Existentials Universals All Only some Values From all

Existentials & Universals All & Only some. Values. From & all. Values. From Supplementary lab exercise Alan Rector & colleagues 1

some. Values. From means “some” • some. Values. From means “some” means “at least 1” • Dog_owner complete Person and has. Pet some. Values. From Dog – means: A Pet_owner is any person who has as a pet some (i. e. at least 1) dog • Dog_owner partial Person and has. Pet some. Values. From Dog – means All Pet_owners are people and have as a pet some (i. e. at least 1) dog. 2

all. Values. From means “only” • all. Values. From means “only” means “no values except” • First_class_lounge complete Lounge and has. Occupants all. Values. From First. Class. Passengers – Means “A ‘first class lounge’ is any lounge where the occupants are only first class passengers” or “A first ‘class lounge’ is any lounge where there are no occupants except first class passengers” • First_class_lounge partial Lounge and has. Occupants all. Values. From First. Class. Passengers – Means “All first class lounges have only occupants who are first class passengers” “All first class lounges have no occupants except first class passengers” “All first class lounges have no occupants who are not first class passengers” 3

“Some” does not mean “only” • A “dog owner” might also own cats, and rats, and guinea pigs, and… – It is an open world, if we want a closed world we must add a closure restriction or axiom • Dog_only_owner complete Person and has. Pet some. Values. From Dog and has. Pet all. Values. From Dog • A “closure restriction” or “closure axiom” – The problem in making maguerita pizza a vegie pizza – Closure axioms use ‘or’ (disjunction) – dog_and_cat_only_owner complete has. Pet some. Values. From Dog and has. Pet some. Values. From Cat and has. Pet all. Values. From (Dog or Cat) 4

“Only” does not mean “some” • There might be nobody in the first class lounge – That would still satisfy the definition – It would not violate the rules • A pizza with no toppings satisfies the definition of a vegetarian pizza – Pizza & has_topping_ingredient all. Values. From Vege • It has no toppings which are meat – It has not toppings which are not vegetables » It has no toppings which aren’t fish… – Analogous to the empty set is a subset of all sets • One reason for a surprising subsumption is that you have made it impossible for there to be any toppings – all. Values. From (cheese and tomato) 5

Closure Restrictions A standard pattern • a. Property some. Values. From Class 1 and a. Property some. Values. From Class 2 and a. Property some. Values. From Class 3 and … a. Property some. Values. From Classn and a. Property all. Values. From (Class 1 or Class 2 or Class 3 or … or Classn) closure restriction • disjoint (Class 1 Class 2 Class 3 … Classn 6

Create an new ontology with the following definitions • Primitive Concepts – Family Child Girl Boy • Roles – has_children • Defined concepts – All_girl_family Family & (restriction has_children all. Values. From Girl) – No_child_family Family & not (restriction has_children some. Values. From Top) – Zero_child_family Family & (restriction has_children max-cardinality=0 Top) 7

Classify it and examine the result • What does this tell you about the use of all. Values. From (Universal qualification) • Why do we say that most ontologies are based on some. Values. From (Existential qualification) • Repair the definition of “All_girl_family” so that it behaves as expected 8