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Competing scientific ontologies represent a pervasive yet under-analyzed failure mode in artificial intelligence applications for materials science. Different classification systems for the same materials, structures, properties, and processes create fundamental incompatibilities that cause AI models to fail in ways that are difficult to diagnose through conventional performance metrics. This paper defines the ontology problem as the inherent challenge of representing material knowledge when multiple, partially incompatible ontologies coexist within the domain, each encoding distinct conceptual boundaries and relational assumptions. It articulates four primary types of ontological competition—category boundary differences, naming conflicts, relationship differences, and granularity differences—that arise repeatedly in materials informatics. These competitions trigger specific failure modes, including transfer failures, evaluation incompatibilities, data integration failures, and communication breakdowns between research communities. Detection relies on explicit ontology audits and cross-ontology testing, while mitigation centers on mapping strategies, ontology-agnostic representations, and community harmonization efforts. By framing ontology competition as a distinct failure mode, the analysis draws on existing literature to propose an ontology-aware framework that strengthens semantic interoperability and model robustness in materials AI. Ultimately, acknowledging and managing competing ontologies is essential for translating data-driven discoveries into reliable, reproducible knowledge.