Highly-Optimized Forgetting for Creating Signature-Based Views of Ontologies

Uniform interpolation (UI) is a non-standard reasoning service that seeks to project an ontology down to its sub-signature --- given an ontology taking a certain signature, and a subset Σ of "relevant names'' of that signature, compute a new ontology, called a uniform interpolant, that uses only the relevant names while preserving the semantics of the relevant names in the uniform interpolant. UI is of great potential importance since it may be used in a variety of applications where suitable views of ontologies need to be computed. However, this potential can only be fully realized if a highly optimized method for computing such views exists. Previous research has shown that computing uniform interpolants of ELH-ontologies is a computationally extremely hard problem --- a finite uniform interpolant does not always exist for ELH, and if it exists, then there exists one of at most triple exponential size in terms of the original ontology, and that, in the worst case, no shorter interpolant exists. Despite the inherent difficulty of the problem, in this paper, we present a highly optimized forgetting method for computing uniform interpolants of ELH-ontologies, and show however that, with good reduction and inference strategies, such uniform interpolants can be efficiently computed. The method is an improvement of the one presented in our previous work. What sets it apart is its flexibility to treat concept names of different types differently, effectively cutting down on the inferences involved. This treatment is primarily driven by the polarities of the concept names within an ontology. A comprehensive evaluation with a prototypical implementation of the method shows >95% average success rates over two popular benchmark datasets and demonstrates a clear computational advantage over state-of-the-art systems.