Constraint Generation and Reasoning in OWL

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Constraint Generationand Reasoning in OWL

• Dissertation Defense
• Thomas H. Briggs, VI
• Advisor Dr. YunPeng
• University of Maryland, Baltimore County

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Introduction

• Property Constraints
• Important to defining the semantics of an
  ontology
• Properties may have domain / range constraints
• Global consequences from local assertions
• 75 of properties are unconstrained
• Property Constraint Generation
• Uses information in the ontology to generate
  constraints
• Can be used to determine missing, suggest new, or
  analyze existing constraints
• Creates default knowledge that must be treated
  differently than other asserted or inferred
  knowledge.

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Thesis
The purpose of this research is to investigate
methods for generating domain and range
constraints from its defining ontology and to
evaluate the quality of this generation. This
work will also investigate the default reasoning
necessary to support generated constraints. A
specific focus will be on management of the
default facts in the knowledge base including
tracking default facts and efficient retraction
operations to restore consistency.
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Research Outcomes

• Outcomes of this work are
• Algorithmic framework to generate and evaluate
  domain and range constraints, and
• Quantitative comparison of the relationship
  between generated and specified constraints, and
• An inference procedure that will enable a limited
  form of default reasoning that maintains the
  completeness, and correctness of OWL reasoners.

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Description Logics
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Description Logics

• Description Logics
• are a branch of crisp logics
• include well-researched languages
• AL, CLASSIC, RACER
• have a long history
• are the basis of the Semantic Web
• have fast and efficient reasoners (for some) DL
• FACT, Pellet

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Description Logics

• Describe some world by
• Defining classes, properties, and individuals
• Classes define types of individuals
• Properties define relationships between
  individuals
• Individuals are things that are instances of
  classes, and are related to other individuals
  through properties.
• Similar to first order logic

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Constraints

• An assertion about the types of fillers of a
  property
• Subject is type of domain of property
• Object is type of range of property
• Unconstrained defaults to Thing/Top
• Different interpretation than traditional
  languages
• Define valid types of individuals
• May force a type cast, but error otherwise

teaches domain(Teacher),
range(Student) teaches(Adam, Bill)
void foo(doublez) printf(f\n, z) char
x 33.0 foo(x)
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Constraints

• An assertion about the types of fillers of a
  property
• Subject is type of domain of property
• Object is type of range of property
• Unconstrained defaults to Thing/Top
• Different interpretation than traditional
  languages
• Define valid types of individuals
• May force a type cast, but error otherwise

teaches domain(Teacher),
range(Student) teaches(Adam, Bill)
Error stringscannot bedoubles!
void foo(doublez) printf(f\n, z) char
x 33.0 foo(x)
Adam is a teacher, Bill a student
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Open World Assumption

• Open World Assumption (OWA)
• Anything that isnt asserted is considered as
  unknown.
• Leads to monotonicity in reasoner.
• Closed World Assumption (CWA)
• Assume all facts are known
• Default knowledge

hasChild(ALICE, BOB)
Does Alice have exactly one child?
Closed World
Open World
Yes!
No!?
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Unique Name Assumption

• Assumption that the name of an item is sufficient
  to make it unique (UNA).
• We make this for classes and properties
• Do not make this for individuals

True only whensame individual
Open World Assumption Because we didnt say
they were different, then the reasoner
canconclude that they are to makethe model true
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Constraint Generation
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Unconstrained Properties

• Domain and range assert types to fillers of
  property
• Unconstrained properties lack these type
  assertions
• Reasons
• Information is unknown
• Artifact of ontology generator
• Avoid conflicts with reuse
• Faulty semantics

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Constraint Generation

• Unconstrained properties are a problem
• Constraint generation is a non-trivial process
• Omitted constraints may be intentional or may not
• Open World Assumption information may not be
  there
• Two sources of information on constraints
• ABox
• TBox

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ABox Generation

• ABox generation problematic
• Depends on individuals class membership
• Individuals may not be defined / UNA
• Frequently do not have a complete set of class
  assertions
• Class assertions overlap

What should the domain andrange of drives be?
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TBox Generation

• Terminology provides definition of the
  relationship between classes.

