From: Axel Polleres <axel.polleres@deri.org>

Date: Tue, 1 Mar 2011 15:00:10 +0000

Cc: "SPARQL Working Group" <public-rdf-dawg@w3.org>, "Andy Seaborne" <andy.seaborne@epimorphics.com>

Message-Id: <FFA7E1BA-0981-486E-AD69-EBFB6E3C975B@deri.org>

To: Birte Glimm <birte.glimm@comlab.ox.ac.uk>

Date: Tue, 1 Mar 2011 15:00:10 +0000

Cc: "SPARQL Working Group" <public-rdf-dawg@w3.org>, "Andy Seaborne" <andy.seaborne@epimorphics.com>

Message-Id: <FFA7E1BA-0981-486E-AD69-EBFB6E3C975B@deri.org>

To: Birte Glimm <birte.glimm@comlab.ox.ac.uk>

On 15 Feb 2011, at 14:19, Birte Glimm wrote: > Hi all, > Andy suggested that we take my concerns about the text in 18.6 to > another thread since this is already old SPARQL 1.0 text and not an > issue with newly introduced features. > > I wrote: > "18.6 Extending SPARQL Basic Graph Matching > I am not quite happy with the text (in particular the formulation of > the conditions) since it is not at all well-aligned with the notation > used in the rest of the document, e.g., "answer set" is everywhere > else "solution sequence" and in this case answer set is even a set of > pattern instance mappings, which is not the case anywhere else, where > a BGP evaluates into a multiset of solution mappings and the RDF > instance mappings just determine the multiplicity. > > We (Markus Krötzsch and I) discuss what is wrong with the conditions in > an ISWC paper and I am happy to suggest a more aligned version of the > conditions, if the WG is interested in this." > > I propose, therefore, to change the text with the purpose of getting > the terminology aligned with the rest of the spec and motivate more > clearly the purpose of the conditions (see also Sec. 4 of the attached > paper for explanations for the proposed changes). > > Current text: > A SPARQL extension to E-entailment must satisfy the following conditions: > 1. The scoping graph SG, corresponding to any consistent active graph > AG, is uniquely specified and is E-equivalent to AG. > 2. For any basic graph pattern BGP and pattern solution mapping P, > P(BGP) is well-formed for E. > 3. For any scoping graph SG and answer set {P_1,...,P_n} for a basic > graph pattern BGP, and where BGP_1, ..., BGP_n is a set of basic graph > patterns all equivalent to BGP, none of which share any blank nodes > with any other or with SG > SG E-entails (SG union P_1(BGP_1) union ... union P_n(BGP_n)). > 4. Each SPARQL extension must provide conditions on answer sets which > guarantee that the set of triples obtained by instantiating BGP with > each solution μ is uniquely specified up to RDF graph equivalence, and > should provide further conditions to prevent trivial infinite answers > as appropriate to the regime. > > Proposed text: > An entailment regime E must provide conditions on basic graph pattern > evaluation such that for any basic graph pattern BGP, any RDF graph G, > and any evaluation that satisfies the conditions, the resulting > multiset of solutions is uniquely determined up to RDF graph > equivalence. We denote the multiset of solutions from evaluating BGP > over G using E with Eval_E(G, BGP). > An entailment regime must further satisfy the following conditions: > 1. For any consistent active graph AG, the entailment regime E > uniquely shouldn't this be "uniquely (up to RDF graph equivalence)" ? > specifies a scoping graph SG that is E-equivalent to AG. > 2. A set of well-formed graphs for E is specified such that, for any > basic graph pattern BGP, scoping graph SG, and solution mapping μ in > Eval_E(SG, BGP), the graph μ(BGP) is well-formed for E. > 3. For any