View source for Propositional function

{{TEX|done}}{{MSC|03B}}

A function whose arguments and values are [[truth value]]s. This term is used when the discussion is about interpretations of a formalized logical language.

If $\Omega$ is the set of truth values of formulas of a given language, then a propositional function is any expression of the type $\Omega^n\to\Omega$ ($n\geq0$). These functions are interpreted as [[propositional connective]]s that allow one to form new statements or formulas. In the classical two-valued interpretation of the set of truth values, i.e. when $\Omega=\{0,1\}$, such functions are also called functions of the algebra of logic.



====Comments====
Propositional functions are also called truth functions. When $\Omega=\{0,1\}$, they are also called Boolean functions.

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

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  S.C. Kleene,   "Introduction to metamathematics" , North-Holland  (1959)  pp. 144; 226</TD></TR></table>