Theorem proving for classical logic with partial functions by reduction to Kleene logic

Partial functions are abundant in mathematics and program specifications. Unfortunately, their importance has been mostly ignored in automated theorem proving. In this paper, we develop a theorem proving strategy for Partial Classical Logic (PCL). Proof search takes place in Kleene Logic. We show that PCL theories can be translated into equivalent sets of formulas in Kleene logic. For proof search we use a three-valued adaptation of geometric resolution. We prove that the calculus is sound and complete.