I hope you can give me some tips on how to translate part of the following sentence into predicate logic:

“No woman loves a man that loves multiple women”.

Which quantifier would you use to express the part “multiple”? It of course means “more than one”, so the existential quantifier (expressing: at least one) as such does not seem enough... Any ideas?

Thank you in advance for any help you can give me!

  • 3
    $\begingroup$ "more than one" is "at least two". $\endgroup$ – Mauro ALLEGRANZA Jan 22 '19 at 15:38
  • $\begingroup$ Thanks, yes I agree, but then my question becomes: how do I express that? Sorry, just starting out with predicate logic, so maybe the answer should be obvious... $\endgroup$ – user637252 Jan 22 '19 at 16:36

Rephrase that part as

There are two different women loved by the man

$\exists x\exists y:$ Woman$(x)\, \land\,$Woman$(y)\, \land\, \lnot(x=y)\,\land\,$Love$(m,x)\, \land\,$Love$(m, y)$

  • $\begingroup$ I would instead write $\exists x,y\in\text{Women}$, but it's the same concept. $\endgroup$ – Don Thousand Jan 22 '19 at 16:01
  • $\begingroup$ thanks! that makes sense! $\endgroup$ – user637252 Jan 22 '19 at 16:39

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