Resolution as Syntax

Resolution is a purely syntactic uniform proof procedure. Resolution does not consider what predicates may mean, but only what logical conclusions may be derived from the axioms.

Advantage: Resolution is universally applicable to problems that can be described in first-order logic. Work on the theorem prover can be decoupled from any particular domain.

Disadvantage: Resolution by itself cannot make use of any domain-dependent heuristics. Despite many attempts to improve the efficiency of resolution, it often takes exponential time.

A contradiction in the axiom set allows anything to be ``proved''. Unfortunately, consistency of the axiom set is not decidable.

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