Sub-sub-intuitionistic logic

Jonte Deakin, Jim de Groot
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Abstract

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.
次直觉逻辑
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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