🤖 AI Summary
This paper addresses the fundamental challenge of formalizing intelligence—characterized by conceptual vagueness, polysemy, and resistance to rigorous axiomatization. We propose a novel meta-framework grounded in set theory and category theory, offering the first axiomatic definition of intelligence as “a structure within the universe of sets endowed with temporal evolution and interactive capacity.” Innovatively, we introduce the primitive notion of *activity* to formally capture intelligence’s intrinsic time-dependence; further, we construct the *temporal category* and *intelligence category*, linked by functors that abstractly represent system evolution and imitation mechanisms. Our framework unifies and distinguishes Hebbian learning, backpropagation, and biological reflexes along structural, temporal, and biologically plausible dimensions. Moreover, it naturally extends to axiomatize higher-order mental phenomena—including consciousness and emotion—thereby establishing a new foundational paradigm for artificial intelligence theory.
📝 Abstract
This study aims to construct an axiomatic definition of intelligence within a meta-framework that defines the method of definition, addressing intelligence as an inherently naive and polysemous concept. Initially, we formalize a set-theoretic representation of the universe as the domain wherein intelligence exists and characterize intelligence as a structure that involves temporal evolution and interaction with other sets. Starting from a naive definition of intelligence as"an entity possessing structures for externally inputting, internally processing, and externally outputting information or matter,"we axiomatically reformulate it within this set-theoretical depiction of the universe. Applying this axiomatic definition, we compare and interpret three examples -- Hebbian non-optimized neural networks (NNs), backpropagation-optimized NNs, and biological reflexive systems -- in terms of their intelligence, structural properties, and biological plausibility. Furthermore, by extending our definition into a categorical framework, we introduce two categories,"Time Category"and"Intelligence Category,"along with the functorial relationships between them, demonstrating the potential to represent changes and mimicry relationships among intelligent systems abstractly. Additionally, since intelligence, as defined herein, functions effectively only when accompanied by temporal interactions, we introduce the concept of"activity"and explore how activity-based conditions influence classifications and interpretations of intelligence. Finally, we suggest that our definitional methodology is not limited to intelligence alone, but can be similarly applied to other concepts, such as consciousness and emotion, advocating for their formal reinterpretation through the same procedural steps: defining a universal representation, selecting naive definitions, and axiomatic formalization.