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

16 pagesPublished: December 14, 2015

Abstract

We introduce a theorem proving strategy for Partial Classical Logic (PCL) that
is 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 of
geometric resolution.

The translation to Kleene logic does not only open the way to theorem proving, but
it also sheds light on the relation between PCL, Kleene Logic, and classical logic.

Keyphrases: Logics for partial functions, theorem proving, three-valued logic

In: Christoph Benzmüller and Jens Otten (editors). ARQNL 2014. Automated Reasoning in Quantified Non-Classical Logics, vol 33, pages 71--86