Difference between revisions of "Propositional function"
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| − | 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 | + | 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. |
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| + | 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. | ||
Latest revision as of 17:37, 23 November 2014
2020 Mathematics Subject Classification: Primary: 03B [MSN][ZBL]
A function whose arguments and values are truth values. 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 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=32391