reasoning about situation similarity c. anagnostopoulos, y. ntarladimas, s. hadjiefthymiades p...
Post on 19-Dec-2015
216 views
TRANSCRIPT
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
IEEE IS 2006@LondonIEEE IS 2006@London
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
IEEE IS 2006@LondonIEEE IS 2006@London
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