Knowledge Representation and Inference Formalism in Semantic Web

1
Knowledge Representation and Inference Formalism
in Semantic Web

• Andrei G. Stoica

University of South Carolina
2
Outline

• Relationship between Logic Programming and XML by
  Harold Boley
• Relationship between Logic Programming and RDF by
  Harold Boley
• XML Logic Formalism - LOX

3
XML elements as Ground Structures

• Direct correspondence between XML elements and
  Prolog ground structures
• The power formula 23 in XML format
• ltpowergt
• ltbasegt 2 lt/basegt
• ltexponentgt 3 lt/exponentgt
• lt/powergt
• The Prolog corresponding ground structure is
• power(base(2), exponent(3))

4
Text?XML?RDF?Horn Facts

• XYZ sold 123 copies of ABC.
• ltsentencegt XYZ sold 123 copies of ABC
• lt/sentencegt
• lttriplegt
• ltsubjectgt XYZ lt/subjectgt
• ltpredicategt sold lt/predicategt
• ltobjectgt 123 copies of ABC lt/objectgt
• lt/triplegt

5
Text?XML?RDF?Horn Facts

• lttriplegt
• ltsubject resourcehttp//www.xyz.com /gt
• ltpredicategt sales lt/predicategt
• ltobject resourcehttp//www.xyz.com/ID001/gt
• lt/triplegt

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Text?XML?RDF?Horn Facts

• lttriplegt
• ltsubject resourcehttp//www.xyz.com/ID001/gt
• ltpredicategt name lt/predicategt
• ltobjectgt ABC lt/objectgt
• lt/triplegt

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Text?XML?RDF?Horn Facts

• lttriplegt
• ltsubject resourcehttp//www.xyz.com/ID001/gt
• ltpredicategt quantity lt/predicategt
• ltobjectgt 123 lt/objectgt
• lt/triplegt

8
Text?XML?RDF?Horn Facts

• ltrdfRDFgt
• ltrdfDescription abouthttp//www.xyz.comgt
• ltsales rdfresource http//www.xyz.com/ID00
  1/gt
• lt/rdfDescriptiongt
• ltrdfDescription abouthttp//www.xyz.com/ID00
  1gt
• ltnamegt ABC lt/namegt
• ltquantitygt 123 lt/quantitygt
• lt/rdfDescriptiongt
• lt/rdfRDFgt

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Text?XML?RDF?Horn Facts

• sales (http//www.xyz.com,
• http//www.xyz.com/ID001).
• name (http//www.xyz.com/ID001, ABC).
• quantity (http//www.xyz.com/ID001, 123).

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Containers in RDF

• Containers are treated with a resource node
  standing for a container as a whole.
• Bag becomes a multi set data type of unordered
  elements with repetition
• quantity(http//xyz.com/ID001, bag12,13,14).
• where the sales quantity is the sum of
  unspecified quantities not necessary distinct.

11
RDF Meta-Statements

• Meta-Statements (the statements about statements)
  have an additional property specifying the
  described resource has type Statements.
• Example
• claims(http//www.xyz.com,
• sales(http//www.xyz.com,
• http//www.xyz.com/ID001))
  .

12
Inferential RDF through Horn Rules

• We define a magnitude interval for the number of
  sales. The corresponding ground facts are
• Magnitude(http//www.xyz.com/ID001, 1001)
• Magnitude(http//www.xyz.com/ID001, 1002)
• Magnitude(http//www.xyz.com/ID001, 1001)
• In logic programming
• magnitude(http//www.xyz.com/ID001, Int) -
• lt(1000, Int), lt(Int, 2000).

13
Non-Binary relations in RDF

• Higher arity relations are expressed with an
  additional resource with additional properties
• ltrdfDescription abouthttp//www.xyz.com/ID001
  gt
• ltpricegt
• ltrdfvaluegt 10lt/rdfvaluegt
• ltunits rdfresource http//www.gov.augt
• lt/pricegt
• lt/rdfDescriptiongt
• price(http//www.xyz.com/ID001, aud10).

14
RDF Types

• Special unary predicates are used for variable
  typing
• bookstore(http//www.xyz.com).
• book(http//www.xyz.com/ID001).

15
RDF Schema

• Organize resources of type Class in an hierarchy
• ltrdfDescription IDProductgt
• ltrdftype resourcehttp//www.w3.org /gt
• ltrdfssubClassOf rdfresourcehttp//www.w3.o
  rg /gt
• lt/rdfDescriptiongt
• In Logic Programming
• resource(X) - product(X)

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Summary

• RDF can be considered as a special case of
  knowledge representation with logic programs.
• There is a corresponding formal logic
  representation for RDF queries and inference.
• However not all logic constructs can be
  accommodated on current RDF format

17
Security Perspective

• RDF access control and policy specification
• Semantically enhanced XML document access
• Undesired inference
• Data inference from legitimate access leading to
  protected information in an organization.

18
LOX

• First order language defined to represent an XML
  documents and an ontology concept hierarchies.
• Formally defines the undesired inference from the
  information security point of view.

19
Predicates in LOX

• Generic Predicates
• define the the data values, name of attributes,
  values of attributes and XML document structure
• Specific Predicates
• define the tag names
• Every tag has an associated tag ID and security
  labels

20
Generic Predicates

• Generic Predicates
• PCDATA(i, x) defines the data values
• ATTRIB(i, a, x) defines the attributes names and
  attribute values
• IN(i, j) defines the XML document structure

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Generic Predicates

• Example
• lttriple ID01gt
• ltsubject resourcehttp//xyz.com / ID02gt
• ltpredicate ID03gt sales lt/predicategt
• ltobject resourcehttp//xyz.com/ID001/
  ID04gt
• lt/triplegt
• PCDATA(03, sales)
• ATTRIB(02, resource, http//xyz.com)
• IN(01, 02)

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Specific Predicates

• Example
• lttriple ID01gt
• ltsubject resourcehttp//xyz.com / ID02gt
• ltpredicate ID03gt sales lt/predicategt
• ltobject resourcehttp//xyz.com/ID001/
  ID04gt
• lt/triplegt
• triple(01) subject (02) predicate(03)
  object(04)

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XML Equivalent LOX Format

• lttriple ID01gt
• ltsubject resourcehttp//xyz.com / ID02gt
• ltpredicate ID03gt sales lt/predicategt
• ltobject resourcehttp//xyz.com/ID001/
  ID04gt
• lt/triplegt
• F triple(01) ? subject(02) ? predicate(03) ?
• object(04) ? PCDATA(03, sales) ?
• ATTRIB(02, resource, http//xyz.com) ?
• ATTRIB(04, resource, http//xyz.com/ID001)

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Conclusion
XML
Logic Programs First Order Logic Horn Logic
Programs Description Logic
RDF

• Ontology

• Security
• implications

• Data Inference