Truth function

<p>In <a href="/facts/Logic/8JnpJLtt">logic</a>, a truth function is a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> that accepts <a href="/facts/Truth_value/SY4e2w8l">truth values</a> 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 <a href="/facts/Propositional_calculus/MNt5v31V">propositional logic</a>, wherein a compound statement is constructed using individual statements connected by <a href="/facts/Logical_connective/VkPhUs6M">logical connectives</a>; 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.
</p><p><a href="/facts/Classical_logic/ls62MAms">Classical propositional logic</a> is a truth-functional logic, 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 <a href="/facts/Truth_table/4KsmArDW">truth table</a>), thus every compound statement is a truth function. On the other hand, <a href="/facts/Modal_logic/I7uXvYYT">modal logic</a> is non-truth-functional.
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Truth function open-in-new

Truth function