Reasoning about Situation Similarity

C. Anagnostopoulos, Y. Ntarladimas, S. Hadjiefthymiades

Pervasive Computing Research GroupCommunication Networks Laboratory

Department Informatics and TelecommunicationsUniversity of Athens – Greece

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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

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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 {bleu@di.uoa.gr}Pervasive Computing Research Group {http://p-comp.di.uoa.gr}

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