The Knowledge Cartography – A New Approach to Reasoning over Description Logics Ontologies

1. The Knowledge Cartography –A New Approach to Reasoning over Description Logics Ontologies Krzysztof Goczyła, Teresa Grabowska, Wojciech Waloszek, Michał Zawadzki January 21-27, 2006, Měřín, Czech Republic

2. PIPS Upper layers Knowledge KMS KaSeA KaSeA RDB RDB Data Internet

3. Motivations • PIPS manages knowledge about: • ilnesses, • drugs, • alergies, • diets, • … • Required data are gathered from many internet sources; the number of information is very large.

4. Knowledge Cartography • Main assumptions: • Terminology is updated so rarely that it might be considered constant in time. • A knowledge base is queried much more often than updated (new individual assertions). • A knowledge base should be able to hold and efficiently process information about large numbers of individuals.

5. Knowledge Cartography • Developed to: • simplify reasoning on numerous objects (individuals), • simplify storage of inferred results concerning numerous individuals. • Processes ontological information in accordance to Description Logics and Semantic Web standard.

6. Terminology – an example • Terminology is described by a set of statements - axioms. • Suppose, we want to describe the world of people and their pets: • There are no other creatures except People, Dogs and Cats, • People, Dogs and Cats are disjoint, • Dogs and Cats are CreaturesHavingTails, • People and Cats can be CreaturesTakingCareOfHygiene.

7. Map of concepts There are no other creatures except People, Dogs and Cats People  Dogs  Cats 

8. Map of concepts People, Dogs and Cats are disjoint People  Dogs  People  Cats  Cats  Dogs 

9. Map of concepts Dogs and Cats are CreaturesHavingTails CreaturesHavingTails  Dogs  Cats

10. Map of concepts People and Cats can be CreaturesTakingCareOfHygiene CreaturesTakingCareOfHygiene  People CreaturesTakingCareOfHygiene  Cats

11. Map of concepts

12. 1 2 3 5 4 Map of concepts – signatures 11000 01000  00001 00010  00111 11111 

13. Terminological queries Must every person take care of hygenie? 11000 NO 10011 Is a creature without a tail a person? 11000 YES 11000 Is a creature which have a tail and takes care of hygenie a cat? 00100  YES 00110

14. Individuals’ signatures • Individuals’ signatures describe what we know and what we do not know about individuals Source 1: Fred has a tail 00111 Is Fred a person? 00111 NO 11000 Is Fred a dog? 00111 MAYBE 00001

15. We know something more… Source 2: Fred takes care of hygenie 00111 01100 , 00100 Is Fred a dog? 00100 NO 00001 Is Fred a cat? 00100 YES 00110

16. Restrictions • Role constructors in the form of R.C and R.C are treated as concepts • Such constructors must be explicitly defined in ontology.

17. Deployment in PIPS • Cartographic approach has been succesfully deployed in the first release of PIPS system, • Allowed for achieving short (<1 s) response times for queries in knowledge bases with very large (>10000) number of individuals (sublinear scalability).

18. Future work • Compression of signatures and hierarchical signatures, • Introducing signatures not only for concepts but also for roles (relations) between individuals. • Extending expresiveness of KaSeA in order to support complex queries (cardinality constraints, functional, symetric and transitive roles),

19. Thank you!