I have a problem with the modelling of the following statement in propositional logic (warning, I translated it from italian):

Martha is not a singer, and she doesn't play violin or flute, but not the cello

The exercise ask to use the following simple propositions to model the above:

P = Martha is a singer

Q = Martha plays the violin

R = Martha plays the flute

Z = Martha plays the cello

My solution is $$ \neg P \wedge (\neg Q \vee \neg R) \wedge \neg Z $$

The proposed solution, instead, is $$ \neg P \wedge \neg (Q \vee R) \wedge \neg Z $$

I can't understand why, can somebody help me?

EDIT: I'll write the original italian sentence, for those who might be able to give a more accurate translation:

Marta non è una cantante, e non suona o il violino o il flauto, ma non il violoncello

  • $\begingroup$ Maybe the translation wasn't good, but 'but' is semantically senseless here because 'but' is an adversative conjunction and in this sentence it's not adversative. With regards to the question, maybe the wording is a bit off, perhaps clearer would be "And she doesn't play the violin nor the flute". In hindsight this is better suited for english.S.E. $\endgroup$ – Git Gud Jul 1 '14 at 10:32
  • $\begingroup$ Maybe I'll ask there too, but the problem is exactly this: it's an ambiguous way of writing the statement. Which solution would you pick as the "most accurate one"? $\endgroup$ – Cynical Jul 1 '14 at 10:48
  • $\begingroup$ I think the solution given to you is more accurate and upon reading the original sentence, I think 'nor' is in order. I don't speak italian, though. $\endgroup$ – Git Gud Jul 1 '14 at 10:52
  • $\begingroup$ I'm a native English speaker, and "but" here is simply wrong. Even the other parts are not right, since you can't say "play violin or flute" but must say "play the violin or the flute". I think the closest you can get in English is "Martha is not a singer, and does not play the violin or the flute, or even the cello.", because English has no direct equivalent for this usage of "ma". $\endgroup$ – user21820 May 22 '16 at 11:59

As mentioned in the comment, the translation here is indeed crucial. The use of 'but' does not seem to fit in there (but I have to say that I'm also not a native English speaker).

In any case, spoken languages can hardly cover the subtleties of logic (except for Lojban...). There are several interpretations or conventions for natural languages that are not applicable for logic. The famous example is

Q: "Do you want coffee or tea?"

A: "Yes"

This answer is perfectly valid from a logical point of view.

In this case, one could try to tanslate the logical statements back into the natural language, and see whether they still say the same as the original sentence, but it's difficult for the aforementioned reasons. When inserting brackets to emphasize the difference, the first statement could be translated as

Martha is not a singer, and she does (not play violin or not play flute), and not play cello

The second one could be

Martha is not a singer, and she does not (play violin or play flute), and not play cello

So imagine the facts that are given are

  • Martha is not a singer
  • Martha does play violin
  • Martha does not play the flute
  • Martha does not play cello

Then the first solution would be true, because the part saying

... she does (not play violin or not play flute)

is fulfilled, because she does ... not play the flute.

Maybe when you insert the original (untranslated, Italian) sentence, someone can give you the most appropriate translation.

  • $\begingroup$ While you were writing your answer, I added the original sentence :) $\endgroup$ – Cynical Jul 1 '14 at 10:51
  • $\begingroup$ The Lojban thing is very interesting, I had never heard about it. $\endgroup$ – Git Gud Jul 1 '14 at 10:51

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