Soundness, Completeness Glossary

Definition

A deductive system such as our natural deduction calculus is sound with respect to the standard semantics iff every provable sequent is valid in the sense that its conclusion is true for every interpretation which satisfies all of its premises. The deductive system is complete for the same semantic account iff every valid sequent is provable.

Comments

Ordinary first order logic is in fact sound and complete for the semantics presented in these notes. Free logic is sound, but for completeness the semantic account has to be relaxed to allow functions (including names) to be partial and to include the empty set as a legitimate domain

Links

• Soundness proof
• Completeness proof for propositional logic
• Completeness proof for first order logic