- From: Pat Hayes <phayes@ihmc.us>
- Date: Mon, 26 Feb 2007 17:10:44 -0600
- To: Michael Schneider <m_schnei@gmx.de>, public-owl-dev@w3.org
>Holger Knublauch wrote on Mon, 26 Feb 2007: > >>The goal should be to have some mechanism that allows users to >>enter and display a disjoint union, e.g. in >> >> A = B xor C xor D >> >>assuming xor represents disjoint union. > >Hi, Holger! > >Just a side note (a little offtopic): I believe that the above is >not the best way to describe a disjoint union. Yeh, this is an old trap. Binary xor is not associative, and n-ary xor is not a composition of the binary operation. BTW, I would strongly urge that y'all follow Jim Hendlers advice and treat the assertion of the union and the assertion of disjointness as two separate items. Note that in standard mathematical terminology, disjoint union does not imply disjointness of the sets; a disjoint union, standardly indicated by the plus sign, is also called a discriminated union or a tagged union, and it contains two 'copies' of anything that is in the intersection of the two sets being unioned. Note that this (unlike what y'all are here calling a disjoint union) makes no assertions about the sets, is a genuine set-theoretic function, i.e. it is defined for any two sets, and it is associative, so the n-ary case is gotten by composing the binary case. These are all very desirable properties, which (I suggest) you should not abandon casually. Pat Hayes -- --------------------------------------------------------------------- IHMC (850)434 8903 or (650)494 3973 home 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32502 (850)291 0667 cell phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes
Received on Monday, 26 February 2007 23:11:01 UTC