Editing Law of excluded middle (section)

== Analogous laws ==
Some systems of logic have different but analogous laws. For some finite [[finite-valued logic|''n''-valued logics]], there is an analogous law called the ''law of excluded ''n''+1th''. If negation is [[cyclic negation|cyclic]] and "∨" is a "max operator", then the law can be expressed in the object language by (P ∨ ~P ∨ ~~P ∨ ... ∨ ~...~P), where "~...~" represents ''n''−1 negation signs and "∨ ... ∨" ''n''−1 disjunction signs. It is easy to check that the sentence must receive at least one of the ''n'' [[truth value]]s (and not a value that is not one of the ''n'').

Other systems reject the law entirely.{{specify|date=August 2020}}

=== Law of the weak excluded middle===

A particularly well-studied [[intermediate logic]] is given by [[De Morgan's laws|De Morgan logic]], which adds the axiom <math>\neg P \lor \neg\neg P</math> 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 <math> \neg(P\land Q) \,\leftrightarrow\, \neg P \lor \neg Q </math>
* <math> (P \to Q) \lor (\neg P \to \neg Q)</math>
* <math>(P \to (Q \lor \neg R)) \to ((P \to Q) \lor  (P \to \neg R))</math>