Practical Methods for Concept Interpolation in Realistic Ontologies

Ontologies formulated in description logics are widely used to formalise knowledge and terminologies in domains such as medicine and biology. One central reasoning task for ontologies is to decide whether one concept is subsumed by the other. While modern reasoners can efficiently determine the subsumptions of large-scale ontologies, they offer little insight into the reasoning process itself. Concept interpolation addresses this by computing an intermediate concept in a user-specified vocabulary that witnesses the subsumption. Concept interpolation can be used to solve a range of problems in KR, including explaining reasoning, extracting explicit definitions, and learning concepts from examples. Despite its relevance, no practical methods for concept interpolation in description logics have been developed. Furthermore, to be used for concept learning, an interpolation method needs to support nominals, which are known to make the interpolation problem harder. In this project, we will develop practical methods for deciding the existence and computing concept interpolants in different logics of the ℰℒ and Aℒ families. If they exist, we want to find the “optimal” interpolant based on specific criteria, and compute approximations otherwise.