Sub-Sub-Intuitionistic Logic
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 extensions of sub-sub-intuitionistic logic with a variety of axioms.
Fields of Study & Subjects
Logic
Reasoning
and Knowledge
Advanced Algebra and Logic
Publication details
- Journal / source
- Notre Dame Journal of Formal Logic
- Publisher
- Duke University Press
- Volume
- 67
- Issue
- 3
- Pages
- 305–336
- Publication date
- 13 July 2026
- Language
- EN