Eliminating ontology contradictions based on the Myerson value

Abstract

Ontologies play a pivotal role in knowledge representation across various artificial intelligence domains, serving as foundational frameworks for organizing data and concepts. However, the construction and evolution of ontologies frequently lead to logical contradictions that undermine their utility and accuracy. Typically, these contradictions are addressed using an Integer Linear Programming (ILP) model, which traditionally treats all formulas with equal importance, thereby neglecting the distinct impacts of individual formulas within minimal conflict sets. To advance this method, we integrate cooperative game theory to compute the Shapley value for each formula, reflecting its marginal contribution towards resolving logical contradictions. We further construct a graph-based representation of the ontology, enabling the extension of Shapley values to Myerson values. Subsequently, we introduce a Myerson-weighted ILP model that employs a lexicographic approach to eliminate logical contradictions in ontologies. The model ensures the minimum number of formula deletions, subsequently applying Myerson values to guide the prioritization of deletions. Our comparative analysis across 18 ontologies confirms that our approach not only preserves more graph edges than traditional ILP models but also quantifies formula contributions and establishes deletion priorities, presenting a novel approach to ILP-based contradiction resolution.