propositional function

noun

UK /ˌprɒpəˈzɪʃənəl ˈfʌŋkʃən/

US /ˌprɑːpəˈzɪʃənəl ˈfʌŋkʃən/

A rule that makes a statement with a blank that can be filled in.

The propositional function 'x is even' becomes true when you put 4 in place of x.

SYNONYMS

open sentence predicate statement form sentential function

RELATED WORDS

variable quantifier predicate logic truth value formula

OTHER MEANINGS

2. In logic, an expression containing variables that becomes a proposition when the variables are replaced by specific values.

'x > 5' is a propositional function that is true for x = 7 and false for x = 3.

3. A function whose values are propositions, often used in formal semantics.

The propositional function assigns a truth value to each element of the domain.

4. A statement pattern with placeholders used to study logical structure.

Teachers use a propositional function to show how changing one word changes the whole sentence's truth.