Editing Three-valued logic (section)

{{Short description|System including an indeterminate value}}
{{Distinguish|Three-state logic}}
{{more citations needed|date=January 2011}}

In [[logic]], a '''three-valued logic''' (also '''trinary logic''', '''trivalent''', '''ternary''', or '''trilean''',<ref>{{cite web|title=Trilean (Stanford JavaNLP API) |url=https://nlp.stanford.edu/nlp/javadoc/javanlp/edu/stanford/nlp/util/Trilean.html|website=Stanford University|publisher=Stanford NLP Group |url-status=live |archive-url=https://web.archive.org/web/20230503011712/https://nlp.stanford.edu/nlp/javadoc/javanlp/edu/stanford/nlp/util/Trilean.html |archive-date= May 3, 2023 }}</ref> sometimes abbreviated '''3VL''') is any of several [[many-valued logic]] systems in which there are three [[truth value]]s indicating ''true'', ''false'', and some third value. This is contrasted with the more commonly known [[Principle of bivalence|bivalent]] logics (such as classical sentential or [[Boolean logic]]) which provide only for ''true'' and ''false''.

[[Emil Leon Post]] is credited with first introducing additional logical truth degrees in his 1921 theory of elementary propositions.<ref>{{Cite journal|last=Post|first=Emil L.|date=1921|title=Introduction to a General Theory of Elementary Propositions|journal=American Journal of Mathematics|volume=43|issue=3|pages=163–185|doi=10.2307/2370324|jstor=2370324|hdl=2027/uiuo.ark:/13960/t9j450f7q|issn=0002-9327|hdl-access=free |jstor-access=free |doi-access=free }}</ref> The conceptual form and basic ideas of three-valued logic were initially published by [[Jan Łukasiewicz]] and [[Clarence Irving Lewis]]. These were then re-formulated by [[Grigore Constantin Moisil]] in an axiomatic algebraic form, and also extended to ''n''-valued logics in 1945.