The resolution inference rule is applied repeatedly and new inferences added to the set. The process of determining the unsatisfiability of the negation of a formula is known as refutation . The resolution proof procedure is refutation complete for classical logic as, when applied to an unsatisfiable formula, the procedure is guaranteed to produce false.
Temporal logics are extensions of classical logic, with operators that deal with time.
In particular, temporal logics have been used successfully in the specification of safety, liveness and fairness properties of a range of dynamic systems. Such a logical representation of a system then permits the analysis of the systems properties via logical proof. This involves the transformation of temporal formulae into a normal form, followed by the application of a classical style resolution rule to formulae that occur at the same moment of time. Finally a novel temporal resolution rule is applied that resolves contradictory formula that hold over a time period. The temporal resolution method has been defined, proved correct and has been extended to more complex logics.