Solving a Problem in Relevance Logic with an Automated Theorem Prover

Abstract

A new challenging problem for automated theorem provers (ATP) is presented. It is from the field of relevance logic and is known as “converse of contraction”. We firstly give some background informatlon about relevance logic and the problem itself and then discuss a proof for the theorem which has been found by the Markgraf Karl Refutation Procedure (MKRP), a resolution based theorem prover, under development at the Universities of Karlsruhe and Kaiserslautern.

For solving this problem we implemented a new method to control the application of “generator clauses” like Exy ⇒ Ef(x)f(y). An uncontrolled application of such clauses produces arbitrarily deeply nested and often useless terms f (f (f (f ... which in general cannot be avoided with a global term depth limit because deeply nested terms of more heterogenous structure may occur in the proof.