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Contextualization:an Abstraction Mechanism for
Conceptual ModelingJoint work by: Manos Theodorakis
Anastasia Analyti
Nicolas Spyratos
Panos Constantopoulos
Institute of Computer Science
FORTH-ICS
Greece
FORTH-ICS 2
Outline
Why we need contexts Context definition Structuring the contents of a context Formal Theory Operations on contexts Applications Future Work Conclusions
FORTH-ICS 3
Different Perceptions
Different Perceptions
Ontology of mechanicfor house
Ontology of familyfor house
FORTH-ICS 4
Other examples of context
Distributed databases Travel agencies Anatomical map
Natural language Ambiguity resolution
Organization of large databases
FORTH-ICS 5
Context features
Viewing the information from different viewpoints
Support for context-dependent meaning
Viewing information at different levels of detail
Modular design
context-dependent reachability
Support for synonyms, homonyms
FORTH-ICS 6
Contextual Ontologies
Organize in a single framework,
several contextual representations
Reasoning based on contextual representations
FORTH-ICS 7
Our Definition of Context
A context is a set of objects, in which each object is associated with a set of names and (possibly) a reference to an other context.
Context
names of o object o reference of o(another context).
.
.
FORTH-ICS 8
Example
Context-dependent naming, referencing Viewing the information from different viewpoints Viewing information at different level of detail
Support for synonyms, homonyms Object Sharing
c2
c1
Crete, Kriti: o3
Map: o4Geography: o2
c3
Geography: o2
Transportation: o10
Hotels: o9 c9
c10
c6
c8
Cities: o15
Mountains: o14 c14c15
History: o16Tourist Guide: o1
Athens, Athina: o5
Crete: o3
Map: o7
Attiki: o6
c5
Dining: o8 c8
Greeece: o0
c0
FORTH-ICS 9
Structuring the contents of a context attr(attr_obj,from,to) in(in_obj,from,to) isa(isa_obj,from,to)
15th century: o2
c1
20th century: o3
Crete: o4
c3
City: o6
c4
Village: o7
Chandax: o8
Fortification: o9
A: o10
City: o6
c5
Village: o7
Heraklion: o8
Airport: o13
B: o12
: o11
: o14A: o10
Crete: o4
c2
...
...
in
FORTH-ICS 10
Attribution - Contextualization
c4
Persons: o2
c1
Places: o3
related to: o4
c2
Person: o2
Employee: o7
Student: o6
c3
Place: o3
Domestic Location: o7
Foreign Country: o6
born in: o11
Company: o13
works for: o12
Integer: o15
no of years: o16
located in: o14
Demographic Data: o1
isa
FORTH-ICS 11
Generalization - Contextualizationc0
Organization: o1
Hospital: o2
c'Employee: o3
String: o7
name: o6
cEmployee: o3
String: o7
name: o6
Department: o9
has dep: o6
Doctor: o4 Nurse: o5
isa
Refinement Relation
FORTH-ICS 12
Classification - Contextualization
cd
Schema 1: o1
Instance 1: o
. . .c1
. . . . . .
cin
cInstance 2: o4
Schema 2: o2
The same set of objects can be classified under different schemas Several set of objects can be classified under the same schema
in
FORTH-ICS 13
Context theory
Formal definitions
Model theory
Set of sound & complete inference rules.
FORTH-ICS 14
Formal Definitions
Contents of a context: cnts(c)
Basic SetsO : set of ObjectsCXT : set of ContextsN : set of Names
Reference PathsRPc : set of reference paths starting
from the objects of c
))((to))((from)(,.7,)(|,,)(.6
,)(|,,)(.5,)(|,,)(.4
)(:)()()(:)(.2
)()(.1
tftf
ctftf
ctftf
ctftf
oclexoclexcobjsooppcobjsoppocattrppcobjsoppocisappcobjsoppocin
cobjscrfcobjsclex
cobjs
RPRP
RPCXT3.
