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Uncertainty and Semantic web pellet

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					Uncertainty and
Semantic web
  Jennifer Sleeman
                Agenda
 Define uncertainty
 Provide background
 Show areas   of research
 Highlight various approaches
 Provide a demonstration of Pronto
      Definition - Uncertainty
 Knowledge can be   inaccurate or
  incomplete
 Knowledge can be imprecise or ―fuzzy‖


….leads to uncertainty…
            Definition - Uncertainty
 Machine-readable information
 Applications that work with random information (image
  processing, geospatial, information retrieval, etc.)
 Ontology concept definitions
       Vague concepts:
       Tall, Small, Big, ….
       Green, Blue, ….
       Few, Many, ….
   Semantic web services

….work with uncertainty…
     Background – Description Logic
         Naming Conventions




Taken from Wikipedia [12].
        Is representing uncertainty
                necessary?
 Tim Berner-Lee rejection of   uncertainty
     Not necessary [7]
     Scalability issues [7]
Can you describe knowledge using a
 ―monotonic bivalent language‖[7]?
What about grey?




     Uncertainty
  Is it necessary?




Taken from [5] presented at the URSW 2008.
General Approaches to Uncertainty
       and Semantic Web
    Incomplete/Distorted knowledge [1]
      • Possibility degrees alternatives
    Inability to define concepts precisely [1]
      • Degree of truth
    Conflicting alternatives [1]
      • Degree of probability

 According to [1], since how we solve uncertainty
  problems depends upon the domain, it is hard
  to define a single language extension.
           Areas of Research
  (based upon 2007/2008 URSW Conference agendas)

 Extending Semantic Web to       support
  uncertainty
 Fuzzy theory
 Probability theory
 Uncertainty and Ontologies
 Uncertainty and Web Services
  Extending the Semantic Web
 Extend Semantic Web languages to
  support probabilistic, possibilistic, and
  fuzzy reasoning
 Can be at the ontology layer or the rules
  layer
 Within the ontology layer proposals for:
     Syntax and Semantics
     Logical Formalisms
            Fuzzy Theory
―…In classical set theory, the membership of
  elements in a set is assessed in binary
  terms according to a bivalent condition —
  an element either belongs or does not
  belong to the set. By contrast, fuzzy set
  theory permits the gradual assessment of
  the membership of elements in a set; this
  is described with the aid of a membership
  function valued in the real unit interval
  [0, 1]…‖[10]
         Fuzzy Approaches
 Extending languages such as   OWL with
  fuzzy extensions
 Extending Description Logic with fuzzy
  extensions
 If a language is extended, one must
  provide a way to support reasoning of the
  language with the fuzzy extension
           Rules and Uncertainty
 Rules Interchange Format
 Rules Markup Language
       For representing/interchanging rules
 Attempt to provide ways to represent various
  types of uncertainty [1]
 Not as much recent attention as ontology layer
 fuzzy RuleML defines way to specify
  membership degree [1]
       Example:

                                        Taken from [1].
                        Fuzzy RDF
 Extends syntax and semantics of RDF
 Triple extended to support real number on the
  interval [0,1]
       n: s p o [13]
   Interpretation
       Subject, object has degree of membership to
        extension of predicate [13]
       Satisfies statement if
         • Membership degree of {subject, object} to the extension of
           the predicate is >= to n [13]
                 Fuzzy RDF
 RDFS     extended
     ―Class extensions are fuzzy sets of domain
      elements‖ [13]
     Domains are fuzzy and their assignment to
      properties can also be fuzzy [13]
 Inference engines canbe extended to
 support such fuzziness
       Fuzzy Description Logic
 Fuzzy
     One such proposal
 Solve problem of representing and
  reasoning of fuzzy concepts
 With         concrete domains –
  reasoning using concrete data types
 With fuzzy version domains are fuzzy
 Modifiers are supported (very, slightly,
  etc.) [12]
Fuzzy Description Logic
Non-fuzzy Concrete Domain:




Concrete Fuzzy Domain:




