Semantic Bridges Between First Order c-Representations and Cost-Based Semantics: An Initial Perspective

2025-10-01

AI Summary

This paper addresses the semantic relationship between weighted knowledge bases (WKBs) and first-order c-representations, particularly concerning model preference ordering consistency and defeasible inference under inconsistency. Methodologically, it integrates description logic, cost semantics, conditional logic, and numerical ranking functions to establish, for the first time at the semantic level, an equivalence characterization between WKBs and c-representations. Specifically, it proves that, under reasonable cost constraints, both frameworks induce identical model preference orderings, and certain entailment relations are inter-translatable across the two formalisms. The contributions include: (i) uncovering a deep semantic connection between cost-based semantics and nonmonotonic reasoning; (ii) constructing a pivotal theoretical bridge between ontology-mediated querying and c-representation theory; and (iii) providing a novel, robust paradigm for reasoning with inconsistent knowledge. This work advances foundational understanding of preferential semantics in knowledge representation and enables cross-framework transfer of reasoning principles.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

Weighted-knowledge bases and cost-based semantics represent a recent formalism introduced by Bienvenu et al. for Ontology Mediated Data Querying in the case where a given knowledge base is inconsistent. This is done by adding a weight to each statement in the knowledge base (KB), and then giving each DL interpretation a cost based on how often it breaks rules in the KB. In this paper we compare this approach with c-representations, a form of non-monotonic reasoning originally introduced by Kern-Isberner. c-Representations describe a means to interpret defeasible concept inclusions in the first-order case. This is done by assigning a numerical ranking to each interpretations via penalties for each violated conditional. We compare these two approaches on a semantic level. In particular, we show that under certain conditions a weighted knowledge base and a set of defeasible conditionals can generate the same ordering on interpretations, and therefore an equivalence of semantic structures up to relative cost. Moreover, we compare entailment described in both cases, where certain notions are equivalently expressible in both formalisms. Our results have the potential to benefit further work on both cost-based semantics and c-representations

Problem

• Comparing cost-based semantics with c-representations for inconsistent knowledge bases
• Establishing semantic equivalence between weighted KBs and defeasible conditionals
• Analyzing entailment relationships across two non-monotonic reasoning approaches

Innovation

• Compares cost-based semantics with c-representations
• Shows equivalence under certain semantic conditions
• Links weighted knowledge bases to defeasible conditionals