Post on 19-Mar-2016
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Uncertainty Representation and Reasoning with MEBN/PR-OWL
Kathryn Blackmond LaskeyPaulo C. G. da Costa
The Volgenau School of Information Technology and EngineeringGeorge Mason University - Fairfax, VA
[klaskey, pcosta]@gmu.edu
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Uncertainty and Ambiguity are Ubiquitous
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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
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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
Today’s existential phenomenon is tomorrow’s superseded theory
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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
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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?
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The Trouble with BNs
Traditional BNs are insufficiently Traditional BNs are insufficiently expressive for complex problemsexpressive for complex problemsHow many entities? What are their types?What are their features? How are they related to each other?How do they change over time?
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MEBN to the Rescue!
MEBN can express:Attribute value uncertaintyNumber uncertaintyType uncertaintyReference uncertainty Structure uncertaintyRepeated structure
RecursionExistence uncertaintyParameter uncertaintyStructure uncertainty Quantifiers
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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
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MEBN Theory
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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
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PR-OWL: A Language for Probabilistic Ontologies
Upper OWL Ontology Represents MEBN Theories
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MEBN / PR-OWL
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Logical Reasoning
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Logical *and* Plausible Reasoning
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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.
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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
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THANKS!!!