This is actually a subject when I studied Sharia around 2005 just after I returned from the Holy Mecca. It is a philosophical branch of study. Logic actually has two meanings. The first one describes the use of valid reasoning in some activity. The second one refers to normative study of reasoning or a branch thereof. In the latter sense, it features most prominently in the subjects such as philosophy, mathematics and computer science. Basically I do not care about whatever people talk about science or technology. Because I know that they were all exist only in temporary "time" and "space".
Logic was studied in several ancient civilizations such as India, Persia, Greece and China. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of classical trivium which also included grammar and rhetoric. In our medieval era, logic was extended further by al-Farabi who categorized it into two separate groups which were the idea and proof. Later on, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Buddhists and Jains of ancient India. I am familiar with Buddhist thought since the region where I live right now was a Buddhist region. Buddhism concerns about psychology so you could see most of my posts dealing with psychology issues...
I am basically posting some basics of our logical studies here. We begin with mind and the faculties of intellect within human self. This would later be developed into 'Irfan (Gnosis). Our source for the studies of Gnosticism basically came from Abu Hamid al-Ghazali literary works and he was from the school of Shafi'ie jurisprudence and from the Book of Aphorisms by Ahmad bin Muhammad bin Abd al-Karim bin 'Ataullah Iskandari. Gnosticism is not to be studied by laymen and laymen are strongly discouraged from engaging themselves in this study. Study and practice the basic traditional creeds and pillars of the religion first!
Sealed with prayers for mercy, peace and love, amin!