Editing Truth function (section)

{{Short description|Function in logic}}
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<!-- :''"Truth functional" redirects here. For the truth functional conditional, see [[Material conditional]].''
 IMHO by no means the material conditional may not be referred to or abbreviated as the adjective "truth functional", omitting a noun like "conditional" or "implication". Seems more like an internal link spamming rather than an appropriate dab hatnote. --Incnis Mrsi -->

In [[logic]], a '''truth function'''<ref>Roy T. Cook (2009). ''A Dictionary of Philosophical Logic'', p. 294: Truth Function. Edinburgh University Press.</ref> is a [[function (mathematics)|function]] that accepts [[truth value]]s 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 calculus|propositional logic]], wherein a compound statement is constructed using individual statements connected by [[logical connective]]s; 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'''.<ref>Roy T. Cook (2009). ''A Dictionary of Philosophical Logic'', p. 295: Truth Functional. Edinburgh University Press.</ref>

[[Classical logic|Classical propositional logic]] is a truth-functional logic,<ref>[http://www.iep.utm.edu/prop-log/  Internet Encyclopedia of Philosophy: Propositional Logic], by Kevin C. Klement</ref> 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.<ref>Roy T. Cook (2009). ''A Dictionary of Philosophical Logic'', p. 47: Classical Logic. Edinburgh University Press.</ref> On the other hand, [[modal logic]] is non-truth-functional.