is the property that any sentence that is provable from no premises in that deductive system is also true on all interpretations or structures of the semantic theory for the language upon which that theory is based. Symbolically we write, if then . Some writers will explicitly include the empty set, giving if then . Using the narrow definition of theorem, for sentences provable from no premises, weak soundness says that all theorems are tautologies.

Strong soundness

Strong soundness of a deductive system is the property

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