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A Bayesian Perspective to Semantic Web – Uncertainty modeling in OWL

A Bayesian Perspective to Semantic Web – Uncertainty modeling in OWL. Jyotishman Pathak 04/28/2005. Why did I choose this topic?. My research: Semantic Web ComS 673: Bayesian Network Rendezvous between BN & SW References

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A Bayesian Perspective to Semantic Web – Uncertainty modeling in OWL

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  1. A Bayesian Perspective to Semantic Web – Uncertainty modeling in OWL Jyotishman Pathak 04/28/2005

  2. Why did I choose this topic? • My research: Semantic Web • ComS 673: Bayesian Network • Rendezvous between BN & SW • References • A Bayesian Approach to Ontology in OWL Ontology, Zhongli Ding et al., In Proc. of AISTA-2004 • A Probabilistic Extension to Ontology Language OWL, Zhongli Ding et al., In Proc. of HICSS-2004 http://www.csee.umbc.edu/~zding1 Spring-2005 CS-673 Final Project

  3. Outline • Preliminaries • Semantic Web & related concepts • Motivation • Translating OWL Taxonomy to BN • Encoding Probabilities in Ontology • Structural Translation • Constructing CPTs • Reasoning • Conclusion Spring-2005 CS-673 Final Project

  4. Preliminaries – Semantic Web for Dummies! Semantic Web The book does not really exist! Spring-2005 CS-673 Final Project

  5. Preliminaries – Semantic Web (1) • Current Web Architecture • Network of hyper links • O.K. for human-processing (e.g., Natural Language, Graphics) • Difficult for machine processing (ambiguity, unconstrained data formats) Spring-2005 CS-673 Final Project

  6. Do you like Golf? Do you like Golf? Do you like Golf? No. I prefer Mustang Preliminaries – Semantic Web (2) • Same term, different meaning Spring-2005 CS-673 Final Project

  7. Preliminaries – Semantic Web (3) • The Semantic Web is an extension of the current web that will allow you to find, share, and combine information more easily. • Extend the current web (do NOT define a new one!) • Express information in a format that is: • Unambiguous • Amenable to machine processing • Add metadata(to describe existing or new data) Spring-2005 CS-673 Final Project

  8. Preliminaries – Semantic Web (4) • An Ontology is an engineering artifact: • Describes formal specification & shared understanding of a certain domain • Formal and machine manipulable model of the domain • Decades of research done by KR community • Ontologies have two main components: • Names for important concepts in the domain • Elephant is a concept whose members are a kind of Animal • Background knowledge/constraints on the domain • Every Elephant is either an African_Elephant or an Indian_Elephant Spring-2005 CS-673 Final Project

  9. Preliminaries – Semantic Web (5) • OWL: Web Ontology Language (W3C Recommendation) • Is written using XML-based syntax • Categorizes the basic concepts in terms of Classes: • classes can be viewed as “sets” of possible concepts • E.g., Animal in our example • hierarchies of concepts can be defined as sub-classes • Union, Intersection, Disjoint, Complement etc.. • Properties are defined by: • constraints on their range and domain, or • E.g., type of the Elephant can be either African or Indian • specialization (sub-properties) Property Range Spring-2005 CS-673 Final Project Domain

  10. <owl:Class rdf:ID="Vegetarian"> <rdfs:subClassOf rdf:resource="http://xmlns.com/foaf/0.1/#Person"/> <rdfs:subClassOf> <owl:Restriction> <owl:onProperty rdf:resource="#eats"/> <owl:allValuesFrom rdf:resource="#VegetarianFood"/> </owl:Restriction> </rdfs:subClassOf> </owl:Class> <owl:Class rdf:ID="Vegan"> <rdfs:subClassOf rdf:resource="#Vegetarian"/> <rdfs:subClassOf> <owl:Restriction> <owl:onProperty rdf:resource="#eats"/> <owl:allValuesFrom rdf:resource="#VeganFood"/> </owl:Restriction> </rdfs:subClassOf> </owl:Class> Person subClass Vegetarian subClass Vegan Spring-2005 CS-673 Final Project

