Description logic

1. Description logic • Logic-based formalisms • evolved out of the intuition of that predicate calculus could be used to unambiguously capture fact about the world • Non-logic-based representations • built on more cognitive notions like network structures and rule-based representations derived from experiment on recall from the human memory and human execution of tasks like mathematical puzzles solving

2. Description logic • A family of knowledge representation languages • Can be used to represent the terminological knowledge of a domain of interest in a structured and formally well-understood way • The name description logic refers to: • concept descriptions used to describe a domain • logic-based semantics which can be given by a translation into first-order predicate logic

3. Description Logic • Consists of “concepts” and “terminology”. • Concepts refer to the expression of a DL language • Terminology denotes a hierarchical structure built to provide a representation of the domain of interest.

4. Description Logic • Intensional knowledge • General knowledge about a problem domain • The TBox, which contains intensional knowledge in the form of a terminology, and is built through declarations that describe general properties of concepts • Extensional knowledge • Specific knowledge to a particular problem • The ABox contains extensional knowledge which is knowledge that is specific to the individuals of the domain of discourse

5. TBox • The basic form of declaration in a TBox is a concept definition. This is the definition of a new concept in terms of other previously defined concepts. • Woman ≡ Person ∩ Female • This means that Woman is defined as a female person

6. Abox • The ABox contains extensional knowledge about the domain of interest. This is assertions about individuals, usually called membership assertions • Female ∩ Person (ANNA) • This state that ANNA is a female person. Given the definition of a woman one can derive that ANNA is an instance of the concept Woman

7. Brachman’s levels • Conseptual Level • Actual primitives in the representation • Constants • Person • Female • Male • Ect. • Relationship • Roles

8. Brachman’s levels • Epistemological Level • Types of knowledge representation primitives • Predicates describing a taxonomy of concepts • Cat (Pet) • Mother (Female, Parent) • Predicates describing properties of concepts • Child (hasPet) • Parent (Person, hasPersonChild) • Parent (Cat, hasCatChild)

9. Brachman’s levels • Logical properties • Syntax • Constants, predicates and roles • (defconcept Person) • (defconcept Woman (and Female Person)) • (defprimrole hasPersonChild) • Semantics • Conserns the meaning of symbols • Realised through a set of algorithms-the inferense engine(FaCT) • Woman (and Female Person) means that a woman is a female person • The inferense engine infers implicit knowledge • Inferential point of view • If all the information stored in the knowledge base is true then the inferred information is true as well

10. Brachman’s levels • Implementational Level • Conserns how the representation is implemented • FaCT has a Tell/Ask interface • Knowledge base is implemented in XML for sending/receiving data between client/server in FaCT • Tree structure and inheritanse(graph??)

11. Concept

12. Implementation <DEFCONCEPT NAME=”Female”> <DEFCONCEPT NAME=”Person”> <DEFCONCEPT NAME=”Woman”>

13. Implementation <DEFCONCEPT NAME=”Female”> <DEFCONCEPT NAME=”Person”> <DEFCONCEPT NAME=”Woman”> <EQUALC> <CONCEPT> <PRIMITIVE NAME="Woman"/> </CONCEPT> <CONCEPT> <AND> <PRIMITIVE NAME="Female"/> <PRIMITIVE NAME="Person"/> </AND> </CONCEPT> </EQUALC>

14. TBox • The basic form of declaration in a TBox is a concept definition. This is the definition of a new concept in terms of other previously defined concepts. • Woman ≡ Person ∩ Female • This means that Woman is defined as a female person

15. FaCT's interpretion

16. Concept