Morphisms and Duality for Polarities and Lattices with Operators
Logic
2023-11-08 v2
Abstract
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of morphism between polarity-based structures that generalises the theory of bounded morphisms for Boolean modal logics. It defines a category of such structures that is contravariantly dual to a given category of lattice-based algebras whose additional operations preserve either finite joins or finite meets. Two different versions of the Goldblatt-Thomason theorem are derived in this setting.
Cite
@article{arxiv.1902.09783,
title = {Morphisms and Duality for Polarities and Lattices with Operators},
author = {Robert Goldblatt},
journal= {arXiv preprint arXiv:1902.09783},
year = {2023}
}