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COS4840 - Ontology Engineering

Description Logics

Description logics area subset of a function free FOL with no variables.

Three entities:

  • Concepts names - entity types/classes/unary predicates/universals
  • Roles - relationships/associations/binary predicates/properties
  • Individuals - constants Pasted image 20230508043119.png

Three kinds of axioms in DL:

  1. ABox axioms - assertional axioms capture knowledge about relationships with individuals.

    • concept assertion C(a) -> Mother(Jane) -> Jane is a mother
    • role assertion R(a, b) -> motherOf(Jane, Paul) -> Jane is the mother of Paul
    • individual equality a = b -> Bobby = Robert -> Bobby and Robert are the same person
    • individual inequality a != b -> Steven != Robert -> Steven and Robert are different people

  2. TBox axioms - terminological axioms capture knowledge about relationships between concepts.

    • concept inclusion C lies in D -> Mothers are Parents
    • concept equivalence C = D -> librarians and bookkeepers are the same concept

  3. RBox axioms - relational axioms capture knowledge about relationships between roles.

    • role inclusion R lies in S -> motherOf(x, y) is in parentOf(x, y) -> all mothers are parents
    • role equivalence R = S -> mentorOf(x, y) = guiderOf(x, y) -> mentors are the same roles as guiders
    • complex role inclusion R1 . R2 lies in S -> brotherOf(parentOf(x, y)) lies in uncleOf(x, y) -> the brother of your parent is your uncle
    • role disjointness disjoint(R, S)

See also