---
tag: AZPR5803TY
kind: statement
role: proposition
name: Analogous laws
msc: [03B05]
sources:
  - wikipedia: en:17637@r1370685960
    locator: Law of excluded middle, section Analogous laws
    note: adopted
    mention: wikipedia://en/17637#0GWC
    sections: [Statement]
inventory: [B32CDRRP0Y]
---

## Statement

Some systems of logic have different but analogous laws. For some finite *n*-valued logics, there is an analogous law called the *law of excluded*n*\+1th*. If negation is 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 values (and not a value that is not one of the *n*).

Other systems reject the law entirely.