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PR-OWL: A Framework for Probabilistic Ontologies

PR-OWL is a novel framework designed for the integration of ontologies and probabilistic reasoning. Developed by Paulo C. G. Costa and Kathryn B. Laskey, and presented by Thomas Packer, this framework addresses key challenges in dealing with incomplete and uncertain knowledge. By leveraging Multi-Entity Bayesian Networks (MEBN), PR-OWL enables the representation of logical structures alongside probabilistic information, thus supporting effective reasoning in various contexts. While it shows promise, further standardization and formal evaluation are needed for widespread adoption.

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PR-OWL: A Framework for Probabilistic Ontologies

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

  2. 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? PR-OWL

  3. 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.” PR-OWL

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

  5. 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. PR-OWL

  6. PR-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. PR-OWL

  7. 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. PR-OWL

  8. 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. PR-OWL

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

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

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

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

  13. 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. PR-OWL

  14. Questions PR-OWL

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