Formal Syntax

Created on March 9, 2013, 8:40 p.m. by Hevok & updated by Hevok on May 2, 2013, 5:31 p.m.

The formal definition of Attribute Language with Complement (ALC) allows that complex Classes to be constructed. There can be an Atomic Class, the upper or Lower Class, the can be a Negation complex Class, they can be the Conjunction or Disjunction of complex Classes or Roles in Combination with complex Classes ad existential or universal Quantification.

To put it all together one can form a TBox with the transactional Knowledge which contains all Assertions of the form of Class Inclusion or Class Equivalence where C and D are complex Classes. This is the Terminological Knowledge.

The ABox contains Assertions that certain Individuals belong to specific Classes and other Individuals are connected via specific Roles or Properties.

Both TBox and ABox form an ALC Knowledge Base

  • Production Rules for Creating Classes in ALC: (A is an Atomic Class, C and D are complex Classes and R is a Role)
  • C,D::== A|⊤|⊥|¬C|C⊓D|C⊔D|∃R.C|∀R.C
  • An ALC TBox contains Assertions of the form C ⊑ D and C ≡ D, where C, D are complex Classes.
  • An ALC **Aboxcontains Assertions of the formC(a)andR(a,b)``, where C is a complex Class, R a Role and a,b Individuals.
  • An ALC-**Knowledge Base contains an ABox and a TBox.

Tags: classes, knowledge, logic
Categories: Concept
Parent: Attribute Language with Complement

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