Generation Lemma
Vehicle or Civic
Class Vehicle subClassOf Thing and
(drivenBy some Person) Class Civic subClassOf
Thing and (madeBy only HONDA)
and (drivenBy some Person)
Vehicle
?
Domain must subsumeVehicle union Civic
Vehicle or X
X
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Finding Best

• Using terminology to find best
• Intractable exponential growth
• Requires utility function to measure goodness
• Requires future knowledge or omniscience

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Generation Methods

• Generation Methods
• Construct a constraint that satisfies generation
  lemma
• Three Generation Methods
• Disjunction Method
• Least-Common Named Subsumer
• Vivification

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Disjunction

• Based on Generation Lemma
• Computes the Least Common Subsumer (LCS)
• In languages with disjunction, the LCS is simply
  the disjunction of the concepts
• Generation time linear w.r.t. number classes and
  properties
• Reasoning time is exponential.

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Disjunction Algorithm
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Disjunction Example
Domain for P
Range for P
C
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Disjunction Discussion

• Disjunction is good because
• It is simple to compute
• Most specific / accurate statement of constraint
• Disjunction is bad because
• Does not add useful information
• Disjunction adds non-determinism to reasoner

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Least Common Named Subsumer

• Select a named concept that subsumes concepts
• Trade-off in specificity for concept description
• Quality depends on existence of named concepts
• May be expensive to compute
• Runtime is

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LCNS Algorithm
Subsumption checkingis the dominate cost
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LCNS Example
Disjunction Domain of P
LCNS Domain of P A
LCNS Range of P C
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LCNS Discussion

• LCNS is good because
• It selects a named class in the ontology
• Runtime bound to cost for subsumption checking
• Generalizes concepts from disjunction
• LCNS is bad because
• Requires existence of a named class or LCNS is
  Thing
• Tends to over-generalize in other case as well
• Over-generalization discards too much information

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Vivification

• Balance specificity and over-generalization
• First proposed by Cohen Hirsh 1992
• Difference here is partial absorption
• Starts with disjunction, using inheritance
  relationship summarizes terms with common direct
  super-classes.
• Only terms that do not share a common super-class
  remain in the disjunction

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Absorption

• Moderates the generalization process
• Uses the class inheritance structure for operation

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Vivification Algorithm
Perform Absorption
Vivify a concept list in L for a given
absorption criteria Beta.
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Vivification Example
Property P is usedin the definitionof the
threeyellow classes.
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Vivification Discussion

• Vivification is good because
• It creates general concepts that summarize over
  common super-classes, selecting named subsumers
• It preserves outliers
• It is fast
• Vivification is bad because
• Disjunctions may remain after summarization
• Depends on the completeness of the terminology
• Ignores individual assertions

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Results
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Results - Domain
Generated constraint was equal to originally
specified one.Positive outcome. Correctly
generated constraint with equal specificity.
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Results - Domain
Original more specific than generated. In all
cases, the original constraint subsumed
itself.Making it more specific than the
generated one.
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Results - Domain
Original more general then generated. A negative
to neutral outcome. The original constraintwas
more general than its present usage.
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Results - Domain
Original Top, Generated Top. Both the original
and generated concepts where top.It is a
subclass of the case of row 1 where concepts are
equal.
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Results - Domain
Original Top, Generated More Specific Strongly
positive results. A constraint was generatedfor
a concept that previously lacked one.
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Results - Domain
Generated Top, Original More Specific. A neutral
to negative result. A constraint was generated
as Top whenthe original was not Top. An example
was an ontology that defined hasAuntas the union
of Niece and Nephew, which was equivalent to
Person, and Person was equivalent to everything
hence the generated created Top.
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Results - Domain
Property Unused. Neutral results. A constraint
could not be generated becausethere were no role
restrictions to define the constraints.
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Results - Domain
Processor or Reasoner Failed. There was a runtime
failure of the processor or reasoners.
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Results Range
Range results were similar to domain.
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Results - Normalized
Generation strategies created improved
constraints almost 80 of time.
Vivification created constraints nearly as
specific as Disjunction.
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Results - Runtime
Time Load, Reason, Generate, Build, Reason
1000 Ontologies
Time Load / Reasoning Time
Hypothesis Testing
Vivification faster than disjunctionat 92.6
degree of confidence.
Vivification faster than LCNSat 76.4 degree of
confidence.
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Results Discussion

• Generation
• Remove unused properties gives better picture of
  future as technologies mature.
• Generation a viable method
• Vivification was dominate method
• Generated constraints with near equal specificity
  to LCS
• Able to generalize at appropriate times
• Avoided the over-generalization of LCNS
• All around best performance for generation and
  reasoning

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Default Reasoning
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Default Reasoning

• Monotonicity
• One goal of OWL is to maintain monotonicity the
  property of a reasoner that adding new facts to
  the knowledge base does not cause existing facts
  to be retracted.
• Default Knowledge / Rules
• Default knowledge and rules about the terminology
  make use of Closed World Semantics, give up
  monotonicity.
• A default rule may conflict with future
  statements
• Statements must be retracted.

