Definition:Decision Problem

Definition

Let $\FF$ be a formal system.

The decision problem for $\FF$ is the question as to whether or not there exists an effective procedure for determining whether or not a given well-formed formula of $\FF$ is a theorem of $\FF$.

That is, whether $\FF$ is decidable.

Also see

• Results about decision problems can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): decidable
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): decision problem
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): decidable
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): decision problem