Representation of Parsimonious Covering Theory in OWL-DL


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C. Henson, K. Thirunarayan, A. Sheth and P. Hitzler, Representation of Parsimonious Covering Theory in OWL-DL, OWLED2011, June 2011.

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Representation of Parsimonious Covering Theory in OWL-DL

  1. 1. OWL Experiences and Directions (OWLED 2011)<br />Representation of Parsimonious Covering Theory<br />in OWL-DL<br />Cory Henson, KrishnaprasadThirunarayan, AmitSheth, Pascal Hitzler<br />Ohio Center of Excellence in Knowledge-enabled Computing (Kno.e.sis)<br />Wright State University, Dayton, Ohio, USA<br />Paper at<br />1<br />
  2. 2. Find a set of entities (in the world) that<br />explain a given set of sensor observations<br />2<br />
  3. 3. Characteristics of a Solution<br />Handle incomplete information (graceful degradation)<br />Minimize explanations with additional information (anti-monotonic)<br />Reason over data on the Web (i.e., RDF on LOD)<br />Scalable (tractable)<br />3<br />
  4. 4.<br />4<br />
  5. 5. Semantic Sensor Network (SSN) Ontology<br /><br />5<br />
  6. 6. Parsimonious Covering Theory (PCT)<br />Web Ontology<br />Language (OWL)<br />minimize<br />explanations<br />tractable<br />degrade gracefully<br />Web reasoning<br />Convert PCT to OWL<br />6<br />
  7. 7. Parsimonious Covering Theory<br />Goal is to account for observed symptoms with plausible explanatory hypotheses (abductive logic)<br />Driven by background knowledge modeled as a bipartite graph causally linking disorders to manifestations <br />disorder<br />manifestation<br />causes<br />m1<br />d1<br />m2<br />d2<br />m3<br />d3<br />m4<br />explanation<br />observations<br />YunPeng, James A. Reggia, "Abductive Inference Models for Diagnostic Problem-Solving"<br />7<br />
  8. 8. PCT Parsimonious Cover<br />coverage: an explanation is a cover if, for each observation, there is a causal relation from a disorder contained in the explanation to the observation<br />parsimony: an explanation is parsimonious, or best, if it contains only a single disorder (single disorder assumption)<br />8<br />
  9. 9. Given<br />PCT problem P is a 4-tuple ⟨D, M, C, Γ⟩<br />D is a finite set of disorders<br />M is a finite set of manifestations<br />C is the causation function [C : D ⟶ Powerset(M)]<br />Γ is the set of observations [Γ ⊆ M ]<br /><ul><li>Δ is a valid explanation (i.e., is a parsimonious cover)</li></ul>Goal<br />Translate P into OWL, o(P), such that o(P) ⊧ Δ<br />9<br />
  10. 10. disorders (D)<br />for all d ∈ D, write d rdf:type Disorder<br />ex: flu rdf:type Disorder<br /> cold rdf:type Disorder <br />manifestations (M) <br />for all m ∈ M, write m rdf:type Manifestation<br />ex: fever rdf:type Manifestation<br /> headache rdf:type Manifestation …<br />causes relations (C)<br />for all (d, m) ∈ C, write d causes m<br />ex: flu causes fever<br /> flu causes headache …<br />PCT Background<br />Knowledge in OWL<br />disorder<br />manifestation<br />causes<br />fever<br />headache<br />extreme exhaustion<br />severe ache and pain<br />flu<br />mild ache and pain<br />stuffy nose<br />sneezing<br />cold<br />sore throat<br />severe cough<br />mild cough<br />10<br />
  11. 11. observations (Γ)<br />for mi∈ Γ, i =1 … n, write<br />Explanation owl:equivalentClass<br /> causes value m1 and … causes value mn<br />ex: Explanation owl:equivalentClass<br /> causes value sneezing and<br /> causes value sore-throat <br /> causes value mild-cough<br />explanation (Δ)<br />Δrdf:type Explanation, is deduced<br />ex: cold rdf:type Explanation<br /> flu rdf:type Explanation<br />PCT Observations and <br />Explanations in OWL<br />and<br />11<br />
  12. 12. Ohio Center of Excellence on <br />Knowledge-Enabled Computing (Kno.e.sis)<br />thank you, and please visit us at<br /><br />Kno.e.sis– Ohio Center of Excellence in Knowledge-enabled Computing<br />Wright State University, Dayton, Ohio, USA<br />12<br />
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