The Relevance Logic Theory and the Truth-Functional System Theory; A Comparison and Evaluation Based on the Inference to the Best Explanation and Prest’s Quantitative Model

Recent developments in non-classical logic have raised the question of rational choice in the field of logic. If logic is not an exception, a posterior methodology can be used for rational choice among logical theories. In choosing a logical theory, there are several criteria to consider, such as expressive power and separation of propositions, explanatory power and separation of inferences, consistency and internal coherence, compatibility with evidence, simplicity, and unification. To apply this methodology to logic, we will echo the views of Priest and Williamson and examine their opinions on logic and logical evidence. In this article, we consider, in Priest's opinion, the linguistic concept of "validity" as the subject of logic and partial inferences and our intuitions about their validity as evidence for logical theories. Based on these criteria, we compare Relevance Logic theory and Truth Functional System theory, then calculate the rationality index for each theory. Compared with Relevance Logic, the Truth Functional System theory has a higher rationality index and outperforms it many times over.