Truth value

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In logic and mathematics, a logical value, also called a truth value, is a value indicating the relation of a proposition to truth.

Look up logical in Wiktionary, the free dictionary.

In classical logic, the truth values are true and false. Intuitionistic logic lacks a complete set of truth values because its semantics, the Brouwer-Heyting-Kolmogorov interpretation, is specified in terms of provability conditions, and not directly in terms of the truth of formulae. Multi-valued logics (such as fuzzy logic and relevance logic) allow for more than two truth values, possibly containing some internal structure.

Even non-truth-valuational logics can associate values with logical formulae, as is done in algebraic semantics. For example, the algebraic semantics of intuitionistic logic is given in terms Heyting algebras.

Topos theory uses truth values in special sense: the truth values of a topos are the global elements of the subobject classifier. Having truth values in this sense does not make a logic truth valuational.

[edit] See also

• Boolean domain
• Degrees of truth
• False dilemma
• Fuzzy logic
• Logical connective
• Multivalued logic
• Relativism
• Slingshot argument
• Negation

[edit] External links

• Article on logical constants at the Stanford Encyclopedia of Philosophy
• Weblog entry "How many is two?" by Andrej Bauer discussing the relationship between truth values in intuitionistic logic and topos theory on the one hand and classical logic on the other.