**From:** Zanger Daniel (*[email protected]*)

**Date:** 10/11/00

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I think the two intended definitions are ultimately supposed to be equivalent. It seems to me the second Google reference cited doesn't really come out with an actual tangible definition that is different from standard union, however. As to the exchange, <! QUESTION: what is the value of your disjoint-union when the classes arent disjoint?> > > > > er... the same as the "value" of any other false assertion, > > such as 5<4. > > Actually, I think the whole value of the disjoint union of sets IS for when the classes are NOT disjoint; otherwise in the case when they are disjoint it operates just like the usual union. daniel zanger. > Dan Connolly wrote: > > > > pat hayes wrote: > > > > > > In DAML-ONT: > > > > > > </Property> <Property ID="disjointUnionOf"> > > > <label>disjointUnionOf</label> > > > <domain resource="#Class"/> > > > <range resource="#List"/> > > > <comment> > > > > > > for unionOf(X, Y) read: X is the disjoint union of the classes in > > > the list Y: (a) for any c1 and c2 in Y, disjointWith(c1, c2), > > > and (b) i.e. if something is in any of the classes in Y, it's > > > in X, and vice versa. > > > > > > cf OIL disjoint-covered > > > </comment> </Property> <Property ID="intersectionOf"> > > > > > > <! COMMENT: This isnt the usual notion of 'disjoint-union'. The usual one is the union of two disjoint copies of the arguments. Imagine replacing A and B by A' and B' where A' differs from A in having all the elements of its intersection with B marked as 'first copy', and similarly for B' but marked 'second copy', then the disjoint union of A and B is the union of A' and B'. So for example the disjoint union of a set with itself is a set with two copies of everything in the original set. > > > > > Two copies? in a set? I don't understand. > > > > As to the "usual" notion of disjoint union, > > lemme try google... Ah... now I see what you're talking > > about... > > > > http://mathworld.wolfram.com/DisjointUnion.html > > > > But that's the 2nd hit nominated by google. The 1st > > one is consistent with what I was talking about: > > > > For example, if T represents > > the type of triangles, R the type of rectangles and > > C the type of circles, then we can say that an > > object is a triangle or a rectangle or a circle by > > saying that it belongs to the type T or R or C. In Nuprl > > this type is written T|R|C. > > > > In general if A and B are types, then so is their > > disjoint union, A|B. Semantically, not only is the > > union disjoint, but given an element of A|B, it must be > > possible to decide which component it is in. > > Semantically, not only is the union disjoint, but given > > an element of A|B, it must be possible to decide which > > component it is in. > > http://www.cs.cornell.edu/Info/Projects/NuPrl/book/node39.html > > > > But perhaps something like "partitionedBy" would be less > > ambiguous? > > > > I don't really know what's the common idiom here; > > I added this at the request of somebody else. > > > > > <! QUESTION: what is the value of your disjoint-union when the classes arent disjoint?> > > > > er... the same as the "value" of any other false assertion, > > such as 5<4. > >

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