Despite the rapid integration of artificial intelligence (AI) into various research domains and the lives of everyday people, challenges with communicating and understanding these AI systems arise. The lack of a consistent method of communication highlights the need for a transdisciplinary approach to explain the inner workings of AI systems in a cohesive and accessible manner. We thus propose an ontological visual framework using semantically-enhanced, symbols, providing a symbolic language for conveying the structure, purpose, and characteristics of AI systems. The framework encompasses a generalizable glyph set of various AI system components, ensuring both common and obscure architectures can be represented. In this paper, we present the underlying logical formalisms that dictate the behavior of this visual framework as a means to significantly enhance the comprehensibility and understandability of AI system behaviors.