Reasoning as Data: Representation-Computation Unity and Its Implementation in a Domain-Algebraic Inference Engine
Summary: arXiv:2604.10908v1 Announce Type: new
Abstract: Every existing knowledge system separates storage from computation. We show this separation is unnecessary and eliminate it. In a standard triple is_a(Apple, Company), domain context lives in the query or the programmer’s mind. In a CDC four-tuple is_a(Apple, Company, @Business), domain becomes a structural field embedded in predicate arity. Any system respecting arity automatically performs domain-scoped inference without external rules. We call this representation-computation unity (RCU).
Key Concepts of Representation-Computation Unity (RCU)
RCU fundamentally challenges the traditional separation between data storage and computation within knowledge systems. By introducing a four-tuple structure, RCU allows for the integration of domain context directly into the data representation, which leads to several significant implications:
- Domain-Scoped Closure: This mechanism allows systems to perform inference within specific domains, enhancing the accuracy and relevance of the results.
- Typed Inheritance: By utilizing type information within the data structure, systems can inherit properties and behaviors based on domain-specific types, which streamlines the reasoning process.
- Write-Time Falsification: The engine can detect cycles per domain fiber, ensuring that data integrity is maintained while also allowing for dynamic updates.
Formal Establishment and Implementation of RCU
The authors of the study formally establish the principles of RCU through four theorems, demonstrating its theoretical soundness. Notably, RCU is not just a theoretical concept but is also implementable as evidenced by the development of a working symbolic engine. This engine, consisting of 2400 lines of Python and Prolog code, addresses several engineering challenges:
- Rule-Data Separation: The design allows for a clear distinction between rules and data, enhancing modularity.
- Shared-Fiber Handling: Efficient management of shared resources within the domain context.
- Read-Only Meta-Layer Design: This layer ensures that the foundational data remains immutable to prevent errors.
- Intersective Convergence: The engine converges multiple constraints seamlessly to yield meaningful inferences.
Case Studies and Performance Validation
Two case studies are presented to validate the effectiveness of the inference engine:
- ICD-11 Classification: The engine successfully managed 1247 entities across three axes, demonstrating the capability to resolve multiple inheritance issues through domain fibers.
- CBT Clinical Reasoning: This study illustrated the generalization of the engine’s capabilities to temporal reasoning, with session turns serving as ordered domain indices.
Furthermore, multi-constraint queries were shown to achieve constraint satisfaction problem (CSP) arc-consistency with a complexity of O(m (N/K)²), indicating the efficiency of the domain lattice in governing performance.
Conclusion
In conclusion, the introduction of Representation-Computation Unity represents a significant advancement in the field of knowledge systems. By integrating domain context directly into the data representation, RCU not only simplifies the inference process but also enhances the system’s overall performance and accuracy. The implications of this research are far-reaching, potentially transforming how we approach reasoning in artificial intelligence.