I found this question in an old exam paper. I have no idea what is expected from a question like this.

Consider the Tarski's world below. This world illustrates that ¬∃xTet(x) is NOT a logical consequence of the premises below. Explain why/

1. ∀x∀y [LeftOf(x, y] → Larger(x, y)]
2. ∀x∀y [Smaller(y, x) → (Cube(x) ∧ Dodec(y))]

enter image description here

This is worth 6 marks.

I think the obvious things are that you cannot infer ¬∃xTet(x) from the premisses.

Maybe I just don't really understand the question


In order to show that the conclusion is not a logical consequence of the premises, we have to find a counter-example, i.e. a "world" were the premsies are ture and the conclusion is not.

After having checked that the two premises are satisfied in the "world" depicted, we can conlude that ¬∃xTet(x) it is not true, simply because there are two tetrahedra.

  • I understand what you are saying, but do you think that is worth 6 marks?
    – Leon
    Oct 29 '14 at 9:23
  • @Leon - I do not know what are "marks"; you have to ask to your instructor ... Oct 29 '14 at 9:24
  • I'm referring to the number of points rewarded for a correct answer in the exam.
    – Leon
    Oct 29 '14 at 9:28
  • 1
    @Leon - it seems to me that the gist of the question is "Explain why". Thus, we have to supplement the answer : "that we cannot infer the conclusion from the premisses" with an argument showing that in the world depicted the two premises are satisfied... I think. :) Oct 29 '14 at 10:09

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