Avicenna has divided the conditionals to the real cogent (i.e. with possible antecedent) and the verbal cogent (i.e. with the impossible antecedent). Denying the truth of the latter, he caused controversies among Moslem logicians. At the paper, we report the controversies, analyze the real and verbal cogent conditionals, formalize them in Modern Modal and Relevant Logics, and finally, defend ideas of Moslem logicians. In this regards, three controversial subject matters are explained and Islamic logicians’ positions on them is defended by real cogent conditional. The three are as follows: conversion of conditional, equivalences of conditionals, and Al-Razi’s claim on the necessity of consistency between antecedent and consequent of true cogent conditional.
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