Probabilistic Description Logics for Subjective Uncertainty

We propose a new family of probabilistic description logics (DLs) that, in contrast to most existing approaches, are derived in a principled way from Halpern’s probabilistic firstorder logic. The resulting probabilistic DLs have a twodimensional semantics similar to certain popular combinations of DLs with temporal logic and are well-suited for capturing subjective probabilities. Our main contribution is a detailed study of the complexity of reasoning in the new family of probabilistic DLs, showing that it ranges from PTIME for weak variants based on the lightweight DL EL to undecidable for some expressive variants based on the DL ALC. Motivation Description logics (DLs) are a popular family of knowledge representation formalisms that underlie ontology languages such as the W3C standard OWL. Since traditional DLs are essentially fragments of first-order logic (FOL), they allow only the representation of crisp and definite knowledge, whereas no built-in means are provided to repre...

• Type: Conference
• Year: 2010
• Where: KR
• Authors: Carsten Lutz, Lutz Schröder
• Keywords: Automated Reasoning, KR 2010, Probabilistic Dls, Probabilistic firstorder Logic, Traditional Dls