The Study of Consequent Negation Rule

According to a rule in Avicenna's logic, there exists cohesion between any two necessary hypothetic propositions with identical quantity, different quality, identical antecedent, and denial of the consequent. The rule is introduced and has been argued for, by Avecinna. After him, this rule is criticized by Avicennian logicians. Khunaji questioned Avecinna’s pre-assumptions of this proof by examples of natural language. After Khunaji, some logicians like Nasir al-Din Tusi, Qutb al-Din al-Razi, and Qutb al-Din al-Shirazi tried to answer Khunaji’s critiques by presenting some better formalizations of Avecinna’s arguments or defending his pre-assumptions. In this paper, after introducing the arguments of both sides together with their detailed formalizations, it is concluded that the answers to Khunaji’s critiques are not enough to prove the aforementioned rule, and accepting this rule still requires new arguments.