Ma`rifat Falsafi

The most important type of conditionals, in Ibn Sina’s logic, is “concomitant hypothetical propositions”. The nearest conditional element of the modern logic to this type of conditionals is “relevant concomitance”. That part of modern logic that deals with such concomitance is called, “relevance logic”. There is a debate among relevance logicians on whether accepting a contradiction implies any arbitrary proposition. In other words, is a contradictory proposition related to any arbitrary proposition? A positive answer leads to a logic called “KR”, which benefits from a simpler and more intuitive semantic, compared to other relevance logics which reject concluding arbitrary propositions from contradiction. Determining the validity of arguments in various systems and semantics of relevance logic is a difficult task, which is rarely dealt with in the literature of relevance logic. Inspired by Hughes’ and Cresswell’s valuation method in modal logic, called “relevance testing”, the author in this article suggests a relevance testing for KR logic, and shows its use through some examples.