On May 9, 4:46 am, wren ng thornton <w...@freegeek.org> wrote: > John Creighton wrote: > > On May 6, 4:30 am, Bartek Ćwikłowski <paczesi...@gmail.com> wrote: > >> 2010/5/6 John Creighton <johns2...@gmail.com>: > > >>> "a" isa "d" if their exists a "b" and "c" such that the following > >>> conditions hold: > >>> "a" isa subset of "b", > >>> "b" isa "c" > >>> "c" is a subset of "d" > >> This definition doesn't make sense - it's recursive, but there's no > >> base case, unless this is some kind of co-recursion. > > >> Are you sure that "subset" isn't what you really want? With subset you > >> can already ask questions such as "is tabby cat an animal?". If so, my > >> code (from hpaste) already has this (iirc isDescendentOf ). > > > When I succeed in implementing it I'll show you the result. Anyway, > > some perspective (perhaps), I once asked, "what is the difference > > between a subset and an element of a set: > > >http://www.n-n-a.com/science/about33342-0-asc-0.html > > And it's truly an interesting question. Too bad it didn't get a better > discussion going (from what I read of it). Though the link Peter_Smith > posted looks interesting. > > > note 1) Okay I'm aware some will argue my definitions here and if it > > helps I could choose new words, the only question really is, is the > > relationship isa which I described a useful abstraction. > > I think the key issue comes down to what you want to do with it. I'm not > entirely sure what the intended reading is for "isa subset of", but I'll > assume you mean the same as "is a subset of"[1]. One apparent side > effect of the definition above is that it collapses the hierarchy. > > That is, with traditional predicates for testing element and subset > membership, we really do construct a hierarchy. If A `elem` B and B > `elem` C, it does not follow that A `elem` C (and similar examples). But > with your definition it seems like there isn't that sort of > stratification going on. If the requirements are A `subset` B, B `elem` > C, and C `subset` D--- well we can set C=D, and now: A `elem` D = A > `subset` B && B `elem` D. > > Depending on the ontology you're trying to construct, that may be > perfectly fine, but it's certainly a nonstandard definition for elements > and subsets. I don't know if this mathematical object has been worked on > before, but it's not a hierarchy of sets. > > [1] My other, equivalent, guess would be you mean "A isa (powerset B)" > but avoided that notation because it looks strange. > > -- > Live well, > ~wren > _______________________________________________ > Haskell-Cafe mailing list > haskell-c...@haskell.orghttp://www.haskell.org/mailman/listinfo/haskell-cafe > > -- > You received this message because you are subscribed to the Google Groups > "Haskell-cafe" group. > To post to this group, send email to haskell-c...@googlegroups.com. > To unsubscribe from this group, send email to > haskell-cafe+unsubscr...@googlegroups.com. > For more options, visit this group > athttp://groups.google.com/group/haskell-cafe?hl=en.
Keep in mind that my recent definition of "is a" > >>> "a" isa "d" if their exists a "b" and "c" such that the following > >>> conditions hold: > >>> "a" isa subset of "b", > >>> "b" isa "c" > >>> "c" is a subset of "d" is distinct from the question I asked a long time ago of the difference between a set and an element. The question I asked a long time ago is largely philosophical but can have axiomatic consequences in set theory. Ignoring the philosophical meanings behind a set, both the operations of subset and "element of", define a partial order. The subset relationship seems to define things that are more similar then the "element of" relationship. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
