Presentation on YouTube.

Description Logics (DL) are formal languages for knowledge representation, enabling structured ontology creation and logical reasoning. This talk presents an optimization-based framework for enhancing reasoning in DL by employing mixed-integer programming methods. The framework exploits a novel approach of mapping DL axioms to a set of inequalities, enabling the use of advanced optimization techniques. The integration of column generation and branch-and-price algorithms addresses the complexity of the resulting inequality system, offering a scalable solution for handling large ontological datasets. In a preliminary set of experiments, the framework's performance is evidenced by its application to the ontology of the Canadian Parliament, where it outperforms traditional reasoning methods. This work could mark a significant advancement for the Semantic Web community by merging ontology reasoning with sophisticated optimization methods to meet the challenges of semantic data processing.