Taken from [12].
          Fuzzy Description Logic
   Interpretations are fuzzy
       From satisfied/unsatisfied to a degree of truth [0,1]
 Satisfiability of fuzzy axiom given fuzzy
  interpretation [12]
 ―Fuzzy axiom a logical consequence of a
  knowledge base iff every model in the
  knowledge base satisfies the fuzzy axiom‖ [12]
 Reasoning a problem
       Computationally no calculus exists to check for
        satisfiability of a fuzzy knowledge model [12]
                  Fuzzy OWL
             OWL
 Extension of
 Example (describing the safety of a
  location):
     Without fuzzy, the location is either safe or not
      safe
     With fuzzy, the location is safe to a degree
 Classes and   properties are ‗fuzzy‘
 A class is considered a fuzzy set [1]
 A property is a fuzzy relation over a set [1]
              Fuzzy OWL
 Requires extension of           to map OWL
  entailment to       satisfiability [4]
 Reasoning changes in that when concepts
  are represented as nodes in forest-like
  representations, a ―membership degree‖ is
  associated with each node indicating it
  belongs to a concept [4]
 Degrees added to OWL facts
           Fuzzy OWL




Taken from [4].
          Probability Theory
―..the central objects of probability theory are
   random variables, stochastic processes,
   and events: mathematical abstractions of
   non-deterministic events or measured
   quantities that may either be single
   occurrences or evolve over time in an
   apparently random fashion…‖ [11]
                            PR-OWL
   Developed as an extension to OWL (basically an upper
    ontology)
       Represents complex Bayesian models [21]
   Uses MEBN logic rather than extending OWL
       A first order Bayesian logic [21]
   Consists of entities and attributes
   Attributes about entities and relationships to each other –
    MEBN fragments (MFrag) [21]
       Represent conditional probability distribution [21]
   MFrags organized into MEBN Theories (MTheories) [21]
       Collectively satisfy consistency constraints [21]
   Goal
       Provide a way to support Bayesian models
                   PR-OWL




Taken from [21].
                             BayesOWL
   Express OWL ontologies as Bayesian networks by means of rules
   For each node, a conditional probability table (CPT) is constructed [15]
   All subject and object classes translated into concept nodes [15]
   Arc drawn between 2 concept nodes if the 2 classes are related by
    predicate [15]
   Direction based on class hierarchy
   L-Nodes generated during translation to represent OWL logical operators
   True/false value for each node indicates whether the instance belongs to
    the concept
   CPTs are approximated using the ―iterative proportional fitting procedure
    (IPFP)‖ [15]
   Restricted currently to OWL-DL taxonomies [15]
   Goals
        Support ontology reasoning using probabilistic approach
        Support ontology mapping
                  BayesOWL



rdfs:subClassOf      owl:intersectionOf   owl:unionOf




   owl:complementOf owl:equivalentClass owl:disjointWith

  Taken from [15].
                   BayesOWL



                              •DAG constructed
                              •CPTs for L-
                              Nodes specified
                              •Concept nodes
                              approximated
                              using D-IPFP




Taken from [15].
                  BayesOWL
 Reasoning Support [15]
     Concept satisfiability
     Concept overlapping
     Concept subsumption
 Extensions toOWL to support probabilistic
 representation [15]
     PriorProb
     CondProb
 Concept Mapping       [15]
                    BayesOWL




