This is what it looks like in English:

There is a large sphere, and all large things are to the right of b. Therefore, there is a sphere to the right of b.

Which I translated as:

  1. [Premise 1] ∃x(S(x)∧L(x))
  2. [Premise 2] ∀x(L(x)→RightOf(x,b))
  3. [Conclusion] ∃x(S(x)∧RightOf(x,b))

Where S stands for Sphere, L for large, RightOf for 'right of'*, b for 'b', and 'x' is a variable.

*So RightOf(x,b) would read as 'x is to the right of b'.

I'm unsure about my translation though, and before working on the formal proof, I would like to know if it is correct.

Thank you

1 Answer 1


Yes, that’s right, except if there is a requirement in your system that a single English sentence be translated into a single premise. In that case, the two premises would be joined by a conjunction.

  • No requirement, but if I wanted to join them, wouldn't it simply look like this: (∃x(S(x)∧L(x))) ∧ (∀x(L(x)→RightOf(x,b))) ? Not sure that I understand what you mean by 'construction', do you mean a conjunction? or 'mixing' the quantifiers?
    – 35308
    Nov 27, 2018 at 0:40
  • Yes and sorry, voice recognition failure. It’s conjunction of course! Nov 27, 2018 at 0:41

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