The Aristotelian formal logic which Muslims have admirably expanded and organized is the most ancient logical system appeared over twenty three centuries ago and is still seriously employed among philosophers and logicians, especially among the Muslims. What this paper is pursuing is to explain the frameworks and foundations of this logical system. It intends to propose several categories of axiomatic principles and to show that as far as formal logic deals with form (proposition and analogy) it is based on these principles. Although Muslim logicians may not have been negligent of these principles, they have not – as far as the author’s knowledge allows – explicitly and coherently dealt with or talked about them. Others have reviewed the quadruple relations between two universals as well as relations between the contradictories of the two universals, but this article has followed up the task showing that whenever there exists one of the four relations between two universals then what relation may the essence (‘ayn) of one have with the contradictory (naqīḍ) of the other. It is by virtue of these principles that it explicates the rulings of propositions by a non-deductive method and recounts the issues concerning the logic of definition (propositions and their rulings) without any dependence on the logic of argument. Furthermore, it states that if there exists one of the quadruple relations between one universal and the second universal and between the second universal and the third universal, then what relation will there exist between the first and third universal; and thereupon, presents an in-depth method for elucidating the four forms of analogy which can by itself comprise a system for inference, too. In addition, it brings to light some points which might have been neglected so far; e.g., why the relation between “contradictories of general and peculiar in some respect” and the “two divergents” is that of partial divergence; namely, sometimes it is “generality and peculiarity in some respect” and sometimes “universal divergence”.
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