Definition:Variable/Predicate Logic

Definition
A variable is a label which is used to refer to an unspecified object. The collection of all possible objects that the variable may refer to will need to be specified.

A variable can be identified by means of a symbol, for example, $$x$$, $$y$$, $$z$$, $$A$$, $$B$$, $$C$$, $$\phi$$, $$\psi$$, $$\aleph$$. It is often convenient to append a subscript letter or number to distinguish between different objects of a similar type:


 * $$a_0, a_1, a_2, \ldots, a_n; S_\phi, S_{\phi_x}, \ldots$$

The type of symbol used to define a variable is purely conventional. Particular types of object, as they are introduced, frequently have a particular range of symbols specified to define them, but there are no strict rules on the subject.

Object Variable
In the context of predicate logic, a variable is often called an object variable.

Value
A variable $$x$$ may be (temporarily, conceptually) identified with a partcular object.

If so, then that object is called the value of $$x$$.