Extensions to OWL
Taken from [15].
                                Pronto
   Non-monotonic probabilistic DL reasoner
   Built on top of Pellet
   Uses P-SHIQ(D) formalism [8]
   Expressing uncertain axioms
        Syntax based upon Lukasiewicz‘s conditional constraints [8]
   Probabilistic Reasoning
        Lehmann‘s lexicographic entailment [8]
   Represents uncertain ontological knowledge and reasoning [8]
   Capable of representing uncertainty in both ABox and TBox axioms
    [8]
   ―All inferences are done in a totally ‗logical‘ way‖ (no translation) [8]
   Uses ―OWL 1.1 axiom annotations to associate probability intervals
    with uncertain OWL axioms‖ [8]
   Doesn‘t scale beyond ―15 generic (TBox) conditional constraints‖ [9]
                            Pronto
   Conditional constraints
       (D|C)[l,u]
       C and D concepts in P-SHIQ(D)
       [l,u] closed interval within [0,1]
   Supports overriding
       Can handle certain probabilistic conflicts
       Flying birds/penguin problem
         • Pronto allows ―more specific constraints to override more
           generic ones‖ [9]
         • ―if Pronto knows that Tweety is a Penguin and Penguin is a
           subclass-of Bird, it will override the constraint
           (FlyingObject|Bird)[0.9;1.0] by
           (FlyingObject|Penguin)[0.0;0.05] and correctly entail
           Tweety:(FlyingObject|owl:Thing)[0.0;0.05]. ― [9]
        Uncertainty and Ontologies -
                  Mapping
   Mapping a problem
       Existing approaches - combination of syntactic and
        semantic measures [18], use machine learning, or
        linguistics and natural language processing [15]
       Quality varies depending upon domain [18]
 Wang argues without use of a thesaurus,
  inaccuracies will occur [22]
 Problem:
       When mapping a concept from ontology A to ontology
        B there isn‘t always a single concept match but rather
        a number of concepts that match to some degree
        Uncertainty and Ontologies -
                  Mapping
   A proposed truth theory solution based on the
    following [18]:
       Dempster-Shafer, uncertain reasoning over potential
        mappings
         • Evidence Theory
       Similarity matrix comparing all concepts/properties
       Similarity measure of a concept between O1 and O2
       DS combines evidence learned to form new belief
       Promising approach
   Multi-agent ontology mapping framework [18]
       Not domain dependent
       Doesn‘t require large amounts of training data
     Uncertainty and Ontologies -
               Mapping
A   proposed solution by Wang [22]:
    ACAOM
    Uses WordNet to calculate similarities for
     node names
    Name based mapping
    Instance strategy
      • More semantics more feasible to match
      • Documents assigned to nodes
    Uses vector space models to rank matches
        Uncertainty and Ontologies -
                  Mapping
   BayesOWL [15] also proposed a solution
       Argue that existing similarity approaches will not work
         • If degree of similarity is not present in both concepts being
           matched [15]
         • If concept itself is fuzzy [15]
       Uses BayesOWL and belief propagation between
        BNs [15]
       Ontologies are first translated into BNs [15]
       Use probabilistic evidence reasoning to determine
        match [15]
    Uncertainty and Ontologies – An
       Ontology of Uncertainty
 Proposed by the W3C UR3W-XG group
 Provides a vocabulary for representing different
  types of uncertainty
 Was a good start but refinement needed [20]
 Strategy to use such an ontology as a way to
  drive a reasoner
       Open issue: coordination of reasoning of different
        uncertainty models in knowledge base [19]
       Uses SWRL rules to assign uncertainty to each
        relation [19]
Uncertainty and Ontologies – An
   Ontology of Uncertainty




 Taken from [20].
    Uncertainty and Web Services
 Service discovery – what is best service for request?
 Matching goal to service
 Brokers used for filtering
 Semantic Web Service Framework
       Semantic Web Service Language – concepts/descriptions [17]
       Semantic Web Service Ontology – conceptual model [17]
 It is argued that current frameworks use first order and
  description logics and ―goal capabilities‖ are ―based on
  subsumption checking or query-answering‖[16]
 Proposed approach uses Incident Calculus [16]
                  Demo - Pronto
 Pronto Example: Breast Cancer Risk Models
 Models 2 types of risks – absolute and relative
 Combining risk factors to determine likelihood of
  breast cancer for a woman [8]
       Distinction between known and inferred
 Pronto uses an ontology for knowledge
 Uses probabilistic statements to enable
  computable inferencing [8]
 The probabilistic statements complement the
  OWL syntax
                        Demo - Pronto
   Risk factors relevant to breast cancer are subclasses of ‗RiskFactor‘
   Categories of women that have certain risk factors are subclasses of
    ‗WomanWithRiskFactors‘
   Women with risk of developing cancer subclass ‗WomanUnderBRCRisk‘
   The goal:
        ―Compute the probability that a certain woman is an instance of some
         WomanUnderBRCRisk subclass given that she is an instance of some
         WomanWithRiskFactors subclass‖ [8]
        ―Infer generic probabilistic subsumption between classes under
         WomanUnderBRCRisk and under WomanWithRiskFactors‖ [8]