  11. Outline • Preliminaries • Semantic Web & related concepts • Motivation • Translating OWL Taxonomy to BN • Encoding Probabilities in Ontology • Structural Translation • Constructing CPTs • Reasoning • Conclusion Spring-2005 CS-673 Final Project

  12. Introduction and Motivation - I • OWL allows us to define classes, properties etc. • Unfortunately, OWL is based on crisp logic • A vegan only eats vegan food • An elephant can be either African or Indian • Real life (data) has uncertainty associated Spring-2005 CS-673 Final Project

  13. Introduction and Motivation - II • Uncertainty in Ontology Representation • Degree of Inclusion • Besides AsubclassOfB, also A is a small subset of B • Degree of Overlap (Intersection) • A and B overlap, but noneis a subclass of the other B B A B A B A A Spring-2005 CS-673 Final Project

  14. Introduction and Motivation - III • Uncertainty in Ontology Mapping • Similarity between concepts in different ontologies cannot be adequately represented by logical relations • Mappings are hardly 1-to-1 A A B B’ C subClass A’ B subClass subClass Similar / Equivalent B’ C Spring-2005 CS-673 Final Project

  15. Introduction and Motivation - IV • Thus, • Existing logic based approaches are inadequate to model Ontological uncertainty • Uncertainty is more prevalent in presence of multiple Ontologies • Reasoning becomes a problem • Leverage on approaches for graphical models • This work builds on Bayesian Network. Why? • Structural similarity between the DAG of a BN and the graph of OWL ontology • BN semantics is compatible with that of OWL • Rich set of efficient algorithms for probabilistic reasoning and learning Spring-2005 CS-673 Final Project

  16. Probabilistic annotation OWL-BN translation Overview of Uncertainty Modeling in Ontology Onto P-Onto BN Reasoning • Encoding Probabilities in Ontology • Not supported by current OWL • Define new classes for prior and conditional probabilities • Structural Translation • Class hierarchy: set theoretic approach • Logical relations (equivalence, complement, disjoint, union, intersection): introducing control nodes • Constructing CPTs • Decomposed Iterative Proportional Fitting Procedure (D-IPFP) Spring-2005 CS-673 Final Project

  17. Outline • Preliminaries • Semantic Web & related concepts • Motivation • Translating OWL Taxonomy to BN • Encoding Probabilities in Ontology • Structural Translation • Constructing CPTs • Reasoning • Conclusion Spring-2005 CS-673 Final Project

  18. Encoding Probabilities in Ontology - I • Two kinds of probabilistic information • Prior or marginal probability P(C); • Conditional probability P(C|OC), where OCC, C≠, OC≠. • Three new OWL classes: “PriorProb”, “CondProb”, “Variable” • PriorProb: “hasVariable”, “hasProbValue” • CondProb: “hasCondition” (1 or more), “hasVariable”, “hasProbValue” • Variable: “hasClass”, “hasState” Spring-2005 CS-673 Final Project

  19. Encoding Probabilities in Ontology - II • Example 1: P(c) = 0.8 <Variable rdf:ID="c"> <hasClass>C</hasClass> <hasState>True</hasState> </Variable> <PriorProb rdf:ID="P(c)"> <hasVariable>c</hasVariable> <hasProbValue>0.8</hasProbValue> </PriorProb> • Example 2: P(c|p1,p2,p3) = 0.8 <Variable rdf:ID="c"> <hasClass>C</hasClass> <hasState>True</hasState> </Variable> <Variable rdf:ID="p1"> <hasClass>P1</hasClass> <hasState>True</hasState> </Variable> <Variable rdf:ID="p2"> <hasClass>P2</hasClass> <hasState>True</hasState> </Variable> <Variable rdf:ID="p3"> <hasClass>P3</hasClass> <hasState>True</hasState> </Variable> <CondProb rdf:ID="P(c|p1, p2, p3)"> <hasCondition>p1</hasCondition> <hasCondition>p2</hasCondition> <hasCondition>p3</hasCondition> <hasVariable>c</hasVariable> <hasProbValue>0.8</hasProbValue> </CondProb> Spring-2005 CS-673 Final Project

