Practical Reasoning in Probabilistic Description Logic

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Abstract

Description Logics (DLs) form a family of languages which correspond to decidable fragments of First-Order Logic (FOL). They have been overwhelmingly successful for constructing ontologies—conceptual structures describing domain knowledge. Ontologies proved to be valuable in a range of areas, most notably, bioinformatics, chemistry, Health Care and Life Sciences, and the Semantic Web.One limitation of DLs, as fragments of FOL, is their restricted ability to cope with various forms of uncertainty. For example, medical knowledge often includes statistical relationships, e.g., findings or results of clinical trials. Currently it is maintained separately, e.g., in Bayesian networks or statistical models. This often hinders knowledge integration and reuse, leads to duplication and, consequently, inconsistencies.One answer to this issue is probabilistic logics which allow for smooth integration of classical, i.e., expressible in standard FOL or its sub-languages, and uncertain knowledge. However, probabilistic logics have long been considered impractical because of discouraging computational properties. Those are mostly due to the lack of simplifying assumptions, e.g., independence assumptions which are central to Bayesian networks.In this thesis we demonstrate that deductive reasoning in a particular probabilistic DL, called P-SROIQ, can be computationally practical. We present a range of novel algorithms, in particular, the probabilistic satisfiability procedure (PSAT) which is, to our knowledge, the first scalable PSAT algorithm for a non-propositional probabilistic logic. We perform an extensive performance and scalability evaluation on different synthetic and natural data sets to justify practicality.In addition, we study theoretical properties of P-SROIQ by formally translating it into a fragment of first-order logic of probability. That allows us to gain a better insight into certain important limitations of P-SROIQ. Finally, we investigate its applicability from the practical perspective, for instance, use it to extract all inconsistencies from a real rule-based medical expert system.We believe the thesis will be of interest to developers of probabilistic reasoners. Some of the algorithms, e.g., PSAT, could also be valuable to the Operations Research community since they are heavily based on mathematical programming. Finally, the theoretical analysis could be helpful for designers of future probabilistic logics.

Keyword(s)

Automated reasoning; Description logic; Ontology; Optimization; Probability

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