A plea for KR

Abstract

There is a strong case to be made for thinking that an obscure logic, KR, is better than classical logic and better than any relevant logic. The argument for KR over relevant logics is that KR counts disjunctive syllogism valid, and this is the biggest complaint about relevant logics. The argument for KR over classical logic depends on the normativity of logic and the paradoxes of implication. The paradoxes of implication are taken by relevant logicians to justify relevant logic, but considerations on the normativity of logic show that only some of the paradoxes of implication are genuine. KR avoids all the genuine paradoxes of implication, unlike classical logic. Overall, KR avoids the genuine paradoxes of implication and avoids the major objection to relevant logics. This combination of features provides strong reason to give KR a place in the conversation about the right logic(s).KR counts disjunctive syllogism valid. Among relevant logicians, the main reason for rejecting disjunctive syllogism has been that it is used in the derivation of some of the paradoxes of implication and so is guilty by association. 7 However, once one distinguishes between the genuine paradoxes of implication and the rest, it turns out that disjunctive syllogism is associated with none of the genuine ones. Thus, the main obstacle to accepting disjunctive syllogism is illusory.Overall, the advantage of KR over relevant logics is its inclusion of disjunctive syllogism, and its benefit over classical logic is that it avoids the genuine paradoxes of implication. These two factors make KR a better choice than either a relevant logic or classical logic.The paper is divided into four parts. In the first section, I introduce relevant logics, the common argument for them, and the superrelevant logics like KR. I explain how KR differs from R and CL. The second section concerns the normativity of logic; in this section, I discuss the views of Gilbert Harman, Florian Steinberger, and Greg Restall in order to establish which paradoxes of implication are genuine and which are illusory. In the third section, I offer an argument for KR over classical logic: KR has none of the genuine paradoxes of implication. In the fourth section, I offer an argument for KR over R: disjunctive syllogism should be counted valid and the major reasons given by relevant logicians for thinking it is invalid are not good. Hence, there is no reason to reject it and plenty of reason to accept it.Remember, this is only a plea for KR to be part of the conversation. What follows are good reasons to think it has substantial benefits over its competitors and so should be taken seriously. However, I do not presume to give a conclusive case. In other words, KR should be considered when weighing the costs and benefits of various logics in the philosophical literature. The standards for success in showing that KR should be part of the conversation are considerably easier to meet than the standards for having conclusively shown that KR is the best logic. Relevant logics, superreleva...

Agile Logical Semantics for Natural Languages

“…Apart from Montague's approach, formalisms of logical representation constitute a large field of investigation in artificial intelligence [16,17]. However, the spirit and the finalities of these systems are very different from those of the present work.…”

“…Moreover, they use variables, first-order or second-order logic, and modal or temporal operators, and the rules of composition are very complex, making KR languages comparable to programming languages. In certain cases they differ radically from classical predicate logic, and can follow very different principles and presuppositions [17].…”

Non-Boolean classical relevant logics II: Classicality through truth-constants

“…4 I should also like to mention a recent novel approach to the implicational paradoxes, namely that argued for by Kerr (2019). Kerr argues that the logic KR-R augmented by A∧∼A → B (which, then, also extends CR)-is both superior to classical logic in that it does not validate genuine implicational paradoxes such as A → (B → A), and superior to R in that it validates disjunctive syllogism.…”