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We transform a user-friendly formulation of aproblem to a machine-friendly one exploiting the variabilityof first-order logic to express facts. The usefulness of tacticsto improve the presentation is shown with several examples.In particular it is shown how tactical and resolution theoremproving can be combined.
A straightforward formulation of a mathematical problem is mostly not ad-equate for resolution theorem proving. We present a method to optimize suchformulations by exploiting the variability of first-order logic. The optimizingtransformation is described as logic morphisms, whose operationalizations aretactics. The different behaviour of a resolution theorem prover for the sourceand target formulations is demonstrated by several examples. It is shown howtactical and resolution-style theorem proving can be combined.
Even though it is not very often admitted, partial functions do play asignificant role in many practical applications of deduction systems. Kleenehas already given a semantic account of partial functions using three-valuedlogic decades ago, but there has not been a satisfactory mechanization. Recentyears have seen a thorough investigation of the framework of many-valuedtruth-functional logics. However, strong Kleene logic, where quantificationis restricted and therefore not truth-functional, does not fit the frameworkdirectly. We solve this problem by applying recent methods from sorted logics.This paper presents a resolution calculus that combines the proper treatmentof partial functions with the efficiency of sorted calculi.