Definition:Consistent (Logic)

Definition
Let $\mathcal L$ be a logical language.

Let $\mathscr P$ be a proof system for $\mathcal L$.

Also defined as
Common confusion arises in the precise interpretation of consistency in logic.

On, consistency is placed in the realm of proof systems.

It is also common to place it in the realm of formal semantics.

That is, to define consistent as what is satisfiable on.

Because of the variation, any use of these terms in a source work should be treated with the utmost care and precision to determine the exact meaning.

Also see

 * Definition:Provable Consequence
 * Definition:Inconsistent


 * Definition:Satisfiable