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The sentence I want to formalize is the following:

Every Italian likes to eat pizza.

I come up with the following solutions:

  1. $$\forall x \forall y(Italian(x) \land Pizza(y) \implies LikeToEat(x,y))$$
  2. $$\forall x: (Italian(x) \implies LikeToEatPizza(x))$$ (Is the colon synthatically right placed?)
  3. $$\forall italian \in Italian: LikeToEatPizza(italian)$$
  4. $$\forall i( L(pizza))$$
  5. $$\forall i: EatingPizza(x)$$
  6. $ \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?

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  • $\begingroup$ 1. is too strong: it means every Italian likes to eat any pizza. 2. is better, but eliminate the colon. Also use the \text{} environment inside a math environment to make text non-italic. $\endgroup$ – Adrian Keister Jul 19 '18 at 15:20
  • $\begingroup$ 4. is wrongly written and 2. and 3. are "variants". $\endgroup$ – Mauro ALLEGRANZA Jul 19 '18 at 19:09
  • $\begingroup$ @AdrianKeister I have a question regarding of removing the parenthesis from 1. and 2.. That would make x and y unbound after AND and the Implikation and would be wrong, right? And about the colon: is this wrong or just not "beauty"? $\endgroup$ – user3352632 Jul 20 '18 at 11:52
  • $\begingroup$ @MauroALLEGRANZA 1. and 2. withouth parenthesis around the formula would make both wrong, right? $\endgroup$ – user3352632 Jul 20 '18 at 11:55
  • $\begingroup$ Is there a rule to name predicates with capital letters? $\endgroup$ – user3352632 Jul 20 '18 at 11:58

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