To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Predicate variable

From Wikipedia, the free encyclopedia

In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not been specifically assigned any particular relation (or meaning). Common symbols for denoting predicate variables include capital roman letters such as , and , and common variables such as .[1] In first-order logic, they can be more properly called metalinguistic variables. In higher-order logic, predicate variables correspond to propositional variables which can stand for well-formed formulas of the same logic, and such variables can be quantified by means of (at least) second-order quantifiers.


In the metavariable sense, a predicate variable can be used to define an axiom schema. Predicate variables should be distinguished from predicate constants, which could be represented either with a different (exclusive) set of predicate letters, or by their own symbols which really do have their own specific meaning in their domain of discourse: e.g. .

If letters are used for predicate constants as well as for predicate variables, then there has to be a way of distinguishing between them. For example, letters W, X, Y, Z could be designated to represent predicate variables, whereas letters A, B, C,..., U, V could represent predicate "constants". If these letters are not enough, then numerical subscripts can be appended after the letter in question (as in X1, X2, X3). However, if the predicate variables are not perceived (or defined) as belonging to the vocabulary of the predicate calculus, then they are predicate metavariables, whereas the rest of the predicate letters are just called "predicate letters". The metavariables are thus understood to be used to code for axiom schemata and theorem schemata (derived from the axiom schemata).

Whether the "predicate letters" are constants or variables is a subtle point: they are not constants in the same sense that are predicate constants, or that are numerical constants.

Another option is to use Greek lower-case letters to represent such metavariable predicates. Then, such letters could be used to represent entire well-formed formulae (wff) of the predicate calculus: any free variable terms of the wff could be incorporated as terms of the Greek-letter predicate. This is the first step towards creating a higher-order logic.

If "predicate variables" are only allowed to be bound to predicate letters of zero arity (which have no arguments), where such letters represent propositions, then such variables are propositional variables, and any predicate logic which allows second-order quantifiers to be used to bind such propositional variables is a second-order predicate calculus, or second-order logic.

If predicate variables are also allowed to be bound to predicate letters which are unary or have higher arity, and when such letters represent propositional functions, such that the domain of the arguments is mapped to a range of different propositions, and when such variables can be bound by quantifiers to such sets of propositions, then the result is a higher-order predicate calculus, or higher-order logic.

See also


  1. ^ "Predicate variable - Encyclopedia of Mathematics". Retrieved 2020-08-20.


This page was last edited on 25 October 2021, at 14:49
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.