Re: Text for 18.6 Extending SPARQL Basic Graph Matching

On 1 March 2011 15:00, Axel Polleres <axel.polleres@deri.org> wrote:

>
> 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)"
> ?
>

It wasn't that even in the original version (I tried to change only what
really needs chaning) and I understand the text still as saying that it has
to be specified exactly (i.e., uniquely) what the scoping graph SG is, but
that SG can be anything as long as it is E-equivalent to AG, which allows
for renaming bnodes. There shouldn't be any choice such that, e.g., one
implementation understands SG to be the lean version of AG and another one
understands it as exactly AG, etc. So that is how I read uniquely specified.

Birte


> > 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>
>
>


-- 
Dr. Birte Glimm, Room 309
Computing Laboratory
Parks Road
Oxford
OX1 3QD
United Kingdom
+44 (0)1865 283520