## completeness theorem

**completeness theorem** A theorem about a logical system *L* and a semantics *S* stating that a formula is provable in the logic *L* if and only if it is valid in the semantics *S*. A completeness theorem consists of a soundness and an adequacy theorem: it confirms that the logic is expressing and deriving precisely the properties that are valid according to the semantics.

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## completeness theorem

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**completeness theorem**