1. Slide 1 of 18 Uncertainty Representation and Reasoning with MEBN/PR-OWL Kathryn Blackmond Laskey Paulo C. G. da Costa The Volgenau School of Information Technology and Engineering George Mason University - Fairfax, VA [klaskey, pcosta]@gmu.edu

2. Slide 2 of 18 Uncertainty and Ambiguity are Ubiquitous

3. Slide 3 of 18 Semantic Awareness in an Uncertain World Ontologies formalize our knowledge about entities and relationships in the world Many relationships are intrinsically uncertain Traditional ontology formalisms lack built-in means for handling uncertainty Without a means of expressing uncertainty we are unable to say much of what we know Methodologies and tools are needed for principled handling of uncertainty in semantically aware systems

4. Slide 4 of 18 Is Probability Ontological or Epistemic? Intrinsically probabilistic phenomena may exist in Nature There is an urgent practical need for sound and principled representation of uncertainties associated with our knowledge Todays existential phenomenon is tomorrows superseded theory

5. Slide 5 of 18 Why Bayes? Requirement: reason in the presence of uncertainty about… Input data Existence of relationships among entities Strength of relationships Constraints governing relationships Solution: Bayesian inference Combine expert knowledge with statistical data Represent cause and effect relationships Learn from observations Prevent over-fitting Clear and understandable semantics Logically coherent

6. Slide 6 of 18 Bayesian Network Parsimonious specification for joint probability distribution over many random variables Graph encodes dependence relationships Local distributions encode numerical probability information Implicitly specifies full joint distribution Computational architecture for evidential reasoning Condition on evidence Compute updated beliefs on unobserved variables Efficient local computations Bi-directional reasoning Are BNs a suitable formal basis for probabilistic ontology?

7. Slide 7 of 18 The Trouble with BNs Traditional BNs are insufficiently expressive for complex problems How many entities? What are their types? What are their features? How are they related to each other? How do they change over time?

8. Slide 8 of 18 MEBN to the Rescue! MEBN can express: Attribute value uncertainty Number uncertainty Type uncertainty Reference uncertainty Structure uncertainty Repeated structure Recursion Existence uncertainty Parameter uncertainty Structure uncertainty Quantifiers

9. Slide 9 of 18 MEBN: A First-Order Bayesian Logic Represents knowledge as parameterized fragments of Bayesian networks Expresses repeated structure Represents probability distribution on interpretations of associated first-order theory Expressive enough to express anything that can be said in FOL Suitable logical basis for probabilistic ontology

10. Slide 10 of 18 MEBN Theory

11. Slide 11 of 18 Situation Specific Bayesian Network Own ship, 4 other starships, 1 zone, 4 reports, 2 time steps Ordinary Bayesian network constructed to process probabilistic query on a MEBN Theory

12. Slide 12 of 18 PR-OWL: A Language for Probabilistic Ontologies Upper OWL Ontology Represents MEBN Theories

13. Slide 13 of 18 MEBN / PR-OWL

14. Slide 14 of 18 Logical Reasoning

15. Slide 15 of 18 Logical *and* Plausible Reasoning

16. Slide 16 of 18 MEBN/PR-OWL Probabilistic Ontologies Allow both probabilistic and deterministic reasoning The probabilistic part is a complete or partial MEBN theory Different people will build different MEBN theories of their domains. MEBN logic is expressive enough to provide logical basis for semantic integration.

17. Slide 17 of 18 Probabilistic Semantic Mapping Costa, P., Laskey, K.B. and Laskey, K.J., Probabilistic Ontologies for Efficient Resource Sharing in Semantic Web Services, Workshop on Uncertainty in the Semantic Web, International Semantic Web Conference, November 2006. A probabilistic ontology augments a standard ontology with a representation of uncertainty A mapping ontology represents mapping of terms between domain ontologies

18. Slide 18 of 18 THANKS!!!