Change: Class Inclusion and Equivalence

created on March 9, 2013, 8:22 p.m. by Hevok & updated on March 9, 2013, 8:22 p.m. by Hevok

When one constructs a Knowledge Base one has to define Classes. One does this with help of Class Inclusion and Class Equivalence.

In a Class Inclusion one says that one Class is Subclass of another Class. Here it meas the the Professor class is a Subclass of Faculty Member. One can also describe this with an Equal Expression in First Order Logic, which states for all Variables X it holds that if X a Professor, then X is also a Faculty Member.

Alternatively one can have a Class Equivalence as the Professor might be equivalent to a Faculty Member which equals the first Order Logic that uses and universal Quantifier and equivalence, instead of Implication. This both methods are quite the same.

• Class Inclusion
  • Professor ⊑ FacultyMember
    • every Professor is a Faculty Member
    • equals (∀x)(Professor(x) → Faculty Member
• Class Equivalence
  • Professor ≡ FacultyMember
    • the Factuality Members are exactly the Professors
    • equals (x)(∀x)(Professor(x) <-> FacultyMember

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