From: Roman Kontchakov <roman@dcs.bbk.ac.uk>

Date: Tue, 16 Jun 2015 16:42:51 +0100

Message-Id: <7A08FF72-0CED-454C-A268-E8351CA7CED7@dcs.bbk.ac.uk>

To: public-rdf-dawg-comments@w3.org

Date: Tue, 16 Jun 2015 16:42:51 +0100

Message-Id: <7A08FF72-0CED-454C-A268-E8351CA7CED7@dcs.bbk.ac.uk>

To: public-rdf-dawg-comments@w3.org

Dear Andy It seems to me that the fix to the "written in full" definition of LeftJoin as described in http://www.w3.org/2013/sparql-errata#sparql11-query does not quite work. For example, let Ω1 = { (?X -> :a) }, Ω2 = { (?X -> :a, ?A -> 20), (?X -> :b, ?A -> 30) } and F = ?A = 30. Using the normative definition, LeftJoin(Ω1,Ω2,F) = Filter(F, Join(Ω1,Ω2)) union Diff(Ω1,Ω2,F), we obtain - Join(Ω1,Ω2) = { (?X -> :a, ?A -> 20) } and so Filter(F, Join(Ω1,Ω2)) is empty; - on the other hand, Diff(Ω1,Ω2,F) = { (?X -> :a) } because for the only mapping μ1 in Ω1, the first mapping in Ω2 is compatible with μ1 but the effective boolean value of F is false and the second mapping in Ω2 is not compatible with μ1. Thus, LeftJoin(Ω, Ω2, F) = { (?X -> :a) } (1) Using the "written in full" definition from the errata, LeftJoin(Ω1, Ω2, F) = { merge(μ1, μ2) | μ1 in Ω1 and μ2 in Ω2, μ1 and μ2 are compatible and F(merge(μ1, μ2)) is true } ∪ { μ1 | μ1 in Ω1, ∀ μ2 in Ω2, μ1 and μ2 are not compatible, or Ω2 is empty } ∪ { μ1 | μ1 in Ω1, ∀ μ2 in Ω2, μ1 and μ2 are compatible and F(merge(μ1, μ2)) is false } we obtain, respectively, - the empty set (see above), - the empty set (because Ω2 is not empty and contains a mapping compatible with the only mapping in Ω1), - the empty set (because the first mapping in Ω2 is compatible with the only mapping in Ω1 but F is false). The result, therefore, is the empty set, which is not equal to (1). In fact, I suspect, there is no simple way of translating the two components in the union of the normative definition into some sort of `three-component' union. So, in my view, it is easier to replace the current "written in full" version of LeftJoin with Filter over Join + Diff (or omit it altogether to avoid any confusion). Best regards Roman -- Roman Kontchakov Birkbeck, University of LondonReceived on Thursday, 18 June 2015 09:46:13 UTC

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