We present a novel conceptual framework called the "knowledge field" aimed at providing a structured foundation for modeling intelligence across different levels of cognition. This proposed knowledge field represents a formalized informational space, analogous to physical fields in physics, which encapsulates the distributed landscape of beliefs, concepts, semantic relationships and informational elements pertaining to the manifestation of intelligence.
Within this knowledge field framework, the various informational elements are assigned differing levels of topological significance and connection strengths based on considerations such as contextual validity, semantic relevance and perceptual salience. The overall configuration of the knowledge field is dynamic, with agents continuously integrating across weighted elements to draw inferences and update their beliefs, allowing the state of the field to evolve in response to new knowledge.
A key hypothesis in the theory of the knowledge field is that intelligence emerges from the execution of specific computable functions that operate on and interact with the contents of the field. The class of functions being applied determines the kind of cognitive capabilities exhibited, with simple aggregative functions enabling basic reasoning, change functions supporting learning through updating field structure, decay functions being involved in memory consolidation and retrieval, and so on.
Clearly enumerating and defining these functional classes in terms of their scope of operation and grounding their mechanisms firmly within the semantic topology of the knowledge field is considered crucially important for substantiating the link between the model and observable, measurable manifestations of intelligent behavior.
Presently, large language models display a limited implicit approximation of the knowledge field paradigm, capable of limited functional manipulation of informational elements. However, engendering higher, human-analogous cognition requires sophisticated knowledge field representations coupled with recursive, composable computational functions.
As an illustration, effectively solving differential equations necessitates embedding the mathematical formalisms within a precisely encoded knowledge field module, alongside intelligent functions that can undertake symbolic manipulation of mathematical constructs. More broadly, capturing the multi-faceted nature of general intelligence within this framework requires elucidating a comprehensive taxonomy of knowledge fields and functional varieties.
In essence, the knowledge field proposes a unified computational substrate for grounding distributed, heterogeneous conceptual structures and informational elements, within which the mechanisms of cognition can be formalized as executable functions. By tracing the emergence of intelligence to the programmatic orchestration of knowledge field dynamics, this novel methodology attempts to reverse engineer the genesis of thought itself and elucidate the mathematical bedrock underlying cognition.