Domain-Contextualized Concept Graphs: A Computable Framework for Knowledge Representation

TL;DR

The paper tackles the limitation of fixed ontologies in traditional knowledge graphs by introducing Domain-Contextualized Concept Graphs (CDC), where domains are explicit, first-class elements that define the scope of relations. CDC employs a C–D–C triple structure and an on-demand Domain Space to enable context-aware, cross-domain reasoning, grounded in cognitive-linguistic isomorphism and implemented in Prolog for full inferencing. It standardizes a compact set of over twenty relation predicates across structural, logical, cross-domain, and temporal categories, and demonstrates through education, enterprise, and technical documentation case studies how CDC supports analogies, knowledge fusion, and personalized explanations without ontology fragmentation. The work presents a theoretical Foundation (Domain Separation Theorem), a practical Prolog-based reference implementation, and a roadmap for future extensions including probabilistic reasoning, temporal dynamics, and distributed deployments, highlighting CDC’s potential to unify interdisciplinary knowledge modeling and context-sensitive AI reasoning.

Abstract

Traditional knowledge graphs are constrained by fixed ontologies that organize concepts within rigid hierarchical structures. The root cause lies in treating domains as implicit context rather than as explicit, reasoning-level components. To overcome these limitations, we propose the Domain-Contextualized Concept Graph (CDC), a novel knowledge modeling framework that elevates domains to first-class elements of conceptual representation. CDC adopts a C-D-C triple structure - <Concept, Relation@Domain, Concept'> - where domain specifications serve as dynamic classification dimensions defined on demand. Grounded in a cognitive-linguistic isomorphic mapping principle, CDC operationalizes how humans understand concepts through contextual frames. We formalize more than twenty standardized relation predicates (structural, logical, cross-domain, and temporal) and implement CDC in Prolog for full inference capability. Case studies in education, enterprise knowledge systems, and technical documentation demonstrate that CDC enables context-aware reasoning, cross-domain analogy, and personalized knowledge modeling - capabilities unattainable under traditional ontology-based frameworks.