The principle of bivalence

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The principle of bivalence states that every declarative sentence expressing a proposition has exactly one truth value, true or false, not both, not neither.

A logic that acknowledges this principle is called a two-valued or bivalent logic.

In formal logic, the principle of bivalence becomes a property of semantics - given semantics may or may not possess it.

Bivalence is not the same as the law of excluded middle (EM); there are logics that recognize EM without being bivalent.

For example, the three-valued Logic of Paradox (LP) upholds the law of excluded middle, but not the law of non-contradiction, ¬(P ∧ ¬P), and its intended semantics is not bivalent.

In classical two-valued logic both the law of excluded middle and the law of non-contradiction hold.

Many modern logic programming systems replace the law of the excluded middle with the concept of negation as failure (NAF).

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