What is "decidability"

n. (context logic computer science English) the state or condition of being decidable.

The word decidable may refer to:

• Decidable language
• Decidability (logic) for the equivalent in mathematical logic
• Gödel's incompleteness theorem, a theorem on the indecidability of languages consisting of "true statements" in mathematical logic.
• Recursive set, a "decidable set" in recursion theory

In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a Boolean true or false value (instead of looping indefinitely). Logical systems such as propositional logic are decidable if membership in their set of logically valid formulas (or theorems) can be effectively determined. A theory (set of sentences closed under logical consequence) 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 can exist for them.