In mathematical logic, a truth function is a function from a set of truth values to truth-values. Classically the domain and range of a truth function are {truth,falsehood}, but they may have any number of truth-values, including an infinity of them.
A sentence is truth-functional if the truth-value of the sentence is a function of the truth-value of its subsentences. A class of sentences is truth-functional if each of its members is. For example, the sentence "Apples are fruits and carrots are vegetables" is truth-functional since it is true just in case each of its subsentences "apples are fruits" and "carrots are vegetables" is true, and it is false otherwise. Not all sentences of a natural language, such as English, are truth-functional.
Sentences of the form "x believes that..." are typical examples of sentences that are not truth-functional. Let us say that Mary mistakenly believes that Al Gore was President of the USA on April 20, 2000, but she does not believe that the moon is made of green cheese. Then the sentence
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Subject: Truth function 
Sun Nov 21, 2010 9:14 am
