Principle of Bivalence - Relationship With The Law of The Excluded Middle

Relationship With The Law of The Excluded Middle

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 and the law is important because there are logics which validate the law but which do not validate 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. 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. The programmer may wish to add the law of the excluded middle by explicitly asserting it as true; however, it is not assumed a priori.

Read more about this topic:  Principle Of Bivalence

Famous quotes containing the words relationship, law, excluded and/or middle:

    Our mother gives us our earliest lessons in love—and its partner, hate. Our father—our “second other”Melaborates on them. Offering us an alternative to the mother-baby relationship . . . presenting a masculine model which can supplement and contrast with the feminine. And providing us with further and perhaps quite different meanings of lovable and loving and being loved.
    Judith Viorst (20th century)

    The law is simply expediency wearing a long white dress.
    Quentin Crisp (b. 1908)

    It may be the first in what I trust will be a rapidly growing and influential genre—the novel designed on purpose to be excluded from the Booker short-list.
    Angela Carter (1940–1992)

    Perhaps if the future existed, concretely and individually, as something that could be discerned by a better brain, the past would not be so seductive: its demands would be balanced by those of the future. Persons might then straddle the middle stretch of the seesaw when considering this or that object. It might be fun.
    Vladimir Nabokov (1899–1977)