Definition (ABox). An ABox A is a finite collection of axioms of the form C(a), R(a, b), where a and b are individual names, C is a concept, and R is a role. An individual assertion can be
- a concept assertion, C(a)
- a role assertion, R(a, b), or a negated role assertion, ¬R(a, b)
- an equality statement, a ≈ b
- an inequality statement, a ≉ b
where a, b ∈ I individual names, C ∈ C a concept expression, and R ∈ R a role.