Sub-sub-intuitionistic logic
Logic
2024-08-23 v1
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.
Keywords
Cite
@article{arxiv.2408.12030,
title = {Sub-sub-intuitionistic logic},
author = {Jonte Deakin and Jim de Groot},
journal= {arXiv preprint arXiv:2408.12030},
year = {2024}
}
Comments
24 pages