The principle of bivalence is related to the law of excluded middle though the latter is a syntactic expression of the language of a logic of the form "P ∨ ¬P". The difference between the principle of bivalence and the law of excluded middle is important because there are logics that validate the law but not the principle. For example, the three-valued Logic of Paradox (LP) validates the law of excluded middle, but not the law of non-contradiction, ¬(P ∧ ¬P), and its intended semantics is not bivalent. (see also An Introduction to Non-Classical Logic) In Intuitionistic logic the law of excluded middle does not hold. In classical two-valued logic both the law of excluded middle and the law of non-contradiction hold.
The principle of bivalence is related to the law of excluded middle though the latter is a syntactic expression of the language of a logic of the form "P ∨ ¬P". The difference between the principle of bivalence and the law of excluded middle is important because there are logics that validate the law but not the principle. For example, the three-valued Logic of Paradox (LP) validates the law of excluded middle, but not the law of non-contradiction, ¬(P ∧ ¬P) and its intended semantics is not bivalent. (see also An Introduction to Non-Classical Logic) In Intuitionistic logic the law of excluded middle does not hold. In classical two-valued logic both the law of excluded midd,le and the law of non-contradiction hold.