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All except students are invited 

This proposition was translated into

No student is invited, and all non-students are invited 

Why was it translated into this conjunction of form A∧B

and not into one of its conjuncts A or B?

  • What is your proposed "A only" translation ? – Mauro ALLEGRANZA Jan 23 at 7:06
  • @MauroALLEGRANZA all non students are invited – user273747 Jan 23 at 7:36
  • "all non students are invited" does not excluded that also students are invited. – Mauro ALLEGRANZA Jan 23 at 7:49
  • @MauroALLEGRANZA but all non students are invited automatically let us to think that ok all students are not invited (excluded) – user273747 Jan 23 at 8:01
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    No, stating that the invitation includes all non-students does not automatically exclude any students. You have to be explicit about it. – Graham Kemp Jan 24 at 1:18
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Consider this similar example (assuming for simplicity that man and woman are the only two genders...) :

All women are humans.

This is the same as : "All non-man are humans".

According to your proposal, this is the same as :

All except men are humans.

  • Thanks for helping me – user273747 Jan 23 at 8:49
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Interesting question, the reason is that except is not as "atomic" as it may sound. Except provides two pieces of information and not one. Therefore, it should be broken down to 2 propositions.

Let A mean No student is invited and B mean all non-students are invited

Let us translate the proposition (with except) to A : No student is invited

Well, if no student is invited, it does not say anything about non-students, while the original proposition with 'except' says that all are invited except students.

Let us translate the proposition (with except) into B : all non-students are invited

Now, does the proposition B say anything about students? it only states that all non-students are invited, while the original proposition states that students are not invited (except students)

That is why you have to add A and B as conjuncts.

Edit

There is no quantifier for "except" in predicate first-order logic, because it can be broken down to "All" and "Some" quantifiers.

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