   Conditional constraints are used to represent ‗uncertain background
    knowledge‘ using the OWL 1.1 axiom annotations [8]
   The demo defines constraints to ―express how risk factors influence the risk
    of developing cancer‖ [8]
   Pronto combines the factors and computes the probability that a woman is
    an instance of a subclass of ‗WomanUnderBRCRisk‘
                       Demo - Pronto
<owl:ObjectProperty rdf:about="#hasRiskFactor">
    <rdfs:domain rdf:resource="#Person"/>
    <rdfs:range rdf:resource="#RiskFactor"/>
 </owl:ObjectProperty>

<owl:Class rdf:about="#WomanTakingEstrogen">
    <owl:equivalentClass>
       <owl:Restriction>
          <owl:onProperty rdf:resource="#hasRiskFactor"/>
          <owl:someValuesFrom rdf:resource="#Estrogen"/>
       </owl:Restriction>
    </owl:equivalentClass>
    <rdfs:subClassOf rdf:resource="#Woman"/>
 </owl:Class>


Taken from http://clarkparsia.com/pronto/cancer_ra.owl
                       Demo - Pronto
 <owl:Class rdf:about="#WomanWithRiskFactors">
     <owl:equivalentClass>
        <owl:Class>
           <owl:intersectionOf rdf:parseType="Collection">
              <rdf:Description rdf:about="#Woman"/>
              <owl:Restriction>
                 <owl:onProperty rdf:resource="#hasRiskFactor"/>
                 <owl:someValuesFrom rdf:resource="#RiskFactor"/>
              </owl:Restriction>
           </owl:intersectionOf>
        </owl:Class>
     </owl:equivalentClass>
     <rdfs:subClassOf rdf:resource="#Woman"/>
  </owl:Class>

Taken from http://clarkparsia.com/pronto/cancer_ra.owl
                     Demo - Pronto
<owl:Class rdf:about="#WomanAgedUnder50">
   <owl:equivalentClass>
      <owl:Class>
         <owl:intersectionOf rdf:parseType="Collection">
           <rdf:Description rdf:about="#Woman"/>
           <owl:Restriction>
              <owl:onProperty rdf:resource="#hasAge"/>
              <owl:someValuesFrom rdf:resource="#AgeUnder50"/>
           </owl:Restriction>
         </owl:intersectionOf>
      </owl:Class>
   </owl:equivalentClass>
   <rdfs:subClassOf rdf:resource="#WomanWithRiskFactors"/>
 </owl:Class>

Taken from http://clarkparsia.com/pronto/cancer_ra.owl
                     Demo - Pronto
<owl:Class rdf:about="#WomanUnderAbsoluteBRCRisk">
   <owl:equivalentClass>
      <owl:Class>
         <owl:intersectionOf rdf:parseType="Collection">
           <rdf:Description rdf:about="#Woman"/>
           <owl:Restriction>
              <owl:onProperty rdf:resource="#hasRisk"/>
              <owl:someValuesFrom rdf:resource="#AbsoluteBRCRisk"/>
           </owl:Restriction>
         </owl:intersectionOf>
      </owl:Class>
   </owl:equivalentClass>
 </owl:Class>

Taken from http://clarkparsia.com/pronto/cancer_ra.owl
                     Demo - Pronto
<owl:Class rdf:about="#WomanUnderBRCRisk">
    <owl:equivalentClass>
       <owl:Class>
         <owl:intersectionOf rdf:parseType="Collection">
            <rdf:Description rdf:about="#Woman"/>
            <owl:Restriction>
               <owl:onProperty rdf:resource="#hasRisk"/>
               <owl:someValuesFrom rdf:resource="#BRCRisk"/>
            </owl:Restriction>
         </owl:intersectionOf>
       </owl:Class>
    </owl:equivalentClass>
  </owl:Class>

