# Logical value

a logical value indicates the degrees of the truth of a sentence in the logic. There are than two logical values in a logical system more, one often rather speaks of quasi-logical values or pseudo logical values. Under a logical value function, also Denotationsfunktion or Weighing function, one understands a function, which illustrates the quantity of the formulas of a logical system on the quantity of its logical values.

In the classical logic each sentence has one of exactly two logical values: It is either true or wrong. Onespeaks also of the principle of bivalence.

In multi-valued logics there are more than two logical values, i.e. the principle of bivalence is given up. The sentence of impossible third is however not given up automatically thereby with. Rather there are multi-valued logics,in those the sentence of impossible third applies, and such, in which it does not apply.

There are logics with finally many logical values, so for example the system Ł 3, one formalized as the first multi-valued logic 1920 of January Łukasiewicztrivalent logic. In addition, there are logics with infinitely many logical values, for example Fuzzy logic.

In extensionalen logics the logical value of a compound sentence is clearly certain from the logical values of its subsets (principle of the Extensionalität or Kompositionalität); one says also: Those Junctors (Konnektive) are truth functional. The classical logic used excluding truth-functional Konnektive, is thus extensional. For the indication of the logical value process of a extensionalen (truth-functional) Konnektivs in endlichwertigen logics gladly truth tables are used.

In intensionalen logics, i.e. such, which (also or only) contain Konnektive,those are not truth functional, are the formalisms substantially more complex and various, with those one the logical value of a complex sentence computed. For some intensionale logics, particularly for Modallogik, Kripke semantics worked for the evaluation of sentences.

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## Literature

• L. Kreiser, S. God forest, W. Stelzner (Hge): Nichtklassi logic. An introduction, Berlin: Academy 2 1990