTandilArgentina

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