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Reasoning about Situation Similarity

Reasoning about Situation Similarity. C. Anagnostopoulos , Y. Ntarladimas, S. Hadjiefthymiades P ervasive C omputing R esearch G roup C ommunication N etworks L aboratory Department Informatics and Telecommunications University of Athens – Greece IEEE IS 2006@London.

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Reasoning about Situation Similarity

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  1. Reasoning about Situation Similarity C. Anagnostopoulos, Y. Ntarladimas, S. Hadjiefthymiades Pervasive Computing Research Group Communication Networks Laboratory Department Informatics and Telecommunications University of Athens – Greece IEEE IS 2006@London

  2. Conceptual Modeling: Concepts and Relations Situation: logically aggregated contexts Reason about: Situational Similarity/Analogy Conceptual Similarity (Pure Similarity) Closure Distance (Restrictions Analogy) Affinity Similarity = Holistic Measure for Similarity IEEE IS 2006@London

  3. Abstract concept Abstract relation Conceptual DL Semantics S R R1 R2 Disjoint with .R R Existential Restriction Common concept .R Universal Restriction C  D If R  S and CR.D Then CS.D .R Closure Axiom .R subsumption relation C  D R  S CR.D Conceptual Taxonomy Relational Taxonomy Disjoint Axiom (Symmetric) Relation (Compatibility)

  4. QSituationΠ ( is Involved By. (Bob Π  has Time. Meeting Hour Π  is Located In. (Interior Room Π  contains. Manager) Π  has Business Role. Partner Π  has Business Role. Business Partner)) Formal MeetingMeetingΠ ( is Involved By. (Partner Π  has Time. Meeting Hour Π  is Located In. (Meeting Room Π  contains. Manager Π  contains. Business Partner) Π  has Business Role. Partner Π  has Business Role. Business Partner)) isInvolvedIn hasContext Situation Person Context Partner Worker Meeting Hour Jogging Meeting Checking E-mails Temporal Business Partner Manager Secretary Working Hour Q Meeting Area Indoor Space Formal Meeting part of+ Spatial Meeting Room Indoor Room Internal Meeting Business Meeting Conference Room Artifact Staff Room Manager Meeting subsumption relation (IS-A) concept PDA Profile Situation Modeling: Ontological Perspective Compatible With relation Disjoint With relation relation DL-Syntax of a situation • Situation = aggregation of concepts derived • from epistemic ontologies • Semantic Web Ontologies: • RDF • RDF(S) {is-a} • OWL-DL (Description Logics) • {existential/quantificational, cardinalityrestrictions}

  5. Temporal Ontology IS-A Q Situation Temporal Context  has Time Local Context Personal Context Time Meeting Time is Involved By  has Temporal Context Local Context AND  has Business Role  has Spatial Context Partner Role  has Business Role AND  has Entry AND  is Located In AND AND Person Bob Example: Q is-a situation, which…  contains  capacity 2 contains Not Alone Manager Interior Room Number Restriction Indoor Context User Profile Ontology Spatial Context Local Context Spatial Ontology IS-A Subsumption role Local Context x Contextual Information Role with semantics x {,}

  6. Taxonomical Similarity Let U(H,C) = U(C) = {D  H | D  C  D  C} e.g., U(F)={A,B,C,D,E,F} Abstract concept A Taxonomical Similarity: B C • e.g., • U(F)  U(M) = {A,B,C,D} • U(F) \ U(M) = {E,F} • U(M) \ U(F) = {M} • TS(F,M) = 0.727, (α=β=0.5) • Important Notice (α [0,0.5]): • A value of 0 implies that the differences of C are notsufficient • to conclude that it is similar to D • A value of 0.5 implies that the differences of C are necessary • to conclude similarity Common concept D E M F Common parents! Conceptual Taxonomy H

  7. Taxonomical Similarity taking into account the Disjoint Axiom Abstract concept Revised Taxonomical Similarity: A grand(grand(parent)) where CF, DF the nearest indirect super-concepts of C and D, respectively, that are disjoint with. grand(parent) B K parent CF DF h E TSD C D CF  DF Conceptual Taxonomy H Position (h) in the taxonomy of the application of the disjoint axiom

  8. Relational Similarity Let U(R) = {S  HR | S  R S  R} Let A(C,R) = {D| C R.D}, Associated concepts of C through R Abstract relation R Relational Similarity: S T Q Relational Taxonomy HR R D1 C D2 Si Chris drives a vehicle Anna drives a vehicle Bob drives a bike Mary drives a car RS(Chris,Bob) RS(Chris,Mary) RS(Chris,Anna) TS(Di, Dj) TS(Si, Sj) D1 Sj R D D2 R D3

  9. Pure Similarity Pure Similarity: (Asserted knowledge in T-Box from expert) IEEE IS 2006@London

  10. Restrictions Analogy Restriction Analogy between two concepts: Two concepts apply the same restrictions over their relations X-Distance (X  {,}): Closure Axiom Closure Concept Relations: RT andST Concepts: AE and BE .T E Q Virtual .T Chris drives at least a bike (drives. bike) Anna drives a at least a vehicle (drives. vehicle ) Mary drives only bikeswhen she drives vehicles (drives. bike ) Bob drives only bikes (drives. bike  drives. bike ) Closure concept of Chris, Anna and Mary is Bob! A B .R .S (d, d) C D (d, d) Closure Distance: Important Notice: A value of 0 means same descriptions and 1 means extremely different w.r.t. CWA

  11. Affinity Similarity: Holistic Similarity Structural: pure is necessary condition to conclude conceptual similarity Semi-structural: both pure and closure are equally necessary conditions to conclude conceptual similarity Non-structural: closure is necessary but not sufficient to conclude conceptual similarity • Affinity Similarity: • A fuzzy implication of: • Pure Similarity • Closure Distance (Analogy)

  12. Reasoning Process over Incompatible/Compatible Situations(?S,Sa) Input: Salist of situations related to ?S Output: Sc list of compatible situations SetSMAX=argmax{sim(?S,Si)} Set HMAXthetaxonomy that contains SMAX Set TMAX the most abstract situation of HMAX(i.e., TMAX SMAX) For each incompatible situation SINC SaDo If SINC.affinity  [TMAX.affinity, SMAX.affinity] Then Sc = Sc{ SINC} End If End For For each compatible situation SC SaDo /*compatible withSMAX*/ If SC HMAX Then If SC.affinity  [TMAX.affinity, SMAX.affinity] and SC  SMAX Then Sc = Sc{ SC} End If Else If SC HMAX Then SC-MAX=argmax{sim(?S,Si)} /* Si HC, HCHMAX*/ Sc = Sc{SC-MAX} End If End For Return Sc Reasoning about Situational Similarity

  13. Behavior of the Similarity Measure Most similar situation: Smax = argmax{affinity(Q,Si)}, Si H IEEE IS 2006@London

  14. Evaluation / Future work • Further Research: • Relational Similarity based on transitive relations (e.g., mereology, part-wholes, Medicine) • Taxonomical Similarity after DL reasoning (e.g., multiple inheritance) • Analogy based on number restrictions • Temporal Similarity based on temporal relations

  15. Thank you! Christos B. Anagnostopoulos {bleu@di.uoa.gr} Pervasive Computing Research Group {http://p-comp.di.uoa.gr} IEEE IS 2006@London

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