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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.