Category Theory as Interpretation Law Model in Artificial Intelligence Era

Nowadays, artificial intelligence entities operate autonomously and they actively participate in everyday social activities. At a macro-perspective, they play the role of mediator between people and their actions, as components of the fundamental structure of every social activity. At a micro-perspective, they can be considered as fixed critical points whose hypostasis is not subject to established legal framework. A key point is that embedding artificial intelligence entities in everyday activities may maximize legal uncertainty both at the macro and micro-level, as well as at the interim phase, i.e., the switch between the two levels. In this paper, we adapt a well-known concept from Category Theory, namely that of the pushout, in order to approximate the core interpretation legal framework of such activities, by considering each level as an open system. The purpose of using Systems Theory in combination with Category Theory is to introduce a mathematical approach to uniquely interpret complex legal social activities and to show that this novel area of artificially enhanced activities is of prime and practical importance and significance to law and computer science practitioners.