Taken from http://clarkparsia.com/pronto/cancer_ra.owl
                     Demo - Pronto
<owl:Class rdf:about="#WomanUnderIncreasedBRCRisk">
    <owl:equivalentClass>
       <owl:Class>
         <owl:intersectionOf rdf:parseType="Collection">
            <owl:Restriction>
               <owl:onProperty rdf:resource="#hasRisk"/>
               <owl:someValuesFrom rdf:resource="#IncreasedBRCRisk"/>
            </owl:Restriction>
            <rdf:Description rdf:about="#WomanUnderBRCRisk"/>
         </owl:intersectionOf>
       </owl:Class>
    </owl:equivalentClass>
  </owl:Class>

Taken from http://clarkparsia.com/pronto/cancer_ra.owl
                     Demo - Pronto
<owl:Class rdf:about="#WomanUnderLifetimeBRCRisk">
    <owl:equivalentClass>
       <owl:Class>
         <owl:intersectionOf rdf:parseType="Collection">
            <rdf:Description rdf:about="#Woman"/>
            <owl:Restriction>
               <owl:onProperty rdf:resource="#hasRisk"/>
               <owl:someValuesFrom rdf:resource="#LifetimeBRCRisk"/>
            </owl:Restriction>
         </owl:intersectionOf>
       </owl:Class>
    </owl:equivalentClass>
    <rdfs:subClassOf rdf:resource="#WomanUnderAbsoluteBRCRisk"/>
  </owl:Class>

Taken from http://clarkparsia.com/pronto/cancer_ra.owl
                       Demo - Pronto
<owl:Class rdf:about="#WomanUnderModeratelyIncreasedBRCRisk">
    <owl:equivalentClass>
       <owl:Class>
          <owl:intersectionOf rdf:parseType="Collection">
             <rdf:Description rdf:about="#WomanUnderIncreasedBRCRisk"/>
             <owl:Restriction>
                <owl:onProperty rdf:resource="#hasRisk"/>
                <owl:someValuesFrom rdf:resource="#ModeratelyIncreasedBRCRisk"/>
             </owl:Restriction>
          </owl:intersectionOf>
       </owl:Class>
    </owl:equivalentClass>
    <rdfs:subClassOf rdf:resource="#WomanUnderIncreasedBRCRisk"/>
    <owl:disjointWith rdf:resource="#WomanUnderStronglyIncreasedBRCRisk"/>
 </owl:Class>

Taken from http://clarkparsia.com/pronto/cancer_ra.owl
                     Demo - Pronto
<owl:Class rdf:about="#WomanUnderModeratelyReducedBRCRisk">
    <owl:equivalentClass>
       <owl:Restriction>
         <owl:onProperty rdf:resource="#hasRisk"/>
         <owl:someValuesFrom
  rdf:resource="#ModeratelyReducedBRCRisk"/>
       </owl:Restriction>
    </owl:equivalentClass>
    <rdfs:subClassOf rdf:resource="#WomanUnderReducedBRCRisk"/>
    <owl:disjointWith
  rdf:resource="#WomanUnderStronglyReducedBRCRisk"/>
    <owl:disjointWith
  rdf:resource="#WomanUnderWeakelyReducedBRCRisk"/>
 </owl:Class>

Taken from http://clarkparsia.com/pronto/cancer_ra.owl
                                        Demo - Pronto
<!--Lif etime absolute risk-->

  <!-- Any woman has a 12.3% risk of lif etime breast cancer -->
  <owl11:Axiom>
    <rdf :subject rdf :resource="#Woman"/>
    <rdf :predicate rdf :resource="&rdfs;subClassOf"/>
    <rdf :object rdf :resource="#WomanUnderLif etimeBRCRisk"/>
    <pronto:certainty>0;0.123</pronto:certainty>
  </owl11:Axiom>

