From: Fred Zemke <fred.zemke@oracle.com>

Date: Fri, 09 Jun 2006 00:01:43 +0000

Message-ID: <4488BA28.2090800@oracle.com>

To: public-rdf-dawg@w3.org

Date: Fri, 09 Jun 2006 00:01:43 +0000

Message-ID: <4488BA28.2090800@oracle.com>

To: public-rdf-dawg@w3.org

2.4 Pattern solutions The definition defines "variable solution" as a partial function and "pattern solution" as a total function. Since the heading on the box calls out "pattern solution", and only the definition of "pattern solution" is in bold, and "variable solution" never appears elsewhere in the document, the reader is led to believe that the important notion is "pattern solution", the total function. However, focusing on total functions is a mistake, as shown by the OPTIONAL and UNION syntaces, which explicitly require partial functions as solutions to patterns. 2.4 Pattern solutions It says that a pattern solution is a total function on V, an infinite set. As pointed out in a separate comment, solutions in general are partial functions on V, when OPTIONAL and UNION are considered. The issue to be raised in this comment is that V is not the appropriate domain, even in the case of matching a triple pattern. Consider SELECT ?a ?b ?c WHERE { ?a ?b ?c } evaluated on a graph containing a single triple, (n:s n:v n:o). Then, according to the definition, a pattern solution is a total function mapping F:V -> {n:s, n:v, n:o} such that F(?a) = n:s, F(?b) = n:v, F(?c) = n:o, and F(v) is unconstrained for all other variables v. There are a countable infinity of these total functions. Now assemble these pattern solutions into a solution sequence and project to retain just the variables ?a, ?b and ?c. You still have an infinite sequence. Thus the result of the query appears to be an infinite sequence (whose every member is the same function on { ?a, ?b, ?c }). If one replies that the projection is to be done before assembling the solution sequence, I observe first that that is not the description in Section 10.1 "solution sequences and result forms", but more importantly, that will produce the wrong cardinality on other queries, for example, SELECT ?a ?b WHERE { ?a ?b ?c } on a dataset with two triples (n:s n:v, n:o1), (n:s, n:v, n:o2). In this example, projecting before assembling the solution sequence will result in only a single solution, whereas there should be two. Instead, I believe that the correct algorithm is to look at pattern solutions whose domain is the set of variables that appear in the specific query to be evaluated (not the infinite set V). And, as pointed out in a separate comment, the focus should be on partial functions rather than total functions. FredReceived on Friday, 9 June 2006 05:40:11 UTC

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