Domain-Contextualized Concept Graphs: A Computable Framework for Knowledge Representation (2510.16802v1)

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.