Namespaces
Variants
Actions

Difference between revisions of "Propositional form"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Importing text file)
 
(zbl link)
 
Line 1: Line 1:
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|Truth value]]).
+
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|propositional formula]], in which symbols of a [[Meta-language|meta-language]] are used instead of propositional variables, and denoting arbitrary formulas of the [[Propositional calculus|propositional calculus]].
+
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====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  E. Mendelson,   "Introduction to mathematical logic" , v. Nostrand (1964)</TD></TR></table>
+
* 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=54103
This article was adapted from an original article by V.N. Grishin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article