Co-Heyting algebra

Summary

A co-Heyting algebra is a bounded lattice with a difference operation $a \setminus b$, the least element $c$ such that $a \le b \vee c$. It is the order dual of a Heyting algebra: turning a co-Heyting algebra upside down gives a Heyting algebra, and conversely. Every co-Heyting algebra is a distributive lattice. The closed sets of a topological space form a co-Heyting algebra, and co-Heyting algebras serve as algebraic models of paraconsistent logics.