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arXiv · 2408.12030

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.

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Jonte Deakin, Jim de Groot. 2024-08-21. Sub-sub-intuitionistic logic. https://arxiv.org/abs/2408.12030

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