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Oct 22, 2013 (3 years and 9 months ago)

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A Bayesian Perspective to
Semantic Web


Uncertainty modeling
in OWL



Jyotishman Pathak

04/28/2005

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
-
2004



http://www.csee.umbc.edu/~zding1

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
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2005 CS
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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
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2005 CS
-
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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
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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
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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
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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

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2005 CS
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<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>

subClass

subClass

Person

Vegan

Vegetarian

04/28/2005

Spring
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2005 CS
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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
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2005 CS
-
673 Final Project

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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

B

B

A

A

B

A

B

A

04/28/2005

Spring
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2005 CS
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673 Final Project

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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

subClass

subClass

A’

A

C

B’

B

Similar /
Equivalent

A

B

C

B’

04/28/2005

Spring
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2005 CS
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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
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2005 CS
-
673 Final Project

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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
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2005 CS
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673 Final Project

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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>

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

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2005 CS
-
673 Final Project

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Structural Translation
-

III

04/28/2005

Spring
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2005 CS
-
673 Final Project

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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

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2005 CS
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673 Final Project

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CPTs for Control Nodes

04/28/2005

Spring
-
2005 CS
-
673 Final Project

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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


CPT

Constraint

04/28/2005

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2005 CS
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673 Final Project

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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
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2005 CS
-
673 Final Project

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CPTs for Regular Nodes
-

I
-
divergence

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2005 CS
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CPTs for Regular Nodes
-

I
-
projection

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2005 CS
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CPTs for Regular Nodes
-

IPFP

04/28/2005

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2005 CS
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673 Final Project

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CPTs for Regular Nodes
-

D
-
IPFP

04/28/2005

Spring
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2005 CS
-
673 Final Project

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Example
-

I

04/28/2005

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2005 CS
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673 Final Project

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Example
-

II

04/28/2005

Spring
-
2005 CS
-
673 Final Project

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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

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

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