Abstract
This work represents the natural continuation of the development of the cognitive architecture developed and named Sophimatics, organically integrating the spatio-temporal processing mechanisms of the Super Time Cognitive Neural Network (STCNN) with the advanced principles of Sophimatics. Sophimatics’ goal is as challenging as it is fraught with obstacles, but its ultimate aim is to achieve a more humanized post-generative artificial intelligence, capable of understanding and analyzing context and evaluating the user’s purpose and intent, viewing time not only as a chronological sequence but also as an experiential continuum. The path to achieving this extremely ambitious goal has been made possible thanks to some previous work in which the philosophical thinking of interest in AI was first inherited as the inspiration for the aforementioned capabilities of the Sophimatic framework, then the issue of mapping concepts and philosophical thinking in Sophimatics’ AI infrastructure was addressed, and finally a cognitive-inspired network such as STCNN was created. This work, on the other hand, addresses the challenge of how to endow the infrastructure with both chronological and experiential time and its powerful implications, such as the innate ability to resolve paradoxes, which generative AI does not have among its prerogatives precisely because of structural limitations. To reach these results, the model operates in the two-dimensional complex time domain ℂ2, extending cognitive processing capabilities through the implementation of dual temporal operators that simultaneously manage the real temporal dimension, where past, present, and future are managed and the imaginary one, that considers memory, creativity, and imagination. The resulting architecture demonstrates superior capabilities in resolving informational paradoxes and integrating apparently contradictory cognitive states, maintaining computational coherence through adaptive Sophimatic mechanisms. In conclusion, this work introduces Phase 4 of the Sophimatic framework, enabling management of two-dimensional time within a novel cognitively inspired neural architecture grounded in philosophical concepts. It connects with existing research on temporal cognition, hybrid symbolic–connectionist models, and ethical AI. The methodology translates philosophical insights into formal computational systems, culminating in a mathematical formalization that supports two-dimensional temporal reasoning and paradox resolution. Experimental results demonstrate efficiency, predictive accuracy, and computational feasibility, highlighting potential real-world applications, future research directions, and present limitations.