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.

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