Definition:Logical Argument

A logical argument (or just "argument") is a process of creating a new statement from one or more existing statements.

An argument proceeds from a set of premises to a conclusion, via a process called logical implication.

An argument may have more than one premise, but only one conclusion.

While statements may be classified as either true or false, an argument may be classified as either valid or invalid.

Loosely speaking, a valid argument is one that leads unshakeably from true statements to other true statements, whereas an invalid one is an argument that can lead you to, for example, a false statement from one which is true.

Thus:
 * An argument may be valid, even though its premises are false.
 * An argument may be invalid, even though its premises are true.
 * An argument may be invalid and its premises false.

If we want to be sure of the truth of a conclusion, we need to make sure that the premises are true and that the argument is valid.

However, while you may not actually know whether a statement is actually true or not, you can investigate the consequences of it being either true or false, and see what effect that has on the truth value of the proposition(s) of which it is a part. That, in short, is what the process of "logical argument" consists of.

An argument may be described symbolically by means of sequents, which specifiy the flow of an argument.

Finitary
A finitary argument is one which starts with a finite number of axioms, and can be translated into a finite number of statements.