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

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