---
tag: DWYCKAKXZD
kind: concept
name: Many-valued logic
msc: [03B50]
sources:
  - url: https://en.wikipedia.org/wiki/Many-valued_logic
same_as:
  wikidata: Q185502
  wikipedia: Many-valued logic
---

## Summary

A many-valued logic is a propositional logic with more than two truth values.
Its connectives are given by tables over the set of truth values, and some values are designated as "true enough".
Examples are the three-valued logics of Łukasiewicz and Kleene, and the infinite-valued Łukasiewicz logic behind fuzzy logic and [[MV-algebras|8T4M7RN9AC]].

## Explanations

### L1 human

Classical logic has two truth values, true and false.
A many-valued logic allows others, such as "unknown" or degrees of truth between $0$ and $1$.
In Łukasiewicz's three-valued logic, the values are $0$, $\tfrac12$ and $1$, and "not $x$" has the value $1 - x$.
There, "$p$ or not $p$", with "or" as maximum, has value $\tfrac12$ when $p$ has value $\tfrac12$, so it is not a law.