次直觉逻辑

arXiv - MATH - Logic Pub Date : 2024-08-21 DOI:arxiv-2408.12030

Jonte Deakin, Jim de Groot

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引用次数: 0

摘要

亚次直觉逻辑是从直觉逻辑中通过弱化蕴涵和去除分配性而得到的。它也可以看作条件弱正逻辑。我们通过带有选择功能的半网格为次直觉逻辑提供了语义，证明了该逻辑代数语义的分类对偶性，并以此推导出完备性。然后，我们考虑用各种公理对次直觉逻辑进行扩展。

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Sub-sub-intuitionistic logic

Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic logic by means of semilattices with a selection function, prove a categorical duality for the algebraic semantics of the logic, and use this to derive completeness. We then consider the extension of sub-sub-intuitionistic logic with a variety of axioms.

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arXiv - MATH - Logic

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