1 Contextualization: an Abstraction Mechanism for Conceptual Modeling Joint work by: Manos Theodorakis Anastasia Analyti Nicolas Spyratos Panos Constantopoulos Institute of Computer Science FORTH-ICS Greece

FORTH-ICS2 Outline Why we need contexts Context definition Structuring the contents of a context Formal Theory Operations on contexts Applications Future Work Conclusions

FORTH-ICS3 Different Perceptions Ontology of mechanic for house Ontology of family for house

FORTH-ICS4 Other examples of context Distributed databases  Travel agencies  Anatomical map Natural language  Ambiguity resolution Organization of large databases

FORTH-ICS5 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-ICS6 Contextual Ontologies Organize in a single framework, several contextual representations Reasoning based on contextual representations

FORTH-ICS7 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 oobject o reference of o (another context)......

FORTH-ICS8 Example  Context-dependent naming, referencing  Viewing the information from different viewpoints  Viewing information at different level of detail  Support for synonyms, homonyms  Object Sharing c2c2 c1c1 Crete, Kriti : o 3 Map : o 4 Geography : o 2 c3c3 Transportation : o 10 Hotels : o 9 c9c9 c 10 c6c6 c8c8 Cities : o 15 Mountains: o 14 c 14 c 15 History : o 16 Tourist Guide : o 1 Athens, Athina : o 5 Crete : o 3 Map : o 7 Attiki : o 6 c5c5 Dining : o 8 c8c8 Greeece : o 0 c0c0

FORTH-ICS9 Structuring the contents of a context attr(attr_obj,from,to) in(in_obj,from,to) isa(isa_obj,from,to) 15 th century : o 2 c1c1 20 th century: o 3 Crete : o 4 c3c3 City : o 6 c4c4 Village: o 7 Chandax : o 8 Fortification : o 9 A : o 10 City : o 6 c5c5 Village: o 7 Heraklion : o 8 Airport : o 13 B : o 12 : o 11 : o 14 A : o 10 Crete : o 4 c2c in

FORTH-ICS10 Attribution - Contextualization c4c4 Persons : o 2 c1c1 Places: o 3 related to : o 4 c2c2 Person : o 2 Employee : o 7 Student : o 6 c3c3 Place : o 3 Domestic Location : o 7 Foreign Country : o 6 born in : o 11 Company : o 13 works for : o 12 Integer : o 15 no of years : o 16 located in : o 14 Demographic Data : o 1 isa

FORTH-ICS11 Generalization - Contextualization c0c0 Organization : o 1 Hospital : o 2 c' Employee : o 3 String: o 7 name : o 6 c Employee : o 3 String: o 7 name : o 6 Department: o 9 has dep : o 6 Doctor : o 4 Nurse : o 5 isa Refinement Relation

FORTH-ICS12 Classification - Contextualization cdcd Schema 1 : o 1 Instance 1 : o... c1c1 c in c Instance 2 : o 4 Schema 2 : o 2  The same set of objects can be classified under different schemas  Several set of objects can be classified under the same schema in

FORTH-ICS13 Context theory Formal definitions Model theory Set of sound & complete inference rules.

FORTH-ICS14 Formal Definitions Contents of a context: cnts(c) Basic Sets O : set of Objects CXT : set of Contexts N : set of Names Reference Paths RP c : set of reference paths starting from the objects of c Contextualized IB

FORTH-ICS15 Predicates - Functions Predicates Functions

FORTH-ICS16 Inference System 1. ISA Reflexivity: 2. ISA Transitivity: 3. Context Refinement: 4. Refinement Reflexivity: 5. Refinement Transitivity: 6. Instance Upward Inheritance:

FORTH-ICS17 Inference System 8. Interaction between Generalization-Contextualization: 9. Interaction between Classification-Generalization-Contextualization: 7. Inheritance of Built-in Information:

FORTH-ICS18 Refinement, Equivalence Relations Refinement Relation Equivalence Relation

FORTH-ICS19 Operations for Creating and Maintaining Contexts CreateCxt( ) insert( o, N, c ) deleteObj( o, c ) deleteName( o, n, c ) copyCxt( c ) deepCopyCxt( c ) Union Intersection Difference

FORTH-ICS20 Context Union c5c5 Dinos: o 1 Head: o 2 Nick, Nikos: o 4 Dinos, Xulouris: o 1 InfSys: o 10 DSS: o 20 InfSys DSS Head: o 2 Nick, Nikos: o 4 Dinos: o 6 c4c4 InfSys : o 10 DSS : o 20 c5c5 Xilouris: o 1 Head: o 2 Dinos: o 6 c4c4

FORTH-ICS21 Context Intersection c/5c/5 Dinos: o 1 Head: o 2 c/4c/4 Xilouris: o 1 Head: o 2 InfSys DSS Dinos, Xilouris: o 1 InfSys: o 10 DSS: o 20 Head: o 2 InfSys : o 10 DSS : o 20 c5c5 Dinos: o 1 Head: o 2 Nick, Nikos: o 4 Xilouris: o 1 Head: o 2 Dinos : o 6 c4c4

FORTH-ICS22 Context Difference c4c4... Manos View : o 1 c1c1 Dr_Xilouris: o 1 : o 4 InfSys : o 10 DSS : o 20 Nicolas View : o 2 c2c2 Dinos: o 1 InfSys : o 10 AVG : o 21 c6c6... Manos View  Nicolas View c' 5 Nick, Nikos: o 4 : o 4 Manos View : o 1 DSS : o 20 c5c5 Dinos: o 1 Head: o 2 Nick, Nikos: o 4 c4c4... InfSys : o 10 c' 1 DSS : o 20 InfSys : o 10 : o 4

FORTH-ICS23 Commutativity: Associativity: Distributivity: (A B) C = (A C) (B C) (A B) C = A (B C) A B = B A Properties of and

FORTH-ICS24 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 : o 1 c1c1 A: o 2 : o 3 D : o 4 E: o 5 A : o 1 c2c2 G: o 3 C: o 6 B : o 1 c3c3 C: o 2 A: o 6 Theorem: Closure of well-definedness under Union, Intersection and Difference

FORTH-ICS25 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-ICS26 Applications (cont.) Pervasive computing Agent context Redefined contexts of agent situations Central Manager  Collects Agent Contexts  Reasons about them  Maintains consistency

FORTH-ICS27 Future Work Extension of the web ontology languages RDF and OWL with contexts Querying and reasoning with:  contextualized RDF  contextualized OWL

FORTH-ICS28 Conclusions A formal notion of context in information modeling  Formal definition  Core axioms  Operations Supported features  Partial views  Relative semantics  Modular design

FORTH-ICS29 Thank you!