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

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.