Difference between revisions of "Propositional form"
From Encyclopedia of Mathematics
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| − | A linguistic expression containing variables, in place of which one may substitute propositions, thereby obtaining new propositions. In formalized languages a propositional form is a formula containing free occurrences of propositional variables taking values in the set of truth values (cf. [[ | + | A linguistic expression containing variables, in place of which one may substitute propositions, thereby obtaining new propositions. In formalized languages a propositional form is a formula containing free occurrences of propositional variables taking values in the set of truth values (cf. [[Truth value]]). |
| − | Sometimes a propositional form is an expression, constructed in analogy with a [[ | + | Sometimes a propositional form is an expression, constructed in analogy with a [[propositional formula]], in which symbols of a [[meta-language]] are used instead of propositional variables, and denoting arbitrary formulas of the [[propositional calculus]]. |
====References==== | ====References==== | ||
| − | + | * E. Mendelson, "Introduction to mathematical logic", v. Nostrand (1964) {{ZBL|0192.01901}} | |
Latest revision as of 14:34, 8 October 2023
A linguistic expression containing variables, in place of which one may substitute propositions, thereby obtaining new propositions. In formalized languages a propositional form is a formula containing free occurrences of propositional variables taking values in the set of truth values (cf. Truth value).
Sometimes a propositional form is an expression, constructed in analogy with a propositional formula, in which symbols of a meta-language are used instead of propositional variables, and denoting arbitrary formulas of the propositional calculus.
References
- E. Mendelson, "Introduction to mathematical logic", v. Nostrand (1964) Zbl 0192.01901
How to Cite This Entry:
Propositional form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Propositional_form&oldid=16154
Propositional form. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Propositional_form&oldid=16154
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article