NPNP
Contextualized IBcnts,,, NCXTO
FORTH-ICS 15
Predicates - FunctionsPredicates
Functions
'refines'.5),,(),,(),,(,)(.4
)(,,),,(.3)(,,),,(.2
)(,,),,(.1
:
ccccppoAttrppoIsappoInppoIsLink
cattrppoppoAttrcisappoppoIsacinppoppoIn
tfctfctfctfc
tftfc
tftfc
tftfc
)(:.4:.3:.2:.1
NPRPCXTRP
RPRP
cc
cc
cc
cc
NamesRefToFrom
OO
FORTH-ICS 16
Inference System1. ISA Reflexivity: ),,( ppoIsac
2. ISA Transitivity: ),,(),,(),,( 313322211 ppoIsappoIsappoIsa ccc 3. Context Refinement:
1111'
'
')(')(')()()()('
)'()(')'()('
)'()('
cccoRefcoRefccoNamesoNamescobjsocobjsocc
cattrcattrcccisacisacc
cincincc
cc
cc
4. Refinement Reflexivity: cc 5. Refinement Transitivity: 313221 cccccc 6. Instance Upward Inheritance:
),,(),,(),,( 313322211 ppoInppoIsappoIn ccc
FORTH-ICS 17
Inference System
8. Interaction between Generalization-Contextualization:
21221121 )()(),,( ccpRefcpRefcppoIsa ccc
9. Interaction between Classification-Generalization-Contextualization:
212211
21
)()()'',,()'',',()',,(
ccoRefcoRefcppoInppoIsappoIn
cc
ccc
7. Inheritance of Built-in Information: nullCc
FORTH-ICS 18
Refinement, Equivalence Relations
)))',(),()',((),()',(:)'((
)()'()()'(
)()'()()'('
corefcorefnilcorefconamesconamescobjso
cisacisacincincattrcattrcobjscobjscc
Refinement Relation
)))',(~),())',(),(((
)',(),(:)(()'()(
)'()()'()()'()('~
corefcorefnilcorefnilcoref
conamesconamescobjsocisacisa
cincincattrcattrcobjscobjscc
Equivalence Relation
FORTH-ICS 19
Operations for Creating and Maintaining Contexts
CreateCxt(<contents>) insert( o, N, c ) deleteObj( o, c ) deleteName( o, n, c ) copyCxt( c ) deepCopyCxt( c )
Union Intersection Difference
20FORTH-ICS
Context Union
c5
Dinos: o1Head: o2
Nick, Nikos: o4
Dinos, Xulouris: o1
InfSys: o10
DSS: o20
InfSys DSS
Head: o2
Nick, Nikos: o4Dinos: o6
c4
InfSys: o10
DSS: o20 c5
Xilouris: o1
Head: o2
Dinos: o6
c4
FORTH-ICS 21
Context Intersection
c/5
Dinos: o1Head: o2
c/4
Xilouris: o1
Head: o2
InfSys DSS
Dinos,Xilouris: o1
InfSys: o10
DSS: o20
Head: o2
InfSys: o10
DSS: o20
c5
Dinos: o1Head: o2
Nick, Nikos: o4
Xilouris: o1
Head: o2
Dinos : o6
c4
22FORTH-ICS
Context Differencec4
. . .
Manos View: o1c1
Dr_Xilouris: o1
: o4
InfSys: o10
DSS: o20
Nicolas View: o2 c2
Dinos: o1
InfSys: o10
AVG: o21
c6. . .
Manos View Nicolas View
c'5Nick, Nikos: o4
: o4
Manos View: o1
DSS: o20
c5
Dinos: o1Head: o2
Nick, Nikos: o4
c4. . .
InfSys: o10 c'1
DSS: o20InfSys: o10
: o4
23FORTH-ICS
Commutativity:
Associativity:
Distributivity: (A B) C = (A C) (B C)(A B) C = (A C) (B C)
(A B) C = A (B C)(A B) C = A (B C)
A B = B AA B = B A
Properties of and
FORTH-ICS 24
Constraint: Well-definedness
A context is called Well-defined iff:• There is a name path that uniquely identifies each object recursively contained in the context• Acyclicity
A, B: o1c1
A: o2
: o3
D: o4
E: o5
A: o1c2
G: o3
C: o6
B: o1c3
C: o2
A: o6
Theorem: Closure of well-definedness under Union, Intersection and Difference
FORTH-ICS 25
Applications Partial View Support
Different people have different views of the same resources
Different applications have different (goal-oriented) models of the same resources
Cooperative work Workspaces: Private, Group, Public
Ontology Integration/Merging
Web search Modelling of user interests/Reply based on query context
FORTH-ICS 26
Applications (cont.)Pervasive computing
Agent context
Redefined contexts of agent situations
Central Manager
Collects Agent Contexts Reasons about them Maintains consistency
FORTH-ICS 27
Future Work
Extension of the web ontology languages RDF and OWL with contexts
Querying and reasoning with: contextualized RDF contextualized OWL
FORTH-ICS 28
Conclusions
A formal notion of context in information modeling
Formal definition Core axioms Operations
Supported features Partial views Relative semantics Modular design
FORTH-ICS 29
Thank you!