带算子的极性与格的态射与对偶性
Morphisms and Duality for Polarities and Lattices with Operators
AI总结：
本文研究带算子非分配格建模的命题逻辑的关系语义，提出极性结构间的一阶态射概念，定义与格代数范畴反变对偶的结构范畴，并推导两种版本的Goldblatt-Thomason定理。
摘要：
基于极性的结构已被用于为命题逻辑提供关系语义，这类逻辑在代数上由带附加算子的非分配格建模。本文提出了极性结构间一阶态射的概念，推广了布尔模态逻辑的有界态射理论。本文定义了这类结构的一个范畴，它与给定的基于格的代数范畴反变对偶，后者的附加运算保持有限并或有限交。本文在该框架下推导出了两种不同版本的Goldblatt-Thomason定理。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
