Difference between revisions of "Propositional function"
(Importing text file) |
(TeX) |
||
| Line 1: | Line 1: | ||
| + | {{TEX|done}} | ||
A function whose arguments and values are truth values (cf. [[Truth value|Truth value]]). This term is used when the discussion is about interpretations of a formalized logical language. | A function whose arguments and values are truth values (cf. [[Truth value|Truth value]]). This term is used when the discussion is about interpretations of a formalized logical language. | ||
| − | If | + | 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 connectives (cf. [[Propositional connective|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 $\Omega=\{0,1\}$, such functions are also called functions of the algebra of logic. |
====Comments==== | ====Comments==== | ||
| − | Propositional functions are also called truth functions. When | + | 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. | More or less equivalently, propositional functions are functions whose arguments and values are propositions. | ||
Revision as of 19:17, 7 July 2014
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 $\Omega$ 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 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 $\Omega=\{0,1\}$, 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
| [a1] | S.C. Kleene, "Introduction to metamathematics" , North-Holland (1959) pp. 144; 226 |
Propositional function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Propositional_function&oldid=18103