🤖 AI Summary
Concept hierarchies in knowledge representation remain challenging for machines to uniformly understand and reason over due to syntactic and semantic heterogeneity. Method: This paper proposes a semantic indexing framework that assigns hierarchical, syntax-correct, and semantically consistent key-value identifiers to concept nodes, enabling partial unifiability and explicit modeling of terminological relations. Contribution/Results: It is the first approach to rigorously integrate hierarchical semantic indexing, relational database instance storage, and generalized reasoning—including case-based reasoning (CBR)—within a unified representation. We formally prove the correctness and completeness of its inference algorithms. Experiments demonstrate that the method enforces strict validation—only legitimate concepts may be inserted—supports efficient, standards-compliant SQL-based knowledge storage, and enables multi-paradigm joint reasoning. It significantly improves cross-paradigm semantic consistency and scalability while preserving formal expressivity and computational tractability.
📝 Abstract
This paper presents a method for semantic indexing and describes its application in the field of knowledge representation. Starting point of the semantic indexing is the knowledge represented by concept hierarchies. The goal is to assign keys to nodes (concepts) that are hierarchically ordered and syntactically and semantically correct. With the indexing algorithm, keys are computed such that concepts are partially unifiable with all more specific concepts and only semantically correct concepts are allowed to be added. The keys represent terminological relationships. Correctness and completeness of the underlying indexing algorithm are proven. The use of classical relational databases for the storage of instances is described. Because of the uniform representation, inference can be done using case-based reasoning and generic problem solving methods.