Jing Mei, Harold Boley

1
A Tutorial Summary ofDescription
LogicandHybrid Rules

• Jing Mei, Harold Boley
• October, 2005

2
Description Logics
d
R(a,d)

• DL Family of (decidable) sublanguages of
  First-Order Logic
• Concept
• Atomic concepts C, C1, C2, D
• Boolean combinations negation, intersection,
  union
• Restrictions existential, universal, number
  qualifications
• Role
• Atomic roles R, S
• Property transitive, symmetric, functional,
  inverse-functional
• Axiom
• TBox subsumption
• ABox assertion

e
R(a,e)
a
R(a,b)
b
3
Rules

• Language
• term constant, variable, function symbol
• atom predicate symbol applied to terms
• literal atom negative atom
• extended literal literal negation as failure
  literal
• Head ? Body
• Without function symbols in atoms H and Bi
• Datalog H ? B1 ? ? Bm
• Datalog? H1 ? ? Hn ? B1 ? ? Bm
• Datalog?? H1 ? ? Hn ? naf B1 ? ? naf
  Bm
• With function symbols in atoms H and Bi
• Horn programs H ? B1 ? ? Bm
• Normal programs H ? naf B1 ? ? naf Bm
• Extended programs H1 ? ? Hn ? nafneg
  B1 ? ? nafneg Bm

4
Hybrid Knowledge Base

• Hybrid KB K (S, R)
• S a finite set of DL axioms in the ontology
  language
• R a finite set of hybrid rules
• Hybrid RulesH ? B1 ? ? Bm Q1 ? ? Qn
• H, Bi are ordinary atoms for rules
• Qj are queries to the DL component S