A slightly more complex logic: ALH

• Like Ex, it operates on “individuals” and “classes”

• But it also have “roles”: binary relations on individuals

• It also has two special symbols: ⊤ and ⊥ (more or less for “true” and “false”)

• ALH also allows more relationships for axioms:

• • A ⊓ B and ⌝A for classes (and also A ⊏ B, like in Ex )
  • • intersection and negation of classes, respectively
  • If R is a role, then A ≣ ∀R.C or B ≣ ∃R.⊤ are also possible
  • • defining classes by restrictions, ie, “all values must be in C”, and “there must be at least one value”