Propositional function

A function whose arguments and values are truth values (cf. Truth value). This term is used when the discussion is about interpretations of a formalized logical language.

If is the set of truth values of formulas of a given language, then a propositional function is any expression of the type (). These functions are interpreted as propositional connectives (cf. Propositional connective) that allow one to form new statements or formulas. In the classical two-valued interpretation of the set of truth values, i.e. when , such functions are also called functions of the algebra of logic.

Comments

Propositional functions are also called truth functions. When , they are also called Boolean functions.

More or less equivalently, propositional functions are functions whose arguments and values are propositions.

References

[a1]	S.C. Kleene, "Introduction to metamathematics" , North-Holland (1959) pp. 144; 226