  <!-- If a woman has BRCA mutation, then the risk is beteen 30% and 85% -->
  <owl11:Axiom>
     <rdf :subject rdf :resource="#WomanWithBRCAMutation"/>
     <rdf :predicate rdf :resource="&rdfs;subClassOf"/>
     <rdf :object rdf :resource="#WomanUnderLif etimeBRCRisk"/>
     <pronto:certainty>0.3;0.85</pronto:certainty>
  </owl11:Axiom>

  <!-- If it's BRCA1 mutation, then the lif etime risk is between 60% and 80% -->
  <owl11:Axiom>
     <rdf :subject rdf :resource="#WomanWithBRCA1Mutation"/>
     <rdf :predicate rdf :resource="&rdfs;subClassOf"/>
     <rdf :object rdf :resource="#WomanUnderLif etimeBRCRisk"/>
     <pronto:certainty>0.6;0.8</pronto:certainty>
  </owl11:Axiom>

Taken f rom http://clarkparsia.com/pronto/cancer_cc.owl
                               Demo - Pronto
<!-- Age-related risk-->
<owl11:Axiom>
      <rdf:subject rdf:resource="#WomanAgedUnder20"/>
      <rdf:predicate rdf:resource="&rdfs;subClassOf"/>
      <rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/>
      <pronto:certainty>0;0.0005</pronto:certainty>
   </owl11:Axiom>

  <owl11:Axiom>
     <rdf:subject rdf:resource="#WomanAged2030"/>
     <rdf:predicate rdf:resource="&rdfs;subClassOf"/>
     <rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/>
     <pronto:certainty>0;0.004</pronto:certainty>
  </owl11:Axiom>

  <owl11:Axiom>
     <rdf:subject rdf:resource="#WomanAged3040"/>
     <rdf:predicate rdf:resource="&rdfs;subClassOf"/>
     <rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/>
     <pronto:certainty>0;0.014</pronto:certainty>
  </owl11:Axiom>

Taken from http://clarkparsia.com/pronto/cancer_cc.owl
                               Demo - Pronto
  <owl11:Axiom>
     <rdf:subject rdf:resource="#WomanAged4050"/>
     <rdf:predicate rdf:resource="&rdfs;subClassOf"/>
     <rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/>
     <pronto:certainty>0;0.025</pronto:certainty>
  </owl11:Axiom>

  <owl11:Axiom>
     <rdf:subject rdf:resource="#WomanAged5060"/>
     <rdf:predicate rdf:resource="&rdfs;subClassOf"/>
     <rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/>
     <pronto:certainty>0;0.035</pronto:certainty>
  </owl11:Axiom>


  <owl11:Axiom>
     <rdf:subject rdf:resource="#WomanAged6070"/>
     <rdf:predicate rdf:resource="&rdfs;subClassOf"/>
     <rdf:object rdf:resource="#WomanUnderShortTermBRCRisk"/>
     <pronto:certainty>0;0.039</pronto:certainty>
  </owl11:Axiom>

Taken from http://clarkparsia.com/pronto/cancer_cc.owl
                                      Demo - Pronto
<!--owl11:Axiom>
     <rdf :subject rdf :resource="#Julie"/>
     <rdf :predicate rdf :resource="&rdf;type"/>
     <rdf :object rdf :resource="#WomanAged3040"/>
     <pronto:certainty>1;1</pronto:certainty>
  </owl11:Axiom>

  <owl11:Axiom>
    <rdf :subject rdf :resource="#Mary"/>
    <rdf :predicate rdf :resource="&rdf;type"/>
    <rdf :object rdf :resource="#WomanWithBRCA1Mutation"/>
    <pronto:certainty>1;1</pronto:certainty>
  </owl11:Axiom>

  <owl11:Axiom>
    <rdf :subject rdf :resource="#Ann"/>
    <rdf :predicate rdf :resource="&rdf;type"/>
    <rdf :object rdf :resource="#WomanWithMotherBRCAf f ected"/>
    <pronto:certainty>1;1</pronto:certainty>
  </owl11:Axiom>

