PR-OWL 1

PR-OWL: A Framework for ProbabilisticOntologies

byPaulo C. G. COSTA, Kathryn B. LASKEY

George Mason University

presented byThomas Packer

PR-OWL 2

Problem Area

• Ontologies are useful: – Machine usable description of shared knowledge– Support inferences using classical logic

• Probabilities are useful:– More effective merging (sharing?) of knowledge.– Support principled reasoning over noisy,

uncertain, contradictory or incomplete knowledge.

• Can we use both at the same time?

PR-OWL 3

Dealing with Incomplete Knowledge

• What concept does the term “Washington” correspond to?

• With limited prior knowledge, it has some probability of representing:– US Capital– State– Baseball team

• New evidence (from context ) changes that distribution.• “Washington voiced strong objections to the proposed

policy.”

PR-OWL 4

Probabilistic Ontologies

We need / they present:• The beginning of a coherent framework– Formal definition– Extension of OWL consistent with formal

definition (PR-OWL)

PR-OWL 5

Previous Approaches

• Annotate objects and properties in an OWL ontology with probabilities.– Allows translation into Bayesian Network. – BNs have limited attribute-value representations.– Cannot represent probabilities dependent on more

structure.– Cannot be used to infer probabilities of structures that are

not explicit in the ontology.• Probabilistic extensions of DL.– Limited ability to represent constraints on the instances

that can participate in a relationship.

PR-OWL 6

PR-OWL

• Based on a probabilistic logic: MEBN.• MEBN: Multi-Entity Bayesian Networks– First-order Bayesian logic– Integrates first-order logic with probability theory.– Provides a logically coherent representation of uncertainty.

• FOL: First-order logic– By far the most commonly used, studied and implemented

logical system.– Logical basis for most current AI systems and ontology

languages.

PR-OWL 7

MEBN

• Represents a coherent probability distribution:– Probability of any option is between 0 and 1.– Probability of all options sum to 1.– Can reduce to classical logic (all probabilities are exactly 0 or 1).

• Entities, attributes and relationships are described with conditional probability distributions.– Entity X has identity x1 with probability p1 given the identities

of related entities. (MFrags)– Collectively provides a joint probability distribution. (MTheory)

• Bayes theorem provide a mathematical foundation for learning and inference.

PR-OWL 8

MEBN Intentions

• Upper ontology (meta-model?)• A proposal for a W3C Standard• A set of classes, subclasses and properties that

collectively form a framework for building probabilistic ontologies.

PR-OWL 9

Main Elements of the PR-OWL Upper Ontology

PR-OWL 10

How to Use PR-OWL

1. Import into any OWL editor an OWL file containing PR-OWL classes, subclasses and properties.

2. Construct domain-specific concepts using the PR-OWL definitions to represent uncertainty about their attributes and relationships.

3. Define concept instances about which probabilities can be expressed. (Everything need not be probabilistic.)

4. Feed probabilistic ontology into a probabilistic reasoner to answer probabilistic queries.

PR-OWL 11

Conclusion (Strengths)

• Compelling approach to combining probabilities and ontologies.

PR-OWL 12

Conclusion (Weaknesses)

• No formal evaluation.• Not standardized.• No supporting tools.

PR-OWL 13

Conclusion

• Good start.• Probabilistic ontologies are useful enough that

I believe they will eventually become standardized.

• This and other research will help push the SW community toward that goal.

PR-OWL 14

Questions