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OWL - DL

OWL - DL. 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. vocabulary.

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OWL - DL

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  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

  7. Examples

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

  9. subsumtion • Tree ⊑ plant

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

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

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

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

  14. giraffe = herbivores ∏  eats.leaf

  15. Lion=carnivore ∏  eats.herbivore

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

  17. Back to DL

  18. 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

  19. 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:

  20. A world description (ABox).

  21. 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

  22. 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.

  23. Expansion of the family T-Box

  24. ABox

  25. Owl-DL Constructs

  26. Owl-DL Axioms

  27. Reasoning

  28. Inference

  29. DL Inferences

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

  31. Structural Subsumption

  32. Structural Subsumption

  33. Example: Structural Subsumption

  34. More expressive DLs

  35. Negation Normal Form (NNF) Example

  36. Tableau inferencing

  37. Tableau

  38. Transformation rules • Example

  39. Example - Tableau Proof

  40. Mad Cow Example

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