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Jarrar.lecture notes.aai.2011s.descriptionlogic
1. Dr. Mustafa Jarrar [email_address] www.jarrar.info University of Birzeit Description Logic (and business rules) Advanced Artificial Intelligence (SCOM7341) Lecture Notes, Advanced Artificial Intelligence (SCOM7341) University of Birzeit 2 nd Semester, 2011
2. Reading Material D. Nardi, R. J. Brachman. An Introduction to Description Logics . In the Description Logic Handbook, edited by F. Baader, D. Calvanese, D.L. McGuinness, D. Nardi, P.F. Patel-Schneider, Cambridge University Press, 2002, pages 5-44. http://www.inf.unibz.it/~franconi/dl/course/dlhb/dlhb-01.pdf Only Sections 2.1 and 2.2 are required (= the first 32 pages)
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7. Description logic ALC (Syntax and Semantic) Woman ⊑ Person ⊓ Female Parent ⊑ Person ⊓ hasChild. ⊤ Man ⊑ Person ⊓ Female NotParent ⊑ Person ⊓ hasChild. ⊥ Examples: Constructor Syntax Semantics Primitive concept A A I I Primitive role R R I I I Top ⊤ I Bottom ⊥ Complement C I C I Conjunction C ⊓ D C I D I Disjunction C ⊔ D C I D I Universal quantifier R.C { x | y . R I ( x , y ) C I ( y )} Extensional quantifier R.C { x | y . R I ( x , y ) C I ( y )}
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19. Some extensions of ALC Constructor Syntax Semantics Primitive concept A A I I Primitive role R R I I I Top ⊤ I Bottom ⊥ Complement C I C I Conjunction C ⊓ D C I D I Disjunction C ⊔ D C I D I Universal quantifier R.C { x | y . R I ( x , y ) C I ( y )} Extensional quantifier R.C { x | y . R I ( x , y ) C I ( y )}
20. Some extensions of ALC Constructor Syntax Semantics Primitive concept A A I I Primitive role R R I I I Top ⊤ I Bottom ⊥ Complement C I C I Conjunction C ⊓ D C I D I Disjunction C ⊔ D C I D I Universal quantifier R.C { x | y . R I ( x , y ) C I ( y )} Extensional quantifier R.C { x | y . R I ( x , y ) C I ( y )} Cardinality ( N ) ≥ n R { x | #{ y | R I ( x , y ) } ≥ n } ≤ n R { x | #{ y | R I ( x , y ) } ≥ n } Qual. cardinality ( Q ) ≥ n R.C { x | #{ y | R I ( x , y ) C I ( y )} ≥ n } ≤ n R.C { x | #{ y | R I ( x , y ) C I ( y )} ≥ n } Enumeration ( O ) { a 1 … a n } { a I 1 … a I n } Selection ( F ) f : C { x Dom( f I ) | C I ( f I ( x ))}
36. UML Class diagram (with a contradiction and an implication) Student ⊑ Person PhDStudent ⊑ Person Employee ⊑ Person PhD Student ⊑ Student ⊓ Employee Student ⊓ Employee ≐ ⊥ {disjoint} Person Student Employee PhD Student
37. Infinite Domain: the democratic company [Franconi 2007] Supervisor ⊑ =2 Supervises.Employee Employee ⊑ Supervisor Supervises 2..2 0..1 implies “ the classes Employee and Supervisor necessarily contain an infinite number of instances”. Since legal world descriptions are finite possible worlds satisfying the constraints imposed by the conceptual schema, the schema is inconsistent . Supervisor Employee
38. Example (in UML, EER and ORM) Employee Project WorksFor TopManager Manages Employee Project WorksFor Manages 1..1 1..1 TopManger WorksFor Manages Project TopManger Employee 1..1 1..1