Reasoning about Situation Similarity

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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_at_London

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• 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

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Abstract concept
Abstract relation
Conceptual DL Semantics
S
R
R1
R2
Disjoint with
?.R
Existential Restriction
R
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)
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• Situation Modeling Ontological Perspective

isInvolvedIn
hasContext
Situation
Person
Context
Partner
Worker
Meeting Hour
Meeting
Checking E-mails
Jogging
Temporal
Working Hour
Manager
Business Partner
Secretary
Q
Indoor Space
Meeting Area
Formal Meeting
Spatial
part of
Indoor Room
Meeting Room
Internal Meeting
Business Meeting
Artifact
Conference Room
Staff Room
Manager Meeting
subsumption relation (IS-A)
concept
PDA Profile
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, cardinality
  restrictions

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Temporal Ontology

• Example Q is-a situation, which

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
Role
Partner
? has Business Role
AND
? has Entry
AND
? is Located In
AND
AND
Bob
Person
? contains
? capacity
?2 contains
Not Alone
Interior Room
Manager
Number Restriction
Indoor Context
User Profile Ontology
Spatial Context
Local Context
Spatial Ontology
IS-A
Subsumption role
Local Context
x
Role with semantics x ??,?
Contextual Information
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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, (aß0.5)
• Important Notice (a ?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

Common concept
D
E
M
F
Common parents!
Conceptual Taxonomy H
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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.
B
K
grand(parent)
DF
CF
parent
h
E
TSD
C
D
CF ? ?DF
Conceptual Taxonomy H
Position (h) in the taxonomy of the application
of the disjoint axiom
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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
D1
R
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
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Pure Similarity
Pure Similarity (Asserted knowledge in T-Box
from expert)
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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 and S?T Concepts A?E and B?E
?.T
Q
E
Virtual
?.T
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!
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
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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)

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• Reasoning about Situational Similarity

Reasoning Process over Incompatible/Compatible
Situations(?S,Sa)  Input Sa list of situations
related to ?S Output Sc list of compatible
situations Set SMAXargmaxsim(?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
If End 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-MAXargmaxsim(?S,Si) / Si ?
HC, HC? HMAX / Sc Sc
?SC-MAX End If End For Return Sc
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• Behavior of the Similarity Measure

Most similar situation Smax argmaxaffinity(Q,S
i), ?Si ?H
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• 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

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Thank you!
Christos B. Anagnostopoulos bleu_at_di.uoa.gr Perva
sive Computing Research Group http//p-comp.di.uo
a.gr
IEEE IS 2006_at_London