The sentence I want to formalize is the following:
Every Italian likes to eat pizza.
I come up with the following solutions:
- $$\forall x \forall y(Italian(x) \land Pizza(y) \implies LikeToEat(x,y))$$
- $$\forall x: (Italian(x) \implies LikeToEatPizza(x))$$ (Is the colon synthatically right placed?)
- $$\forall italian \in Italian: LikeToEatPizza(italian)$$
- $$\forall i( L(pizza))$$
- $$\forall i: EatingPizza(x)$$
- $ \forall x: L(x) $ where x:Italian and L: likes to eat pizza
Are these formalizations of the sentence above syntacially and semantically correct in predicate logic?
Thanks in advance
Updated 5. and 6. formula - what about that one?