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arXiv · 2212.14663

Polyatomic Logics and Generalised Blok-Esakia Theory

Rodrigo Nicolau Almeida
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Abstract

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.

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Rodrigo Nicolau Almeida. 2022-12-30. Polyatomic Logics and Generalised Blok-Esakia Theory. https://arxiv.org/abs/2212.14663

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