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

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

Journal Article (2017)

Author(s)

Sabine Frittella (Ethics & Philosophy of Technology)

Alessandra Palmigiano (Ethics & Philosophy of Technology)

Luigi Santocanale (Aix Marseille Université)

Algorithmic correspondence theory Dual characterization Finite lattices Monotone modal logic

DOI related publication

https://doi.org/10.1093/logcom/exw011 Final published version

To reference this document use

https://resolver.tudelft.nl/uuid:0b968161-d0e0-47d0-b4b3-9875188dc935

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Publication Year

2017

Language

English

Issue number

3

Volume number

27

Pages (from-to)

639-678

Downloads counter

138

Abstract

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.