basic graph pattern BGP and scoping graph SG, if μ_1, ..., > μ_n in Eval_E(SG, BGP) and BGP_1, ..., BGP_n are basic graph patterns > all equivalent to BGP but not sharing any blank nodes with each other > or with SG, then > SG E-entails SG union μ_1(BGP_1) union ... union μ_n(BGP_n) > 4. Entailment regimes should provide conditions to prevent trivial > infinite solution multisets as appropriate to the regime. > > The uniqueness requirement of condition 4 is moved above all other > conditions, since 2. and 3. don't make sense if the solution multiset > was not defined in this sense. I am happy to turn the text into XML if > we decide to replace the current text with the proposed one. > > The notes (18.6.1 Notes) on BGP matching extensions also have some > inconsistent use of pattern instance mappings as solutions/answers: > > (b) ... If the extension does not allow answer bindings to blank > nodes, then this condition can be simplified to the condition: > SG E-entails P(BGP) for each pattern solution P. > should be > (b) ... If the extension does not allow bindings to blank nodes, then > this condition can be simplified to the condition: > SG E-entails μ(BGP) for each solution mapping μ. > > (d) ...an empty answer set. > should be > (d) ...an empty solution sequence. > > (e) ... Every answer P_i is the solution mapping restriction of a > SPARQL instance M_i such that M_i(BGP_i) is a subgraph of SG. Since > BGP_i and SG have no blank nodes in common, the range of M_i contains > no blank nodes from BGP_i; therefore, the solution mapping P_i and RDF > instance mapping I_i components of M_i commute, so M_i(BGP_i) = > I_i(P_i(BGP_i)). So > M_1(BGP_1) union ... union M_n(BGP_n) > = I_1(P_1(BGP_1)) union ... union I_n(P_n(BGP_n)) > = [ I_1 + ... + I_n]( P_1(BGP_1) union ... union P_n(BGP_n) ) > since the domains of the I_i instance mappings are all mutually > exclusive. Since they are also exclusive from SG, > SG union [ I_1 + ... + I_n]( P_1(BGP_1) union ... union P_n(BGP_n) ) > = [ I_1 + ... + I_n](SG union P_1(BGP_1) union ... union P_n(BGP_n) ) > i.e. > SG union P_1(BGP_1) union ... union P_n(BGP_n) > has an instance which is a subgraph of SG, so is simply entailed by SG > by the RDF interpolation lemma [RDF-MT]. > should be > > (e) ... For every solution mapping μ_i, there is, by definition of > basic graph pattern matching, an RDF instance mapping σ_i such that > P_i(BGP_i) is a subgraph of SG where P_i is the pattern instance > mapping composed of μ_i and σ_i. Since BGP_i and SG have no blank > nodes in common, the ranges of σ_i and μ_i contain no blank nodes from > BGP_i; therefore, the solution mapping μ_i and the RDF instance > mapping σ_i of P_i commute, so P_i(BGP_i) = σ_i(μ_i(BGP_i)). So > P_1(BGP_1) union ... union P_n(BGP_n) > = σ_1(μ_1(BGP_1)) union ... union σ_n(μ_n(BGP_n)) > = [ σ_1 + ... + σ_n]( μ_1(BGP_1) union ... union μ_n(BGP_n) ) > since the domains of the σ_i RDF instance mappings are all mutually > exclusive. Since they are also exclusive from SG, > SG union [ σ_1 + ... + σ_n]( μ_1(BGP_1) union ... union μ_n(BGP_n) ) > = [ σ_1 + ... + σ_n](SG union μ_1(BGP_1) union ... union μ_n(BGP_n) ) > i.e. > SG union μ_1(BGP_1) union ... union μ_n(BGP_n) > has an instance which is a subgraph of SG, so is simply entailed by SG > by the RDF interpolation lemma [RDF-MT]. > > Best regards, > Birte > > > -- > Dr. Birte Glimm, Room 309 > Computing Laboratory > Parks Road > Oxford > OX1 3QD > United Kingdom > +44 (0)1865 283520 > > <paper.pdf>Received on Tuesday, 1 March 2011 15:00:45 GMT

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