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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 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
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
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 CR.D Then CS.D .R Closure Axiom .R subsumption relation C D R S CR.D Conceptual Taxonomy Relational Taxonomy Disjoint Axiom (Symmetric) Relation (Compatibility)
QSituationΠ ( 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 MeetingMeetingΠ ( 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}
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 {,}
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
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
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
Pure Similarity Pure Similarity: (Asserted knowledge in T-Box from expert) IEEE IS 2006@London
Restrictions Analogy Restriction Analogy between two concepts: Two concepts apply the same restrictions over their relations X-Distance (X {,}): Closure Axiom Closure Concept Relations: RT andST Concepts: AE and BE .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
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)
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, HCHMAX*/ Sc = Sc{SC-MAX} End If End For Return Sc Reasoning about Situational Similarity
Behavior of the Similarity Measure Most similar situation: Smax = argmax{affinity(Q,Si)}, Si H IEEE IS 2006@London
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
Thank you! Christos B. Anagnostopoulos {bleu@di.uoa.gr} Pervasive Computing Research Group {http://p-comp.di.uoa.gr} IEEE IS 2006@London