Completeness Theorem

Syntactic Entailment (Propositional Logic) and Semantic Entailment (Propositional Logic) are equivalent. In other words: Let , . Then if and only if .

Proof

Soundness Theorem (Propositional Logic) and Adequacy Theorem (Propositional Logic).

Corollaries

Compactness Theorem (Propositional Logic) Decidability Theorem