Paraconsistent Reasoning Based on Strong Relevant Logic

1 This work is supported in part by The Ministry of Education, Culture, Sports, Science and Technology of Japan under Grant-in-Aid for Exploratory Research No. 09878061 and Grant-in-Aid for Scientific Research (B) No. 11480079. Abstract. Both a body of human knowledge and a knowledge/information system may be incomplete and inconsistent in many ways. Reasoning with incomplete and inconsistent knowledge/information is the rule rather than the exception in our everyday real-life situations and most scientific disciplines. Paraconsistent reasoning, or reasoning in the presence of inconsistency, is indispensable to scientific discovery. This paper intends to answer such a fundamental question: What kind of logic system can satisfactorily underlie paraconsistent reasoning in scientific discovery? We show why classical mathematical logic, its various classical conservative extensions, and traditional (weak) relevant logics cannot satisfactorily underlie paraconsistent reasoning in scientific discovery, and propose that one should adopt strong relevant logic as the fundamental logic to underlie paraconsistent reasoning in scientific discovery.