Enumerating Independent Linear Inferences

A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on side. In this work we leverage recently developed graphical representations formulae to build an implementation that capable more efficiently searching for switch-medial-independent inferences. We use it find four `minimal' 8-variable independent inferences and also prove no smaller ones exist; contrast, previous approach based directly reached computational limits already 7 variables. Two these new derive some previously found The other two (which are dual) exhibit structure seemingly beyond the scope approaches aware of; particular, their existence contradicts conjecture Das Strassburger. were able identify 10 minimal 9-variable all aforementioned inferences, comprising 5 dual pairs, present applications our recent `graph logics'.