ProteinLoverPizza ≡ Pizza ⊓ ∀hasTopping.(Meat ⊓ Fish)
MeatyPizza ≡ Pizza ⊓ ∀hasTopping.Meat
VegetarianPizza ≡ Pizza ⊓ ∀hasTopping.(¬Meat ⊔ ¬Fish)

Posons l'existence d'un individu a tel que:
ProteinLoverPizza(a)
¬MeatyPizza(a)

Alors on a:
(Pizza ⊓ ∀hasTopping.(Meat ⊓ Fish))(a)
¬(Pizza ⊓ ∀hasTopping.Meat)(a)
Pizza(a)
(∀hasTopping.(Meat ⊓ Fish))(a)
(¬Pizza ⊔ ¬∀hasTopping.Meat)(a)
(¬Pizza ⊔ ∃hasTopping.¬Meat)(a)

On a deux possibilités.
¬Pizza(a) est contradictoire avec Pizza(a)

Explorons donc l'autre possibilité:
(∃hasTopping.¬Meat)(a)
hasTopping(a,b)
¬Meat(b)

Selon l'énoncé (∀hasTopping.(Meat ⊓ Fish))(a) on doit déduire:

(Meat ⊓ Fish)(b)
Meat(b)
Fish(b)

On a donc une contradiction.
Last modified: Tuesday, 2 November 2021, 5:20 PM