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

Spring-2005 CS-673 Final Project 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

04/28/2005 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

04/28/2005 Spring-2005 CS-673 Final Project 4 Preliminaries – Semantic Web for Dummies! Semantic Web The book does not really exist!

04/28/2005 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)

04/28/2005 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

04/28/2005 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)

04/28/2005 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

04/28/2005 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 Domain Range

04/28/2005 Spring-2005 CS-673 Final Project 10 subClass Person Vegan Vegetarian

04/28/2005 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

04/28/2005 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

04/28/2005 Spring-2005 CS-673 Final Project 13 Introduction and Motivation - II Uncertainty in Ontology Representation  Degree of Inclusion Besides A subclassOf B, also A is a small subset of B  Degree of Overlap (Intersection) A and B overlap, but none is a subclass of the other BB A A BABA

04/28/2005 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 subClass A’ A C B’ B Similar / Equivalent ABCB’

04/28/2005 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

04/28/2005 Spring-2005 CS-673 Final Project 16 Overview of Uncertainty Modeling in Ontology Onto P-Onto Probabilistic annotation OWL-BN translation BN 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) Reasoning

04/28/2005 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

04/28/2005 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|O C ), where O C   C,  C ≠ , O C ≠ . Three new OWL classes: “PriorProb”, “CondProb”, “Variable”  PriorProb: “hasVariable”, “hasProbValue”  CondProb: “hasCondition” (1 or more), “hasVariable”, “hasProbValue”  Variable: “hasClass”, “hasState”

04/28/2005 Spring-2005 CS-673 Final Project 19 Encoding Probabilities in Ontology - II Example 1: P(c) = 0.8 C True c 0.8 Example 2: P(c|p1,p2,p3) = 0.8 C True P1 True P2 True P3 True p1 p2 p3 c 0.8

04/28/2005 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

04/28/2005 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

04/28/2005 Spring-2005 CS-673 Final Project 22 Structural Translation - II Control Nodes

04/28/2005 Spring-2005 CS-673 Final Project 23 Structural Translation - III

04/28/2005 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

04/28/2005 Spring-2005 CS-673 Final Project 25 Constructing CPTs Two kinds of nodes:  X C : control nodes for bridging nodes which are associated by logical relations  X R : regular nodes for concept classes P(C) or P(C|O C ), where O C   C,  C ≠ , O C ≠   Initially assigned Prior or Conditional probabilities in the OWL file

04/28/2005 Spring-2005 CS-673 Final Project 26 CPTs for Control Nodes

04/28/2005 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 X R, such that P( X R | 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 CPTConstraint

04/28/2005 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 minimizing I-divergence to the original distribution

04/28/2005 Spring-2005 CS-673 Final Project 29 CPTs for Regular Nodes - I-divergence

04/28/2005 Spring-2005 CS-673 Final Project 30 CPTs for Regular Nodes - I-projection

04/28/2005 Spring-2005 CS-673 Final Project 31 CPTs for Regular Nodes - IPFP

04/28/2005 Spring-2005 CS-673 Final Project 32 CPTs for Regular Nodes - D-IPFP

04/28/2005 Spring-2005 CS-673 Final Project 33 Example - I

04/28/2005 Spring-2005 CS-673 Final Project 34 Example - II

04/28/2005 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

04/28/2005 Spring-2005 CS-673 Final Project 36 Reasoning Concept Satisfiability: ? Concept Overlapping: = ? Concept Subsumption …

04/28/2005 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

04/28/2005 Spring-2005 CS-673 Final Project 38 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 BN1 onto1 P-onto1 Probabilistic annotation OWL-BN translation concept mapping Probabilistic ontological information onto2 P-onto2 BN2  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

04/28/2005 Spring-2005 CS-673 Final Project 39