uncertainty representation and reasoning with mebn/pr-owl

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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Today’s existential phenomenon is tomorrow’s superseded theory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!!!

uncertainty representation and reasoning with mebn/pr-owl

Documents

probabilistic query

uncertainty representation

mebn logic

mebn theoryprowl

different mebn theories

joint probability distribution

semantic integration

folsuitable logical