Theorem Proving for Logic with Partial Functions Using Kleene Logic and Geometric Logic

Abstract

We introduce a theorem proving strategy for Partial Classical Logic (PCL) thatis based on geometric logic. The strategy first translates PCL theories into sets of Kleene formulas. After that, the Kleene formulas are translated into 3-valued geometric logic. The resulting formulas can be refuted by an adaptation ofgeometric resolution.The translation to Kleene logic does not only open the way to theorem proving, butit also sheds light on the relation between PCL, Kleene Logic, and classical logic.