The requirements of modern science imply interdisciplinary research that allows a comprehensive analysis of the object to be studied. At the same time, each discipline has its own approaches to research conducted over the years, a system of terms and concepts, and its own intra-disciplinary evidence based practice. The combination of different methods and approaches not always ensures the intellectual rigor of ongoing research at an inter-disciplinary level. As a rule, priority is given to one of the scholar disciplines according to which "rules and regulations" the study is conducted, or it could be noted, that there is minimization of requirements of each of the disciplines in the context if inter-disciplinary dialogue. The aim of the current paper is to find the most effective methodology for conducting inter-disciplinary research at the intersection of Arabic and Computer Sciences and to answer the question How Intellectual Rigor May be Achieved in Inter-Disciplinary Communication? On the example of our recent publications and different scholar projects, we demonstrate the problem solving with the regard to multi- and inter-disciplinary research. Despite certain contradictions of a methodological nature that arise in the process of inter-disciplinary communication, it is the use of mathematical methods that often allows us to verify the results of researches in the field of humanities, to ensure the speed of data processing and their reliability. Assessing the effectiveness of this kind of interaction, the authors analyze the relevant level of intellectual rigor.