2024/08/21 by Deakin, Jonte, de Groot, Jim
#03F55 (Primary) 03B45 #03G10 (Secondary) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2408.12030
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.