Description Logic

Question 1

Intersection constructor (⊓): what does C ⊓ D mean?

Answer 1

C ⊓ D is the class of individuals that are instances of both C and D (logical AND).

Question 2

Union constructor (⊔): what does C ⊔ D mean?

Answer 2

C ⊔ D is the class of individuals that are instances of C or D or both (logical OR).

Question 3

Complement constructor (¬): what does ¬C mean?

Answer 3

¬C is the class of individuals not belonging to C (logical NOT).

Question 4

Existential restriction: what does ∃R.C represent?

Answer 4

∃R.C is the class of individuals that have at least one R-successor in C (some R.C).

Question 5

Universal restriction: what does ∀R.C represent?

Answer 5

∀R.C is the class of individuals whose every R-successor is in C (only R.C).

Question 6

Cardinality restrictions: what do ≥n R, ≤n R, =n R mean?

Answer 6

≥n R: individuals with at least n R-successors; ≤n R: at most n; =n R: exactly n.

Question 7

Concept inclusion axiom: what does C ⊑ D represent?

Answer 7

Every instance of C is also an instance of D (C is a subclass of D).

Question 8

Concept equivalence axiom: what does C ≡ D represent?

Answer 8

C and D have exactly the same instances (C and D are equivalent).

Question 9

Role inclusion axiom: what does R ⊑ S represent?

Answer 9

Every R-related pair is also S-related; R is a subrole of S.

Question 10

Role equivalence axiom: what does R ≡ S represent?

Answer 10

R and S have exactly the same relation pairs; roles are interchangeable.

Question 11

Role transitivity axiom: what does R⁺ ⊑ R represent?

Answer 11

The transitive closure of R is a subrole of R, making R transitive.