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Logical value

What is truth? Pontius Pilate (John 18:38)

In mathematics logical value or truth value is an attribute of a proposition which evaluates the extent to which  the proposition is true.  

In classical logic, the only possible truth values are true and false. Since True represents the truth value of being true and False is opposed to True, there are two generally accepted constraints on truth or falsehood:

Every proposition is true or false [so-called Law of Excluded Middle]

No proposition is both true or false [so-called Law of Non-contradiction]

However, other logical system were developed were also other logical values are possible. For instance, in fuzzy logic or generally in multi-valued logic systems more truth values are allowed.

In the classical algebraic setting the set {True, False} forms a two-element Boolean algebra . Replacing this algebra by some algebras (for instance Heyting algebra    ) may lead to other systems of truth values.

Sometimes shorthand notation 1 or T for being true, and 0 or F for being false is also used.

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