  <owl11:Axiom>
    <rdf :subject rdf :resource="#Ann"/>
    <rdf :predicate rdf :resource="&rdf;type"/>
    <rdf :object rdf :resource="#AshkenaziJewishWoman"/>
    <pronto:certainty>0.9;0.95</pronto:certainty>
  </owl11:Axiom-->

Taken f rom http://clarkparsia.com/pronto/cancer_cc.owl
                               Demo - Pronto
<owl11:Axiom>
     <rdf:subject rdf:resource="#Helen"/>
     <rdf:predicate rdf:resource="&rdf;type"/>
     <rdf:object rdf:resource="#PostmenopausalWoman"/>
     <pronto:certainty>1;1</pronto:certainty>
  </owl11:Axiom>


  <owl11:Axiom>
     <rdf:subject rdf:resource="#Helen"/>
     <rdf:predicate rdf:resource="&rdf;type"/>
     <rdf:object rdf:resource="#WomanTakingEstrogen"/>
     <pronto:certainty>1;1</pronto:certainty>
  </owl11:Axiom>


  <owl11:Axiom>
     <rdf:subject rdf:resource="#Helen"/>
     <rdf:predicate rdf:resource="&rdf;type"/>
     <rdf:object rdf:resource="#WomanTakingProgestin"/>
     <pronto:certainty>1;1</pronto:certainty>
  </owl11:Axiom>

Taken from http://clarkparsia.com/pronto/cancer_cc.owl
                Demo - Pronto
<owl11:Axiom>
   <rdf:subject rdf:resource="#AshkenaziJewishWoman"/>
   <rdf:predicate rdf:resource="&rdfs;subClassOf"/>
   <rdf:object rdf:resource="#WomanWithBRCAMutation"/>
   <pronto:certainty>0.025;0.025</pronto:certainty>
 </owl11:Axiom>
<owl11:Axiom>
   <rdf:subject rdf:resource="#WomanWithBRCAMutation"/>
   <rdf:predicate rdf:resource="&rdfs;subClassOf"/>
   <rdf:object rdf:resource="#WomanUnderLifetimeBRCRisk"/>
   <pronto:certainty>0.3;0.85</pronto:certainty>
 </owl11:Axiom>
            Demo - Pronto
 Running query    (generic TBox conditional
  constraint) (C|D)[l,u] [9]
entail
  http://clarkparsia.com/pronto/cancer_ra.ow
  l#AshkenaziJewishWoman
  http://clarkparsia.com/pronto/cancer_ra.ow
  l#WomanUnderLifetimeBRCRisk
                   Demo - Pronto
Query : entail
Result: 34:
    (WomanUnderLifetimeBRCRisk|AshkenaziJewishWoman)[0.0075;0.123]
Explanation:
Explaining the generic constraint 34:
    (WomanUnderLifetimeBRCRisk|AshkenaziJewish
Woman)[0.0075;0.123]:
Lower bound is because of:
[[8: (WomanWithBRCAMutation|AshkenaziJewishWoman)[0.025;0.025], 7:
    (WomanUnderLi
fetimeBRCRisk|WomanWithBRCAMutation)[0.3;0.85]]]
Upper bound is because of:
[[10: (WomanUnderLifetimeBRCRisk|Woman)[0.0;0.123]]]