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Contraction

• When a clash occurs in a knowledge base with
  default statements, those default facts must be
  removed to restore consistency. This is called a
  contraction.
• How to tell default from non-default?
• Inference leads to multi-path problem
• Default and non-default facts can be used to
  infer new facts
• Default facts may block non-default facts from
  being generated

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Default Example
Class A SubClassOf Thing, P some B Class B
SubClassOf Thing Class C SubClassOf
Thing ObjectProperty P Domain Thing Range
Thing Individual J Individual I Facts P(I,J)
Before generation
Class A SubClassOf Thing, P some B Class B
SubClassOf Thing Class C SubClassOf
Thing ObjectProperty P Domain A Range
B Individual J Types B Individual I Types
A Facts P(I,J)
After property generation, domain and range on P
were generated / default.
What if the domain expert adds C SubClassOf P
some B?
Now, the domain of P is generatedas A union C.
I no longer in A!
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Modifications

• Default Descriptor
• Indicates the defaultness of a statement or
  assertion.
• Does not change the meaning of the term
• Inference
• Inference rules modified to propagate descriptor
• Non-default statement must replace default
  statement

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Concept Strength

• Concept Strength between concepts C and D
• Strength Relationship
• If C is default and D is not, then C weaker than
  D
• If C and D have same defaultness, then equal
• If C is not default and D, then C stronger than D

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Reasoner

• Reasoner was implemented from transformation
  rules such as
• Depends on contains and union operation.

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Modified Reasoner

• The reasoners rules are modified
• Contains Rule
• The contains(x) predicate will be modified
• Return true if A contains some y, such that yx,
  and x is not stronger than y.
• Union Update Procedure
• The union operator to update the KB will be
  modified to replace any equivalent weaker term
  with a stronger term

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Contraction Triggering

• An inconsistent knowledge base contains either a
  true clash or a default clash.
• True Clash clash occurs between two
  non-default statements
• Default Clash clash involves at least one
  default statement
• A knowledge base that contains only default
  clashes can be contracted by removing all default
  facts.
• Default facts can be rebuilt using new state of
  the KB

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Reasoner Completeness
Extends Baader and Nutts Completeness of Tableau
Reasoner
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Reasoner Soundness
Extends Baaders Soundness Theorem
Assume the transformation rules defined for a
non-default Description Logic are
truth-preserving. Assume the ABox S is obtained
from a finite set of Aboxes S by application of a
transformation rule including the modified
contains and union operations. Then S is
consistent if and only if S is.
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Reasoner Example
Reasoner
indicates defaultness
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Reasoner Conclusion

• Default rules can create clashes
• True clashes different than default clashes
• Default clashes can be contracted and resolved
• Defaultness can be propagated through inference
• Modify inference rules, contains, and union
• Sound and Complete

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Conclusion
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Conclusion

• Constraints can be generated
• Disjunction Most specific, but slow
• LCNS Tends to over generalize, slowest
• Vivification - Balanced generalization, fast
• Default Reasoning
• Track defaultness
• Retract default statements
• Balanced by efficient generation and reasoning

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Future Work

• Future Work
• Investigate individual assertions
• Extend to support OWL 1.1 domain/range pairings
• Use of external data sources (e.g. Cyc, WordNet)
  to improve constraint generation
• Investigate application to improve search
  performance and results
• Extend default reasoning to support SWRL
  terminology rules.

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Final Words

• Thesis statement was supported
• An algorithm forconstraint generation was
  described
• Its impact on reasoner performance was assessed
• Default reasoning, sufficient for this work, was
  described
• Expected outcomes were met
• A set of tools to generate property constraints
  was created
• A qualitative assessment of generation was
  applied to all available ontologies
• A default reasoner using described rules was
  implemented