MGL7160: Exercice #1 -- Solutions

16 janvier 2001

1. Quantificateurs et concepts

[10] a)

1.

  CONCEPT grand_patron( e: employe ) VALUE( b: boolean )
    WHERE b <=> ~SOME( e1: employe :: supervise(e1, e) )

  CONCEPT grand_patron( e: employe ) VALUE( b: boolean )
    WHERE b <=> NUMBER( e1: employe SUCH THAT supervise(e1, e) :: e1 ) = 0

2.

  CONCEPT nb_bureaux( e: employe ) VALUE( n: nat )
    WHERE n = NUMBER( b: bureau SUCH THAT utilise(e, b) :: b  )

3.

  CONCEPT bureau( e: employe SUCH THAT grand_patron(e) ) VALUE( b: bureau )
    WHERE utilise(e, b)

[15] b)

*

  ~SOME( e: employe :: supervise(e, e) )

  ALL( e: employe :: ~supervise(e, e) )

*

  ~SOME( b: bureau ::
         NUMBER(e: employe SUCH THAT utilise(e, b) :: e) > capacite(b) )

  ALL( b: bureau ::
       NUMBER(e: employe SUCH THAT utilise(e, b) :: e) <= capacite(b) )

*

  ALL( e: employe, b1 b2: bureau SUCH THAT b1 ~= b2 ::
       utilise(e, b1) & utilise(e, b2) => telephone(b1) = telephone(b2) )

  ALL( e: employe, b1 b2: bureau SUCH THAT b1 ~= b2 & utilise(e, b1) & utilise(e, b2) ::
       telephone(b1) = telephone(b2) )

*

  ALL( p: employe SUCH THAT grand_patron(p) ::
       NUMBER( e: employe SUCH THAT utilise(e, bureau(p)) :: e ) = 1 )

  ALL( p: employe SUCH THAT grand_patron(p) ::
       ~SOME( e: employe SUCH THAT e ~= p :: utilise(e, bureau(p)) ) )

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MGL7160: Exercice #1 -- Solutions

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