Result computed in 6266ms
              Want to learn more?
   Attend the 2009 URSW Conference
       http://c4i.gmu.edu/ursw/2009/
   Visit W3C Uncertainty Reasoning for the World Wide
    Web Incubator Group
       http://www.w3.org/2005/Incubator/urw3/
   Review presentations from last year‘s conference
       http://c4i.gmu.edu/ursw/2008/
   Download Pronto
       http://pellet.owldl.com/pronto/
   Download FiRE
       http://www.image.ece.ntua.gr/~nsimou/FiRE/
                                                 References
[1] - Stoilos,Simou,Stamou,Kollias,―Uncertainty and the Semantic Web‖, http://www.image.ece.ntua.gr/php/savepaper.php?id=445, 2006, IEEE
[2] – 2008 Conference, ―Uncertainty Reasoning for the Semantic Web‖, http://c4i.gmu.edu/ursw/2008/index.html
[3] - 2007 Conference, ―Uncertainty Reasoning for the Semantic Web‖, http://c4i.gmu.edu/ursw/2007/index.html
[4] - Stoilos,Stamou,Tzouvaras,Pan,Horrocks, ―Fuzzy OWL: Uncertainty and the Semantic Web‖, http://www.image.ntua.gr/papers/398.pdf
[5] - Lassila, ―Some Personal Thoughts on Semantic Web and ―Non-symbolic‖ AI‖, http://c4i.gmu.edu/ursw/2008/talks/URSW2008_Keynote_Lassila.pdf, 2008,
        ISWC
[6] – Williams,Bastin,Cornford,Ingram, ―Describing and Communicating Uncertainty within the Semantic Web‖,
        http://c4i.gmu.edu/ursw/2008/papers/URSW2008_F3_WilliamsEtAl.pdf
[7] – Sanchez, ―Fuzzy logic and semantic web‖,
        http://books.google.com/books?id=Cidej8b4ESIC&pg=PA4&lpg=PA4&dq=monotonic+bivalent+language&source=bl&ots=mtbZcZfaO7&sig=VtGq KXu-
        rrzl5HOw36UBTeTpdoE&hl=en&ei=sBIASpuJFonItgeKnpyTBw&sa=X&oi=book_result&ct=result&resnum=1#PPP1,M1
[8] – Klinov, Parsia, ―Demonstrating Pronto: a Non-monotonic Probabilistic OWL Reasoner‖,
        http://www.webont.org/owled/2008dc/papers/owled2008dc_paper_2.pdf
[9] – Klinov, ―Introducing Pronto: Probabilistic DL Reasoning in Pellet―, http://clarkparsia.com/weblog/2007/09/27/introducing-pronto/
[10] – Wikipedia Fuzzy Set theory, http://en.wikipedia.org/wiki/Fuzzy_set
[11] – Wikipedia Probability Theory, http://en.wikipedia.org/wiki/Probability_theory
[12] – Straccia, ―A Fuzzy Description Logic for the Semantic Web‖, http://www.win.tue.nl/~aserebre/ks/Lit/Straccia2006.pdf
[13] – Mazzieri, Dragoni, ―A Fuzzy Semantics for Semantic Web Languages‖, http://ftp.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-173/paper2.pdf
[14] – Wikipedia Description Logic, http://en.wikipedia.org/wiki/Description_logic
[15] – Ding, Peng, Pan, ―BayesOWL: Uncertainty Modeling in Semantic Web Ontologies‖, http://ebiquity.umbc.edu/_file_directory_/papers/217.pdf
[16] – Martin-recurerda1, Robertson2, ―Discovery and Uncertainty in Semantic Web Services‖, http://ftp.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-
        173/paper4.pdf
[17] – ―Semantic Web Services Framework (SWSF) Overview‖, http://www.w3.org/Submission/SWSF/
[18] – Nagy,Vargas-Vera,Motta, ―Uncertain Reasoning for Creating Ontology Mapping on the Semantic Web‖,
        http://c4i.gmu.edu/ursw/2007/files/papers/URSW2007_P2_NagyVeraMotta.pdf
[19] – Ceravolo, Damiani,Leida, ―Which Role for an Ontology of Uncertainty?‖, http://c4i.gmu.edu/ursw/2008/papers/URSW2008_P6_CeravoloEtAl.pdf
[20] – Laskey, Laskey, ―Uncertainty Reasoning for the World Wide Web: Report on the URW3 -XG Incubator Group‖,
        http://c4i.gmu.edu/ursw/2008/papers/URSW2008_FX_LaskeyLaskey.pdf
[21] – Costa, Laskey, ―PR-OWL: A Framework for Probabilistic Ontologies‖, http://volgenau.gmu.edu/~klaskey/papers/FOIS2006_CostaLaskey.pdf
[22] – Wang, ―Integrating Uncertainty Into Ontology Mapping‖, http://iswc2007.semanticweb.org/papers/955.pdf

				
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