Theorem 1.

Propositional logic is sound with respect to truth-value semantics.

Proof.

Basically, we need to show that every axiom is a tautology, and that the inference rule modus ponens preserves truth. Since theorems are deduced from axioms and by applications of modus ponens, they are tautologies as a result.

— truth-value semantics for propositional logic is sound

— PlanetMath

2013.12.15 Sunday ACHK