From: Andrew Newman <andrewfnewman@gmail.com>

Date: Fri, 14 Mar 2008 14:33:56 +1000

Message-ID: <2db5a5c40803132133w167e70f6j8f5aeae383b89972@mail.gmail.com>

To: "Lee Feigenbaum" <lee@thefigtrees.net>

Cc: public-rdf-dawg-comments@w3.org, "Arjohn Kampman" <arjohn.kampman@aduna-software.com>

Date: Fri, 14 Mar 2008 14:33:56 +1000

Message-ID: <2db5a5c40803132133w167e70f6j8f5aeae383b89972@mail.gmail.com>

To: "Lee Feigenbaum" <lee@thefigtrees.net>

Cc: public-rdf-dawg-comments@w3.org, "Arjohn Kampman" <arjohn.kampman@aduna-software.com>

On 14/03/2008, Lee Feigenbaum <lee@thefigtrees.net> wrote: > Andrew Newman wrote: > This is, I suppose, the set containing the empty relation. I'm not sure > which, if either, of U and 0 above this is equivalent to. Part of my > confusion is because I'm not sure whether the A, U, and 0 relations you > speak of above are (in SPARQL terms) solutions or sets of solutions. > I don't think there is any important difference in what we are talking about. Even if we're talking about bags rather than sets the identities are the same (a Union u = u, a Intersect 0 = 0). > > On the other hand: > > select distinct ?s ?p ?o > > where { > > {?s ?p ?o} union {} > > } > > > > Again, you get all triples back - which is the result of A + 0. > > > I don't think that is correct behavior. I believe the results of the > above query should be (forgive the lack of rigor in my notation) > set-union({?s ?p ?o}, {}) which is the solution set containing one > solution per triple in the default graph unioned with one solution > containing no bindings. > Yes, my mistake, the correct answer is all the triples plus the empty group pattern. The problem remains though. When used in join, {} gives a result like it's the identity (acting like U) but operates differently in union. If we go back to the +/* notation it's: A * {} = A A + {} = B (where B is as defined as above, A set-union {}) By the definition you gave above {} still seems like it is 0 but operates like U with respect to join. A universal solution set maybe written like {{0}} (where the 0 in this case is the nullary tuple/solution - containing all values) or maybe {{RDF-T}} and 0 (empty solution set) written as {{}}. >From an implementation perspective, identity is handy to do shortcuts during evaluating the results. I take it that if {} isn't an identity then it can't be used as a shortcut. And I shouldn't call anything triples either - sorry if that's confusing.Received on Friday, 14 March 2008 04:34:35 UTC

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