semantic web foundations
DESCRIPTION
Part 1: Modeling in Description Logic Peter Radics. Semantic Web Foundations. Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech. Goal. Goal of presentation: Introduce building blocks of Description Logic Provide starting point for modeling in Description Logic - PowerPoint PPT PresentationTRANSCRIPT
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Semantic Web Foundations
Part 1: Modeling in Description LogicPeter Radics
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Goal Goal of presentation:
Introduce building blocks of Description Logic
Provide starting point for modeling in Description Logic
Take away fear of difficult-sounding domain
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
History
First knowledge representation systems in the 1970s Focused on high level descriptions of the
world for intelligent applications Approaches roughly divided into:
Logic-based formalisms Non-logic-based representations
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
History (cont'd)
Non-logic-based representations Frames Semantic Networks
Rely on network-based representation structures Nodes Links
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
History (cont'd)
However: "...early Semantic Networks suffered from
the drawback that they did not have clear semantics."
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
History (cont'd)
Core features of frames and semantic networks and first-order logic can provide clear semantics
→ Description Logic (DL)
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Aside: First-Order Logic Example of a typical statement:
Hard to read and interpret by non-mathematicians
C≡∃ x ∃ y R a,x ∧ R a,y ∧M x ∧ ¬M y
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
DL: Concepts
DL is “object-centered modeling language”
Concepts (Classes, Nodes) Collections of Individuals with same properties Two default concepts (for reasoning):
Thing Nothing
Modeled as unary symbols in first-order logic
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
DL: Concepts (cont'd)
Concept definition: Provides both necessary and sufficient
information for classifying individual Establishes logical equivalence Acyclic
Classification basic task in constructing terminology
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
DL: Relationships Relationships (Links, Slots, Roles)
Subsumption (is-a relationship) Relationship shared with many other modeling
languages (e.g. Entity-Relationship diagrams) Used for building taxonomy of classes
However, DL allows for arbitrary (binary) relationships
Modeled as binary symbols in first-order logic
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
DL: T-Box
Together, concepts and relationships form terminology (T-Box)
Terminology models intensional knowledge (i.e. general domain knowledge)
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
DL: Individuals
Individuals Instances (members) of classes
Convey assertional/extensional knowledge (i.e. problem specific knowledge about a domain)
Form A-Box
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Aside: Expressiveness Do we have enough to define:
Concept “Male students”? Concept “Friends and family”? Concept “Non-smokers”? Concept “Parents?” Concept “Parents of only girls”? Concept “Parents with three children”?
→Additional building blocks needed
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
DL: Additional building blocks Added to increase expressiveness
Intersection of concepts (logical and) Allows for:
MaleStudent = Male and Student
Union of concepts (logical or) Allows for:
FriendsAndFamily = Friends or Family
Complement of concepts (logical not) Allows for:
NonSmoker = not Smoker
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
DL: Additional building blocks
Existential quantification Allows for:
Parents = exists hasChild (a, x)
Universal quantification Allows for:
ParentsOfOnlyGirls = for all hasChild (a,x) Female(x)
Cardinality restriction Allows for
ParentsWithThreeChildren = (>=3 hasChild) and (<=3 hasChild)
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Example First-Order Logic example:
Becomes: ParentWithSonAndDaughter = hasChild.x and
hasChild.y and x.Male and y.Female
C≡∃ x ∃ y R a,x ∧ R a,y ∧M x ∧ ¬M y
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
DL: Modeling Knowledge base should clearly characterize
the question it can answer.
Model hast to be complete before reasoning can be applied.
Expressiveness of DL language influences complexity of reasoning
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
DL: Making it user-friendly
Two approaches: Providing syntax that is closer to natural language
Providing graphical user interface for specifying relationships
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Real-World examples
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Real world examples
<base:BoltedClampConnection rdf:ID="SmartflexClutchSize3_RotatingBallScrew">
<base:hasPosition rdf:resource="Pos_Connection_Clutch_BallScrew"/>
<base:isConnectionOfObject1 rdf:resource="#SmartflexClutchSize3"/>
<base:isConnectionOfObject2 rdf:resource="#RotatingBallScrew"/>
<base:hasRotationDuringRemovalForObject1 rdf:resource="#NoRotation"/>
<base:hasRotationDuringRemovalForObject2 rdf:resource="#NoRotation"/>
<base:hasDirectionOfRemovalForObject1 rdf:resource="#DOR_Smartflex_BallScrew"/>
<base:hasDirectionOfRemovalForObject2 rdf:resource="#DOR_BallScrew_Smartflex"/>
<base:hasRealizingComponent rdf:resource="owl:Nothing"/>
</base:BoltedClampConnection>
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Conclusion
Description Logic is not “scary”
Allows modeling of real world knowledge in vocabulary similar to natural language
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Recommended Read
Noy, McGuinnes: “Ontology Development 101: A Guide to Creating Your First Ontology”, Tech Report, Knowledge Systems Laboratory, Stanford University, 2001
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Discussion How does modeling in Description Logic
apply to Usable Security?
What are potential benefits?
What are potential downfalls?
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Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
Outlook: Reasoning
Open world assumption of DL Example:
hasChild (Iokaste, Oedipus) hasChild (Iokaste, Polyneikes) hasChild (Oedipus, Polyneikes) hasChild (Polyneikes, Thersandros) Patricide (Oedipus)
Question: Does Iokaste have a child that is a patricide and that itself has a child who is not a patricide?
Usable Security – CS 6204 – Fall, 2009 – Dennis Kafura – Virginia Tech
¬Patricide Thersandros