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Re: Text for 18.6 Extending SPARQL Basic Graph Matching

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>

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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