论文标题
多原子逻辑和广义blok-esakia理论
Polyatomic Logics and Generalised Blok-Esakia Theory
论文作者
论文摘要
本文提出了一个多原子逻辑的新颖概念，并启动了系统研究。这种方法是受好奇语义的启发，是通过获取给定逻辑的变体获得的，该方法是通过查看选择器项所涵盖的片段而获得的。我们为这些逻辑引入了代数语义，并证明了代数的完整性。这些逻辑与翻译有关，通过引入许多涉及选择器项的翻译类别，这些翻译在代数逻辑中被普遍存在。在这种情况下，我们还引入了广义的blok-esakia理论，可以为特殊的翻译类别开发。最后，我们通过展示了多原子逻辑理论与一般有趣的翻译类别的一般Blok-esakia理论之间的一些系统联系。
This paper presents a novel concept of a Polyatomic Logic and initiates its systematic study. This approach, inspired by Inquisitive semantics, is obtained by taking a variant of a given logic, obtained by looking at the fragment covered by a selector term. We introduce an algebraic semantics for these logics and prove algebraic completeness. These logics are then related to translations, through the introduction of a number of classes of translations involving selector terms, which are noted to be ubiquitous in algebraic logic. In this setting, we also introduce a generalised Blok-Esakia theory which can be developed for special classes of translations. We conclude by showing some systematic connections between the theory of Polyatomic Logics and the general Blok-Esakia theory for a wide class of interesting translations.
