Model-Finding for Externally Verifying FOL Ontologies: A Study of Spatial Ontologies

Use and reuse of an ontology requires prior ontology verification which encompasses, at least, proving that the ontology is internally consistent and consistent with representative datasets. First-order logic (FOL) model finders are among the only available tools to aid us in this undertaking, but proving consistency of FOL ontologies is theoretically intractable while also rarely succeeding in practice, with FOL model finders scaling even worse than FOL theorem provers. This issue is further exacerbated when verifying FOL ontologies against datasets, which requires constructing models with larger domain sizes. This paper presents a first systematic study of the general feasibility of SAT-based model finding with FOL ontologies. We use select spatial ontologies and carefully controlled synthetic datasets to identify key measures that determine the size and difficulty of the resulting SAT problems. We experimentally show that these measures are closely correlated with the runtimes of Vampire and Paradox, two state-of-the-art model finders. We propose a definition elimination technique and demonstrate that it can be a highly effective measure for reducing the problem size and improving the runtime and scalability of model finding.