Fuzzy Relevant Logic: What Is It and Why Study It?

For any correct argument in scientific reasoning as well as our everyday reasoning, the premises of the argument must be in some way relevant to the conclusion of that argument, and vice versa. On the other hand, in scientific reasoning as well as our everyday reasoning, many arguments may be correct to some degree, and therefore, a reasoning consisting of such fuzzy arguments is approximate. As a generalization of Boolean classical logic, fuzzy logic was established in order to deal with those fuzzy propositions and to underlie approximate reasoning. However, an approximate reasoning based on fuzzy logic is not necessarily relevant. In this paper, the author intends to call for attentions to such a fundamental research problem: Can we establish a formal logic system to underlie those reasoning that are both relevant and approximate? The paper presents the motivation to study fuzzy relevant logic and discusses possible research directions, problems, and difficulties to establish a formal fuzzy relevant logic system to underlie approximate and relevant reasoning.