3.7.200. Pure functional dependency

A constraint for which the meaning is completely captured by one or more functional dependancies. The negation of such constraints can be directly expressed as a disjunction between the different functional dependancies. We illustrate this point on different examples:

  • The negation of the 𝚗𝚟𝚊𝚕𝚞𝚎(n,v 1 ,v 2 ,,v m ) constraint is defined by 𝚗𝚟𝚊𝚕𝚞𝚎(p,v 1 ,v 2 ,,v m ) np.

  • The negation of the 𝚌𝚘𝚖𝚖𝚘𝚗(n 1 ,n 2 ,u 1 ,u 2 ,,u p ,v 1 ,v 2 ,,v q ) constraint is defined by 𝚌𝚘𝚖𝚖𝚘𝚗(m 1 ,m 2 ,u 1 ,u 2 ,,u p ,v 1 ,v 2 ,,v q )(n 1 m 1 n 2 m 2 ).

  • The negation of the 𝚎𝚕𝚎𝚖𝚎𝚗𝚝𝚜(𝚒𝚗𝚍𝚎𝚡-i 1 𝚟𝚊𝚕𝚞𝚎-u 1 ,𝚒𝚗𝚍𝚎𝚡-i 2 𝚟𝚊𝚕𝚞𝚎-u 2 ,,𝚒𝚗𝚍𝚎𝚡-i n 𝚟𝚊𝚕𝚞𝚎-u n ,𝚒𝚗𝚍𝚎𝚡-1 𝚟𝚊𝚕𝚞𝚎-v 1 ,𝚒𝚗𝚍𝚎𝚡-2 𝚟𝚊𝚕𝚞𝚎-v 2 ,,𝚒𝚗𝚍𝚎𝚡-n 𝚟𝚊𝚕𝚞𝚎-v n ) constraint is defined by 𝚎𝚕𝚎𝚖𝚎𝚗𝚝𝚜(𝚒𝚗𝚍𝚎𝚡-i 1 𝚟𝚊𝚕𝚞𝚎-w 1 ,𝚒𝚗𝚍𝚎𝚡-i 2 𝚟𝚊𝚕𝚞𝚎-w 2 ,,𝚒𝚗𝚍𝚎𝚡-i n 𝚟𝚊𝚕𝚞𝚎-w n ,𝚒𝚗𝚍𝚎𝚡-1 𝚟𝚊𝚕𝚞𝚎-v 1 ,𝚒𝚗𝚍𝚎𝚡-2 𝚟𝚊𝚕𝚞𝚎-v 2 ,,𝚒𝚗𝚍𝚎𝚡-n 𝚟𝚊𝚕𝚞𝚎-v n ) (u 1 w 1 u 2 w 2 u n w n ).

  • The negation of the 𝚜𝚘𝚛𝚝(u 1 ,u 2 ,,u n ,v 1 ,v 2 ,,v n ) constraint is defined by 𝚜𝚘𝚛𝚝(u 1 ,u 2 ,,u n ,w 1 ,w 2 ,,w n ) 𝚕𝚎𝚡_𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝(v 1 ,v 2 ,,v n ,w 1 ,w 2 ,,w n ).