On the Relationship between Description Logic-based and F-Logic-based Ontologies

Abstract

Many popular ontology languages are based on (subsets of) first-order predicate logic, with classes represented by unary predicates and properties by binary predicates. Specifically, the SemanticWeb ontology language OWL DL is based on the Description Logic SHOIN. F-Logic is an ontology language which is also based on first-order logic, but classes and properties are modeled as terms rather than predicates. Our goal is to enable interoperation between predicate-based and F-Logic-based ontology languages. To this end, we define an intuitive translation from predicate-based ontologies to F-Logic ontologies and show that this translation preserves entailment for large classes of ontology languages, including most of OWL DL. Specifically, we define the class of equality-safe (E-safe) formulas, show that the Description Logic SHIQ is E-safe, and show that the translation preserves validity of E-safe formulas. We use these results to close the open problem of layering F-Logic programming on top of Description Logic Programs and we show that our results apply to HILOG, a syntactically higher-order, but semantically first-order language. Finally, we show that our results also apply to a meta-modeling extension for Description Logics (v-semantics).