Implementation of Theorem Prover of Relevant Logic

Abstract

The formalization of human deductive reasoning is a main issue in artificial intelligence. Although classical logic is one of the most useful ways for the formalization, the material implication of classical logic has some fallacies. Relevant logic has been studied for the removal of material implication fallacies in classical logic for the formalization of human deductive reasoning. Relevant logic $ER$ is free from fallacies of material implication and has more provability than typical relevant logic $R$. Moreover, ER has a decision procedure, even though almost all relevant logics are undecidable. This is one of the reasons why $ER$ is an appropriate logic for the formalization of human deductive reasoning. This paper implements automated theorem prover of Relevant logic $ER$ and experiments on this theorem prover to check the processing time of implemented automated theorem prover.