An Axiomatic Model for Describing Information‑Processing Systems

This working paper develops an axiomatic model of information processing that formally describes the structural conditions of cognitive systems. The foundational premise is the introduction of a systemic boundary separating the internal cognitive space from external stimulus sources. Within this space, three functional roles operate: sensory presentation, structural–conceptual formation, and model formation. An endogenous context operator relates and weights these elements using two orthogonal modulation operators— the time-invariant informational distance d and the dynamic attentional field a — which modulate the system-relevant context. This establishes the functorial architecture that enables the transformation of phenomenological representations into abstract conceptual objects. A central component of the model is the Gate mechanism, which selects sensory streams in a context-sensitive manner, eliminates irrelevant channels through factorized reduction, and fuses relevant information via a functorial pushout structure. The Gate thus forms the operational foundation for transferring raw signals into phenomenological representations and executing subsequent conceptual abstraction.The axiomatics dictate how stimuli enter the cognitive space at a baseline level (d=1), undergo processing through morphic operations, and are synthesized into higher abstraction orders (d>1) via a directed relational cascade. The theory demonstrates how invariants are extracted, concepts are formed, and persistent structures are stabilized within a dynamic context operator R(t) . The model is substrate-independent and scalable: it describes information processing across diverse scales, ranging from elementary physical processes to complex cognitive operations. This yields a unified theoretical framework for modeling informational flows, encompassing perception, concept formation, and internal structural evolution.In summary, this paper delivers a formal architecture that precisely determines the conditions and limits of model formation in information-processing systems, establishing a rigorous foundation for future applications and extensions. ______________________________________________________________________________________________________________________ Status: Version 1.0 represents the English translation of the German‑language original paper. The author employed AI‑based language models exclusively for linguistic translation and stylistic refinement of the abstract and selected sections. The author welcomes technically grounded feedback on the formal structure and conceptual coherence of the model. Administrative note: The author is currently seeking an arXiv endorsement for this preprint .