  20. Outline • Preliminaries • Semantic Web & related concepts • Motivation • Translating OWL Taxonomy to BN • Encoding Probabilities in Ontology • Structural Translation • Constructing CPTs • Reasoning • Conclusion Spring-2005 CS-673 Final Project

  21. Structural Translation - I • Every primitive or defined concept class C, is mapped into a two-state (either “True” or “False”) variable node in the translated BN; • There is a directed arc from a parent superclass node to a child subclass node; C is true when an instance x belongs to it Spring-2005 CS-673 Final Project

  22. Structural Translation - II Control Nodes Spring-2005 CS-673 Final Project

  23. Structural Translation - III Spring-2005 CS-673 Final Project

  24. Outline • Preliminaries • Semantic Web & related concepts • Motivation • Translating OWL Taxonomy to BN • Encoding Probabilities in Ontology • Structural Translation • Constructing CPTs • Reasoning • Conclusion Spring-2005 CS-673 Final Project

  25. Constructing CPTs • Two kinds of nodes: • XC: control nodes for bridging nodes which are associated by logical relations • XR: regular nodes for concept classes • P(C) or P(C|OC), where OCC, C≠, OC≠ • Initially assigned Prior or Conditional probabilities in the OWL file Spring-2005 CS-673 Final Project

  26. CPTs for Control Nodes Spring-2005 CS-673 Final Project

  27. CPT for Regular Nodes • CT: the situation in which all the control nodes in BN are “True” • Logical relations defined in original Ontology are held in the translated BN • Goal: To construct CPT’s for regular nodes in XR, such that P(XR | CT) is consistent with initial constraints • Problem: • Constraints not given in the form of CPT • P(C | A, B) vs. P(C | A) • We cannot determine CPT for node C directly CPT Constraint Spring-2005 CS-673 Final Project

  28. CPTs for Regular Nodes - Method • Solution: • Decomposed Iterative Proportional Fitting Procedure (D-IPFP) • IPFP: a well-known mathematical procedure that modifies a given distribution to meet a set of constraints while minimizingI-divergenceto the original distribution Spring-2005 CS-673 Final Project

  29. CPTs for Regular Nodes - I-divergence Spring-2005 CS-673 Final Project

  30. CPTs for Regular Nodes - I-projection Spring-2005 CS-673 Final Project

  31. CPTs for Regular Nodes - IPFP Spring-2005 CS-673 Final Project

  32. CPTs for Regular Nodes - D-IPFP Spring-2005 CS-673 Final Project

  33. Example - I Spring-2005 CS-673 Final Project

  34. Example - II Spring-2005 CS-673 Final Project

  35. Outline • Preliminaries • Semantic Web & related concepts • Motivation • Translating OWL Taxonomy to BN • Encoding Probabilities in Ontology • Structural Translation • Constructing CPTs • Reasoning • Conclusion Spring-2005 CS-673 Final Project

  36. Reasoning • Concept Satisfiability: ? • Concept Overlapping: = ? • Concept Subsumption • … Spring-2005 CS-673 Final Project

  37. Outline • Preliminaries • Semantic Web & related concepts • Motivation • Translating OWL Taxonomy to BN • Encoding Probabilities in Ontology • Structural Translation • Constructing CPTs • Reasoning • Conclusion Spring-2005 CS-673 Final Project

  38. onto2 Probabilistic ontological information Probabilistic ontological information P-onto2 Probabilistic annotation BN1 BN2 OWL-BN translation concept mapping Conclusion • Summary • A principled approach to uncertainty modeling in ontology • Allows us to do reasoning in presence of partial knowledge • Can be used successfully for Multi-Ontology Mapping • Current work (as of Summer-2004) • Prototype development • Experimentation with real world Ontologies • Ontology mapping • A parsimonious set of links • Capture similarity between concepts by joint distribution • Mapping as evidential reasoning • BayesOWL: Probabilistic Framework for Uncertainty in Semantic Web onto1 P-onto1 Spring-2005 CS-673 Final Project

  39. Thank You ! Spring-2005 CS-673 Final Project

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