In logic, a truth function[1] is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and output of a truth function are all truth values; a truth function will always output exactly one truth value, and inputting the same truth value(s) will always output the same truth value. The typical example is in propositional logic, wherein a compound statement is constructed using individual statements connected by logical connectives; if the truth value of the compound statement is entirely determined by the truth value(s) of the constituent statement(s), the compound statement is called a truth function, and any logical connectives used are said to be truth functional.[2]
Classical propositional logic is a truth-functional logic,[3] in that every statement has exactly one truth value which is either true or false, and every logical connective is truth functional (with a correspondent truth table), thus every compound statement is a truth function.[4] On the other hand, modal logic is non-truth-functional.
^Roy T. Cook (2009). A Dictionary of Philosophical Logic, p. 294: Truth Function. Edinburgh University Press.
^Roy T. Cook (2009). A Dictionary of Philosophical Logic, p. 295: Truth Functional. Edinburgh University Press.
^Internet Encyclopedia of Philosophy: Propositional Logic, by Kevin C. Klement
^Roy T. Cook (2009). A Dictionary of Philosophical Logic, p. 47: Classical Logic. Edinburgh University Press.
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