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

2014/08/08 by Sabine Frittella, Frittella, Sabine, Alessandra Palmigiano +3 · 1 citation
Computer Science · #Logic, Reasoning, and Knowledge #Advanced Algebra and Logic #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.1408.1843

Abstract

We establish a formal connection between algorithmic correspondence theory\nand certain dual characterization results for finite lattices, similar to\nNation's characterization of a hierarchy of pseudovarieties of finite lattices,\nprogressively generalizing finite distributive lattices. This formal connection\nis mediated through monotone modal logic. Indeed, we adapt the correspondence\nalgorithm ALBA to the setting of monotone modal logic, and we use a certain\nduality-induced encoding of finite lattices as monotone neighbourhood frames to\ntranslate lattice terms into formulas in monotone modal logic.\n

Citations

• Constructive canonicity for lattice-based fixed point logics

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• Non-normal logics: semantic analysis and proof theory (extended version)

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