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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}
}

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24 pages