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Sentencelike expression that may be thought of as obtained from a sentence by substituting variables for constants occurring in the sentence. For example, x was a parent of y may be thought of as obtained from Adam was a parent of Abel. A propositional function therefore has no truth-value, becoming true or false only when its free variables are replaced by constants of appropriate syntactic categories (e.g., Abraham was a parent of Isaac).
This entry comes from Encyclopædia Britannica Concise. For the full entry on propositional function, visit Britannica.com.