PR-OWL: A Framework for Probabilistic Ontologies by Paulo C. G. COSTA, Kathryn B. LASKEY George Mason University presented by Thomas Packer 1PR-OWL

Problem Area Ontologies are useful: – Machine usable description of shared knowledge – Support inferences using classical logic Probabilities are useful: – More effective merging (sharing?) of knowledge. – Support principled reasoning over noisy, uncertain, contradictory or incomplete knowledge. Can we use both at the same time? 2PR-OWL

Dealing with Incomplete Knowledge What concept does the term “Washington” correspond to? With limited prior knowledge, it has some probability of representing: – US Capital – State – Baseball team New evidence (from context ) changes that distribution. “Washington voiced strong objections to the proposed policy.” 3PR-OWL

Probabilistic Ontologies We need / they present: The beginning of a coherent framework – Formal definition – Extension of OWL consistent with formal definition (PR-OWL) 4PR-OWL

Previous Approaches Annotate objects and properties in an OWL ontology with probabilities. – Allows translation into Bayesian Network. – BNs have limited attribute-value representations. – Cannot represent probabilities dependent on more structure. – Cannot be used to infer probabilities of structures that are not explicit in the ontology. Probabilistic extensions of DL. – Limited ability to represent constraints on the instances that can participate in a relationship. 5PR-OWL

Based on a probabilistic logic: MEBN. MEBN: Multi-Entity Bayesian Networks – First-order Bayesian logic – Integrates first-order logic with probability theory. – Provides a logically coherent representation of uncertainty. FOL: First-order logic – By far the most commonly used, studied and implemented logical system. – Logical basis for most current AI systems and ontology languages. 6PR-OWL

MEBN Represents a coherent probability distribution: – Probability of any option is between 0 and 1. – Probability of all options sum to 1. – Can reduce to classical logic (all probabilities are exactly 0 or 1). Entities, attributes and relationships are described with conditional probability distributions. – Entity X has identity x1 with probability p1 given the identities of related entities. (MFrags) – Collectively provides a joint probability distribution. (MTheory) Bayes theorem provide a mathematical foundation for learning and inference. 7PR-OWL

MEBN Intentions Upper ontology (meta-model?) A proposal for a W3C Standard A set of classes, subclasses and properties that collectively form a framework for building probabilistic ontologies. 8PR-OWL

Main Elements of the PR-OWL Upper Ontology 9PR-OWL

How to Use PR-OWL 1.Import into any OWL editor an OWL file containing PR-OWL classes, subclasses and properties. 2.Construct domain-specific concepts using the PR-OWL definitions to represent uncertainty about their attributes and relationships. 3.Define concept instances about which probabilities can be expressed. (Everything need not be probabilistic.) 4.Feed probabilistic ontology into a probabilistic reasoner to answer probabilistic queries. PR-OWL10

Conclusion (Strengths) Compelling approach to combining probabilities and ontologies. 11PR-OWL

Conclusion (Weaknesses) No formal evaluation. Not standardized. No supporting tools. 12PR-OWL

Conclusion Good start. Probabilistic ontologies are useful enough that I believe they will eventually become standardized. This and other research will help push the SW community toward that goal. 13PR-OWL

Questions 14PR-OWL