Structural framework for cognitive representation improves problem solving
A Structural Theory of Cognitive Representation and Problem Solving,Contexts, Invariance, and the Knowledge Space
Artificial Intelligence
Summary
Problem solving depends on how problems are represented in the mind or a machine. The authors propose a simple framework that clearly shows how ideas like context, recognizing what stays the same (invariance), choosing examples, and reusing methods fit together. They imagine concepts and procedures as connected graphs to organize knowledge and actions clearly. Even with a simple problem solver, this structured way of organizing information makes problem solving easier and more efficient.
What this means in practice
- •For ai system designers: Design cognitive architectures that explicitly incorporate context and abstraction operations to improve knowledge reuse in AI problem solvers.
- •For software engineers: Structure software modules with explicit context and procedure graphs to better manage abstraction and reuse in complex systems.
A theory result. No direct application yet.
Authors
Antal Jakovác, András Telcs
Abstract
Learning and problem solving depend critically on the structure of internal representations. While many modern data-driven artificial systems achieve strong predictive performance, their learned representations often lack explicit structure for expressing abstraction, invariance, and task-relevant regularities. We propose a minimal structural framework in which representational operations relevant to problem solving, such as context formation, invariance recognition, representative selection, abstraction, and procedural reuse, are made explicit. The central notion is that of a \emph{context}, formalized as a partition of a subset of an underlying state space, which fixes the distinctions, granularity, and form in which a problem can be posed. Within this setting, invariance recognition and representative selection are treated as fundamental representational operations. The framework is realized as a Knowledge Space composed of two coupled graph structures: a Concept Graph that hosts constructed and refined concepts, and a Procedure Graph that encodes typed operations over representations. Together, these structures provide a minimal cognitive-representational algebra for operating on representations without assuming sophisticated inference, learning, control, perception, or motor mechanisms. Using simple illustrative examples and a finite weak-solver demonstration, we show that appropriate representational organization can simplify the form and scope of admissible regularities, even when problem solving is carried out by a fixed and limited solver. The contribution of the paper is structural rather than algorithmic: it identifies representational prerequisites for abstraction, invariance, and procedural reuse in problem solving, and states explicit success and failure conditions for the weak-solver setting.