1. Information-Flow-based Ontology Mapping Yannis Kalfoglou, University of Southampton Marco Schorlemmer, University of Edinburgh

2. Semantic Web Need the ability to automatically MAP ontologies in the same domain MAP ontologies in the same domain MAP ontologies in different domains that overlap MAP ontologies in different domains that overlap MERGE ontologies once they are mapped MERGE ontologies once they are mapped

3. MAPPING BARRIERS No public technical details available Present systems are so diverse and un- interoperable Mapping systems embedded in these diverse systems Previous mapping based on syntactical clues instead of semantics Lack theory, axioms, and rules

4. PURPOSE Build mathematics and an algorithm to semi-automatically MAP ontologies in RDF

5. OUTLINE Architectural overview Mathematical definitions and proposition IF-map example Basic mapping algorithm Final results Summary My Assessment

6. Architectural Overview

7. IF-map (Information-Flow-Based)

8. Mathematical Definitions and Proposition DEFINITIONS Local Logic Local Logic Logic Infomorphism Logic Infomorphism Ontology Ontology Populated Ontology Populated Ontology Ontology Morphism Ontology Morphism PROPOSITION - Deriving an Ontology Morphism relationship from a REFERENCE (unpopulated ontology) to a LOCAL (populated ontology)

9. LOCAL LOGIC TYPEvehiclecar INSTANCECabrioCoupe

10. SYMBOLS T- type, I-instance Δ - set of types - disjunctively Γ - set of types - conjunctively Set of Sequents (Γ,Δ) [every type, some type]

11. LOGIC INFOMORPHISM (f) links 2 local logics (L, L`) f * (Coupe) |= car f * (Cabrio) |= vehicle

12. ONTOLOGY (O)

13. Populated Ontology (Ỗ) (Local ontology is populated with instances x, classifications c & d, and relations r)

14. ONTOLOGY MORPHISM mapping the change Unpopulated to Populated

15. MAPPING Architecture

16. ONTOLOGY MORPHISM REFERENCE ONTOLOGY (unpop) to LOCAL ONTOLOGY (pop)

17. IF-Map Example REFERENCE ONTOLOGY unpopulated

18. LOCAL ONTOLOGIES

19. CONSTRAINTS to LOGIC INFORMORPHISMS

20. Relate and Map

21. Relationships between types REFERENCE - LOCAL

22. Completes ONE MAPPING f*(car) = automobile (a) arity (b) Infomorphism (c) complete

23. Basic Mapping Algorithm

24. Algorithm in Example Match types (MANUALLY?) REFERENCE - building REFERENCE - building LOCAL - house, cottage LOCAL - house, cottage Do argument types match semantically? If YES – partial map If NO – use ISA hierarchy and check parents and children and list relations which might be merged

25. FINAL RESULTS (RDF)

26. SUMMARY Formalized definitions, mapping, & linking Ontology Ontology Ontology morphism Ontology morphism Logic Infomorphism Logic InfomorphismFUTURE Ontology Merging Ontology Merging Ontology Axioms Ontology Axioms Reasoning about Ontology Evolution Reasoning about Ontology Evolution

27. My Assessment Example – semantic problem between British English and American English (cottage and house) Purpose of the paper changed from the beginning to the end – WEAK EVALUATION Study of 5 CS Dept in the UK Study of 5 CS Dept in the UK Mathematics and algorithm Mathematics and algorithm Hard to tell where Channel Theory left off and their Information Flow Theory began RDF – Missing technical details of change during the IF- map