Truth function

In logic a truth function is a connective for which the truth value is determined systematically by the values of the statements it connects. Well known truth functions include the connectives or, and, not, nor, if... then, iff.

Related Topics:
Logic - Function - Connective - Truth value - Or - And - Not - Nor - If... then - Iff

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A statement or proposition is said to be truth-functional if its truth value is determined by the truth values of its components.

Related Topics:
Statement - Proposition

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For example, since "Paul Martin was Prime Minister of Canada on April 20 2004." is true, and "George Bush was President of the USA on April 20 2004." is also true, the conjunction:

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• "Paul Martin was Prime Minister of Canada and George Bush was President of the USA on April 20 2004."

is true. In this sentence, "and" serves as a truth function.

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In contrast, there is no such correlation between "Al Gore was President of the USA on April 20 2004." and "Britney Spears believes Al Gore was President of the USA on April 20 2004.". Knowing that the former is false does not reveal the truth value of the latter: Britney Spears might or might not believe that Al Gore was President, and the fact that Al Gore was not President on that date is not required to affect the truth value. Thus, the word 'believes' is not a truth function.

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In more mathematical terms, a truth function is a type of Boolean function, and using Boolean variables to hold the results of truth functions is a common practice in computer science. Determining the truth of statements is a fundamental act of both logic and mathematics; as a result, truth functions are commonly discussed in works concerned with the basis of logic and mathematics.

Related Topics:
Boolean function - Boolean variables - Computer science

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Truth function: See also ►