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
• 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.
A DL System
Another representation..
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
Examples
Disjoint
• Animal ∏ plant = • Or
• Plant ⊑ animal
subsumtion
• Tree ⊑ plant
All values from
• Branch ⊑ Is_part_of.tree
All values from
• leaf ⊑ Is_part_of.branch
All values from, role union
• Herbivors=animals ∏ eats.(plant U is_part_of.plant )
Some values from
• Carnivore = animal ∏ eats.animal
• giraffe = herbivores ∏ eats.leaf
• Lion=carnivore ∏ eats.herbivore
Tasty_plant = plant ∏ eaten_by.herbivore ∏ eaten_by.carnivore)
Back to DL
• 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
• 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:
• A world description (ABox).
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
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.
Expansion of the family T-Box
ABox
Owl-DL Constructs
Owl-DL Axioms
Reasoning
Inference
DL Inferences
Structural Subsumption
• Normalize descriptions• Compare syntactical structure of normal
forms
Structural Subsumption
Structural Subsumption
Example: Structural Subsumption
More expressive DLs
Negation Normal Form (NNF)
Example
Tableau inferencing
Tableau
Transformation rules
• Example
Example - Tableau Proof
Mad Cow Example
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