OWL - DL

1. OWL - DL

2. DL System • A knowledge base (KB) comprises two components, • the TBox and the ABox • The TBox introduces the terminology, i.e., the vocabulary of an application domain, • The ABox contains assertions about named individuals in terms of this vocabulary.

3. vocabulary • The vocabulary consists of • concepts, which denote sets of individuals, • and roles, which denote binary relationships between individuals. • DL systems allow their users to build complex descriptions of concepts and roles by using atomic concepts and roles • The TBox can be used to assign names to complex descriptions.

4. A DL System

5. Another representation..

6. Description Language • Elementary descriptions are atomic concepts and atomic roles • Complex descriptions can be built from them inductively with concept constructors • we use the letters A and B for atomic concepts • the letter R for atomic roles, • and the letters C and D for concept descriptions

8. Examples

9. Disjoint • Animal ∏ plant =  • Or • Plant ⊑ animal

10. subsumtion • Tree ⊑ plant

11. All values from • Branch ⊑ Is_part_of.tree

12. All values from • leaf ⊑ Is_part_of.branch

13. All values from, role union • Herbivors=animals ∏eats.(plant U is_part_of.plant )

14. Some values from • Carnivore = animal ∏  eats.animal

15. giraffe = herbivores ∏  eats.leaf

16. Lion=carnivore ∏  eats.herbivore

17. Tasty_plant = plant ∏  eaten_by.herbivore ∏  eaten_by.carnivore)

18. Back to DL

19. Suppose that Person and Female are atomic concepts • those persons that are female • Those that are not female • suppose that hasChild is an atomic role, • those persons that have a child • those persons all of whose children are female • those persons without a child

21. there is a set of objects that are Trees and a binary relation has-branch between objects that leads from a tree to its subtrees. Then the binary trees are the trees with at most two subtrees that are themselves binary trees:

22. A world description (ABox).

23. One sort of reasoning • The simplest form of reasoning involves computing the subsumption relation between two concept expressions, • i.e., verifying whether one expression always denotes a subset of the objects denoted by another expression. • Parent is a specialization of Person, i.e., Person subsumes Parent A B

24. Another sort of reasoning • A more complex reasoning task consists in checking whether a certain assertion is logically implied by a knowledge base. • For example, Bill is an instance of Parent.

26. Expansion of the family T-Box

28. ABox

29. Owl-DL Constructs

30. Owl-DL Axioms

31. Reasoning

32. Inference

34. DL Inferences

35. Structural Subsumption • Normalize descriptions • Compare syntactical structure of normal forms

36. Structural Subsumption

37. Structural Subsumption

38. Example: Structural Subsumption

39. More expressive DLs

41. Negation Normal Form (NNF) Example

42. Tableau inferencing

43. Tableau

44. Transformation rules • Example

45. Example - Tableau Proof

46. Mad Cow Example