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 (or theorems) can be effectively determined. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. 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 for determining membership (returning a correct answer after finite, though possibly very long, time in all cases) can exist for them.
Decidability (logic) - Wikipedia Jump to content From Wikipedia, the free encyclopedia Whether a decision problem has an effective method to derive the answer 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 (or theorems) can be effectively determined. Zeroth-order logic (propositional logic) is decidable, whereas first-order and higher-order logic are not. A theory (set of sentences closed under logical consequence ) in a fixed logical
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