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

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

subsumption Common concept Abstract concept Conceptual Taxonomy relation Relation (Compatibility) R .R.R .R.R .R.R .R.R Existential Restriction Universal Restriction Closure Axiom C  D C  R.D S R1R1 R2R2 R Abstract relation Relational Taxonomy If R  S and C  R.D Then C  S.D R  S Disjoint Axiom (Symmetric) C   D Conceptual DL Semantics Disjoint with

Situation Modeling : Ontological Perspective Q  Situation Π (  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  Meeting Π (  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)) Situation = aggregation of concepts derived from epistemic ontologies Semantic Web Ontologies: RDF RDF(S) {is-a} OWL-DL (Description Logics) {existential/quantificational, cardinality restrictions} DL-Syntax of a situation SituationPersonContext Meeting Formal Meeting Internal Meeting Manager Meeting Temporal Spatial Artifact Meeting Hour Working Hour Indoor Space Indoor Room Meeting Area Meeting Room Staff Room Partner Manager Business Partner isInvolvedInhasContext part of+ Checking s Jogging subsumption relation (IS-A) Compatible With relation relation concept Conference Room Business Meeting Worker Secretary PDA Profile Disjoint With relation Q

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

A E B D C F M Common concept Abstract concept Taxonomical Similarity Conceptual Taxonomy H Let U(H,C) = U(C) = {D  H | D  C  D  C} e.g., U(F)={A,B,C,D,E,F} 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 not sufficient to conclude that it is similar to D A value of 0.5 implies that the differences of C are necessary to conclude similarity Taxonomical Similarity: Common parents!

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

R ST Q Abstract relation Relational Similarity Relational Taxonomy H R Let U(R) = {S  H R | S  R  S  R} Let A(C,R) = {D| C  R.D}, Associated concepts of C through R Relational Similarity: C D D1D1 D2D2 D1D1 D2D2 D3D3 R SiSi SjSj R R TS(D i, D j ) TS(S i, S j ) 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)

Pure Similarity Pure Similarity: (Asserted knowledge in T-Box from expert) IEEE IS

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

Affinity Similarity: Holistic Similarity Affinity Similarity: A fuzzy implication of: Pure Similarity Closure Distance (Analogy) 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

Reasoning Process over Incompatible/Compatible Situations(?S,S a ) Input : S a list of situations related to ?S Output : S c list of compatible situations Set S MAX =argmax{sim(?S, S i )} Set H MAX the taxonomy that contains S MAX Set T MAX the most abstract situation of H MAX (i.e., T MAX  S MAX ) For each incompatible situation S INC  S a Do If S INC.affinity  [ T MAX.affinity, S MAX.affinity] Then S c = S c  { S INC } End If End For For each compatible situation S C  S a Do /*compatible with S MAX */ If S C  H MAX Then If S C.affinity  [ T MAX.affinity, S MAX.affinity] and S C  S MAX Then S c = S c  { S C } End If Else If S C  H MAX Then S C-MAX =argmax{sim(?S, S i )} /* S i  H C, H C  H MAX */ S c = S c  { S C-MAX } End If End For Return S c Reasoning about Situational Similarity

Behavior of the Similarity Measure IEEE IS Most similar situation: S max = argmax{affinity(Q,S i )},  S i  H

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 P ervasive C omputing R esearch G roup { IEEE IS