Re: [Graphs] Proposal for Named Graph Semantics

I propose something that goes very much in the same direction as Alex's 
proposal:

Definition(Graph map) A graph map GM is a partial function from the set 
of IRIs to the set of g-snaps.

Definition(Temporal graph map) A temporal graph map TGM is a partial 
function from [-inf,+inf] which maps a time point to a graph map.

There exists a special temporal graph map, called the HTTPmap, such that 
at any given point in time t, HTTPmap(t) maps a URI to the parsed RDF 
graph of the document retrieved via an HTTP GET of the URI at the time 
t. (if HTTP GET does not provide an RDF serialisation, then the mapping 
is not defined on that URI).

A graph map is application-specific and can be static or temporal. If an 
application implements a versioning system, it is possible to use a 
temporal graph map with a time parameter in the past. However, the 
default behaviour should be to use a temporal graph map with the current 
time.

Now, to implement a graph map different from the HTTPmap, one way is to 
use a format like TriG or Quads where the mapping is syntactically made 
explicit in a file:

:G1 {:x :y :z}
:G2 {:a :b :c}

may be used to say that GM(:G1) = {:x :y :z} and GM(:G2) = {:a :b :c}.

Now, the connection with Dataset and its semantics is as follows: a set 
of URIs (u1, ..., un) and an optional default g-snap G induce a dataset 
(G, <u1,GM(u1)>, ... , <un,GM(un)>).

The rest of the semantics is as in the current Wikipage.

Basically, this says that a dataset is a snapshot of the data you can 
get by looking up certain URI ("looking up" not necessarily meaning 
"using HTTP"). The semantics in the wikipage just says that each graph 
in the dataset are interpreted independently (this can be further 
constrained by semantic extensions, just like RDFS constrains further 
the RDF interpretations).


AZ.

Le 07/04/2011 10:47, Alex Hall a écrit :
> Here is a proposal of a semantics for named graphs in RDF.  My goals here
> are to:
> - Extend http://www.w3.org/2011/rdf-wg/wiki/TF-Graphs/RDF-Datasets-Proposal to
> go beyond (IRI, graph) tuples.
> - Give something that is formally defined enough to serve as a starting
> point for discussion.
> - Specify common semantics for multi-graph serialization formats, or at
> least a starting point.
> - Specify something that is flexible enough to satisfy applications that
> want to treat named graphs as either g-snaps or g-boxes.
>
> Regarding g-boxes, I specifically want to avoid incorporating anything that
> suggests time variance into the semantics, because specifying semantics for
> temporal changes is explicitly out of scope for the existing RDF Semantics
> document.
>
> Here goes...
>
> 1. Graph Identification
> Let I be an IRI.  Define Graph(I) as a unary predicate such that Graph(I)
> implies that the resource identified by I is an RDF graph.  If desired, this
> can be described easily enough in RDF by defining a new class rdfs:Graph and
> mapping Graph(I) to the triple I rdf:type rdfs:Graph.
>
> Define G(I) as a function that returns the RDF graph identified by I.  In
> our parlance, G(I) is a g-snap, invariant over time.  Due to the nature of
> RDF, it is difficult to express the relationship between I and G(I) natively
> in RDF.  Graph literals, which I understand to be the encoding of some set
> of triples as a single node in a graph, are one possible approach but this
> proposal does not attempt to define graph literals.  Furthermore, in the
> open world it's not possible to have complete knowledge of all the triples
> in G(I) for any given I.
>
> 2. Graph Assertion
> Let I be an IRI and G be an RDF graph.  Define GA(I, G) as a binary
> predicate such that GA(I, G) implies (a) Graph(I) and (b) G(I) entails G.
>
> The notion of graph assertion attempts to capture the semantics of what
> happens when some set of triples is associated with a graph IRI in a
> multi-graph serialization such as TriG.  So the TriG fragment:
>
> :G1 { :a :b :c } .
>
> would be understood to construct a graph G with a single triple :a :b :c and
> then make the assertion GA(:G1 G).
>
> The use of "entails" as opposed to "equals" here is what gives us our
> flexibility.  Applications that want to treat named graphs as g-snaps,
> completely described by the triples associated with the graph IRI, can do so
> by extending (b) to say G(I) equals G instead of entails.  Because every
> graph entails itself, this extension is supported by these semantics, but
> this would not be required behavior.  Indeed, this could lead to trouble in
> the open world where you can have GA(I, G1) and GA(I, G2) with G1 != G2.
>
> Applications that want to treat named graphs as g-boxes would to so by
> essentially maintaining a (time-sensitive) mapping of IRI I to graph G.
>   This aligns pretty closely with my understanding of the notion of graph
> store from SPARQL 1.1 Update.  Poking the g-box to obtain content (either a
> g-text serialization or query results) amounts to asserting GA(I, G) for the
> current value of G at some point in time.  Given a new graph assertion for
> an IRI that is already mapped in the store, an implementation could replace
> the currently mapped graph with the new one (effectively discarding all
> prior graph assertions) or merge them at its discretion; either approach
> would be supported by these semantics.
>
> Any vocabulary for specifying graph literals and attaching them to a graph
> IRI in RDF would be defined as making a graph assertion, not setting the
> value of the identified graph.
>
> 3. RDF Datasets
> I haven't thought this part through entirely, but I think these semantics
> could be aligned with the existing notion of RDF datasets from SPARQL (and
> as proposed on the wiki) by simply mapping the (IRI, graph) tuples in the
> dataset to the appropriate graph assertions.
>
> 4. Graph Equality
> Because it is not the case that (G1 entails G and G2 entails G) implies G1 =
> G2, it is also not the case that (GA(I1, G) and GA(I2, G)) implies I1 and I2
> are the same graph.  Such a conclusion could be reached if you extend the
> definition of GA to mean equals instead of entails as discussed before, but
> again that is an extension and not part of the proposed semantics.
>
> 5. Empty Graphs
> Because every graph trivially entails the empty graph E, the assertion GA(I,
> E) is trivially true for every graph IRI I.  Making that assertion doesn't
> do anything beyond identify the resource denoted by I as a graph.
>
> 6. Graph Merges
> It follows from the definition of GA (and the definition of entails) that
> (GA(I, G1) and GA(I, G2)) implies GA(I, Merge(G1, G2)).  I think this gives
> us a pretty straightforward approach to merging of RDF datasets if this is
> required of the spec.
>
> Hope you find this useful...  or at least that this stirs up some
> interesting debate.
>
> Regards,
> Alex
>


-- 
Antoine Zimmermann
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Database Group
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Received on Friday, 8 April 2011 14:23:26 UTC