Decidability (logic)

In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer. Logical systems are decidable if membership in their set of logically valid formulas can be effectively determined. Zeroth-order logic is decidable, whereas first-order and higher-order logic are not. A theory in a fixed logical system is decidable if there is an effective method for determining whether arbitrary formulas are included in the theory. Many important problems are undecidable, that is, it has been proven that no effective method for determining membership can exist for them.