Law of the weak excluded middle

Statement

A particularly well-studied intermediate logic is given by De Morgan logic, which adds the axiom $\neg P \lor \neg\neg P$ to intuitionistic logic, which is sometimes called the law of the weak excluded middle.

This is equivalent to a few other statements:

• Satisfying all of De Morgan's laws including $\neg(P\land Q) \,\leftrightarrow\, \neg P \lor \neg Q$
• $$(P \to Q) \lor (\neg P \to \neg Q)$$
• $$(P \to (Q \lor \neg R)) \to ((P \to Q) \lor (P \to \neg R))$$