Reasoning about Situation Similarity C. Anagnostopoulos, Y. Ntarladimas, S. Hadjiefthymiades P...
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Transcript of Reasoning about Situation Similarity C. Anagnostopoulos, Y. Ntarladimas, S. Hadjiefthymiades P...
Reasoning about Situation Similarity
C. Anagnostopoulos, Y. Ntarladimas, S. Hadjiefthymiades
Pervasive Computing Research GroupCommunication Networks Laboratory
Department Informatics and TelecommunicationsUniversity of Athens – Greece
IEEE IS 2006@LondonIEEE IS 2006@London
Conceptual Modeling: Concepts and RelationsSituation: 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@LondonIEEE IS 2006@London
subsumption
Commonconcept
Abstractconcept
ConceptualTaxonomy
relation
Relation(Compatibility)
R
.R
.R
.R
.R
ExistentialRestriction
UniversalRestriction
ClosureAxiom
C D CR.D
S
R1 R2
R
Abstractrelation
RelationalTaxonomy
If R S and CR.DThenCS.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 ontologiesSemantic Web Ontologies:•RDF•RDF(S) {is-a}•OWL-DL (Description Logics) {existential/quantificational, cardinality restrictions}
DL-Syntax of a situation
Situation Person Context
Meeting
FormalMeeting
InternalMeeting
ManagerMeeting
Temporal
Spatial
Artifact
MeetingHour
WorkingHour
IndoorSpace
IndoorRoom
MeetingArea
MeetingRoom
StaffRoom
Partner
ManagerBusinessPartner
isInvolvedIn hasContext
part of+
CheckingE-mails
Jogging
subsumption relation (IS-A)
Compatible With relation
relation
concept
ConferenceRoom
BusinessMeeting
Worker
Secretary
PDA Profile
Disjoint With relation
Q
Q SituationIS-A
Bob
AND
AND has Spatial Context
is Involved By
AND
RolePartner
Person
has Business Role
has Entry
AND
InteriorRoom
Manager
is Located In
AND
contains
has Business Role
NumberRestriction
2 contains
SpatialContext
Not Alone
IndoorContext
capacity
PersonalContext
Time
has Time
MeetingTime
TemporalContext
has Temporal Context
Subsumption role
Role with semantics x {,}
Local Context
Contextual Informationx
IS-A
Example: Q is-a situation, which…
Temporal Ontology
Spatial Ontology
User Profile Ontology
Local Context
Local Context
Local Context
A
E
B
D
C
F
M
Commonconcept
Abstractconcept
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}
)C(U\)D(U)D(U\)C(U)D(U)C(U
)D(U)C(U)D,C(TS
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
DF
K
CF
C D
Abstractconcept
Taxonomical Similarity taking into account the Disjoint Axiom
Conceptual Taxonomy H
Revised Taxonomical Similarity:
)D,C(TS)D,C(TS)D,C(TS)D,C(TS FFD
TSD
Position (h) in the taxonomy of the application of the disjoint axiom
h
CF DF
where CF, DF the nearest indirect super-concepts of C and D,respectively, that are disjoint with.
grand(grand(parent))
grand(parent)
parent
R
S T
Q
Abstractrelation
Relational Similarity
Relational Taxonomy HR
Let U(R) = {S HR | S R S R}Let A(C,R) = {D| C R.D}, Associated concepts of C through R
Relational Similarity:
)C,R(A
)}D,R(AD|)D,C(TS).R,R(TSmax{
)D,C(RSi
)C,R(ACjjjiji
ii
C
D
D1
D2
D1
D2
D3
R
Si
Sj
R
R
TS(Di, Dj)TS(Si, Sj)
Chris drives a vehicleAnna drives a vehicle
Bob drives a bikeMary drives a car
RS(Chris,Bob)RS(Chris,Mary)RS(Chris,Anna)
Pure Similarity
Pure Similarity: (Asserted knowledge in T-Box from expert)
RHr
rD )D,C(RSw)1()D,C(TS.)D,C(sim
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Restrictions Analogy
C
A
.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: RT and STConcepts: AE and BE
Closure Axiom
))}T,Q(A),R,C(A(TS).T,R(TS{(min)Q,C(d DRT|R
X
(d, d)
(d, d)
Closure Distance:
},{X
2XX ))Q,D(d)Q,C(d()Q,D,C(d Important Notice:
A value of 0 means same descriptionsand 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 similaritySemi-structural: both pure and closure are equally necessary conditions to conclude conceptual similarityNon-structural: closure is necessary but not sufficient to conclude conceptual similarity
Reasoning Process over Incompatible/Compatible Situations(?S,Sa)
Input: Sa list of situations related to ?SOutput: Sc list of compatible situations Set SMAX=argmax{sim(?S,Si)} Set HMAX the taxonomy that contains SMAX
Set TMAX the most abstract situation of HMAX (i.e., TMAX SMAX)For each incompatible situation SINC Sa Do If SINC.affinity [TMAX.affinity, SMAX.affinity] Then Sc = Sc { SINC} End IfEnd For For each compatible situation SC Sa Do /*compatible with SMAX */ 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 IfEnd ForReturn Sc
Reasoning about Situational Similarity
Behavior of the Similarity Measure
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Most similar situation: Smax = argmax{affinity(Q,Si)}, Si 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 {[email protected]}Pervasive Computing Research Group {http://p-comp.di.uoa.gr}
IEEE IS 2006@LondonIEEE IS 2006@London