A Comparative Study on Paradoxical Conditionals in Classical Mathematical Logic and Strong Relevant Logics

From the viewpoint of logic, we have qualitatively shown that classical mathematical logic, its various classical conservative extensions, and traditional relevant logics are not suitable to underlying forward reasoning and/or deduction for discovery because their logical theorems include a lot of paradoxes of conditional, and shown that strong relevant logics are more hopeful candidates for the purpose. But, it is not clear that how ’bad’ the classical mathematical logic, its various classical conservative extensions, and traditional relevant logics are, and how ’good’ strong relevant logics are, since no quantitative analysis and discussion is reported until now. As the result of a comparative study, in this paper, we present a quantitative analysis and discussion on paradoxical conditionals in classical mathematical logic and strong relevant logics. Our study shows that the problem of paradox is very critical to the development of forward reasoning and/or deduction engines useful in applications in the real world.