1.5 Soundness and Completeness
Propositional logic can be studied in two complementary ways. The semantic approach studies truth under valuations, while the proof theoretic approach studies formal derivations from axioms and inference rules. Soundness and completeness explain how these two approaches are related. Semantic Consequence Let $\Gamma$ be a set of formulas, and let $A$ be a formula. We say that $A$ is a semantic consequence of $\Gamma$ if every valuation that makes all...