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Article Dans Une Revue Journal of Logic and Computation Année : 2016

Dual characterizations for finite lattices via correspondence theory for monotone modal logic

Résumé

We establish a formal connection between algorithmic correspondence theory and certain dual characterization results for finite lattices, similar to Nation's characterization of a hierarchy of pseudovarieties of finite lattices, progressively generalizing finite distributive lattices. This formal connection is mediated through monotone modal logic. Indeed, we adapt the correspondence algorithm ALBA to the setting of monotone modal logic, and we use a certain duality-induced encoding of finite lattices as monotone neighbourhood frames to translate lattice terms into formulas in monotone modal logic.
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hal-01054715 , version 1 (08-08-2014)

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Sabine Frittella, Alessandra Palmigiano, Luigi Santocanale. Dual characterizations for finite lattices via correspondence theory for monotone modal logic. Journal of Logic and Computation, 2016, J Logic Computation 2016, ⟨10.1093/logcom/exw011⟩. ⟨hal-01054715⟩
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