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Re: changes proposed in Semantics for ISSUE-159 (was Re: Proposed response to ISSUE-159)

From: Pat Hayes <phayes@ihmc.us>
Date: Sun, 13 Oct 2013 00:22:42 -0500
Cc: RDF Working Group <public-rdf-wg@w3.org>
Message-Id: <A70B9782-127B-49A5-B573-F1BF363564E7@ihmc.us>
To: "Peter F. Patel-Schneider" <pfpschneider@gmail.com>
This all works, but how about the following alternative strategy, which more directly fits with David's request. Insert a new second paragraph of section 4 as follows:

An <em>interpretation</em> is a mapping from IRIs into a set, together with some constraints upon the set and the mapping. This document defines various notions of interpretation, each corresponding in a standard way to an entailment regime. These are identified by prefixes such as <em>simple interpretation</em>, <em>D-interpretation</em>, RDF interpretation, etc. and are defined in later sections. The unqualified term <em> interpretation</em> may be used to refer to all or some of these, depending upon the context. 

Would that be enough, do you think?

On Oct 12, 2013, at 8:05 AM, Peter F. Patel-Schneider wrote:

> Here are the unqualified and incorrectly qualified uses of the word
> "interpretation" that I found in RDF Semantics, with proposed *additions* and
> *segnahc/changes*.  [My comments are in brackets.]
> I think that these are all editorial, so I *only* need Pat's approval.  :-)
> peter
> 4. Notation and Terminology
> The words denotes and refers to are used interchangeably as synonyms for the
> relationship between an IRI or literal and what it refers to in a given
> interpretation *as defined in this document*, itself called the referent or
> denotation. IRI meanings may
> also be determined by other constraints external to the RDF semantics; when
> we wish to refer to such an externally defined naming relationship, we will
> use the word identify and its cognates. For example, the fact that the IRI
> http://www.w3.org/2001/XMLSchema#decimal is widely used as the name of a
> datatype described in the XML Schema document [XMLSCHEMA11-2] might be
> described by saying that the IRI identifies that datatype. If an IRI
> identifies something it may or may not refer to it in a given
> interpretation, depending on how the semantics is specified. For example, an
> IRI used as a graph name identifying a named graph in an RDF dataset may
> refer to something different from the graph it identifies.
> 5. Simple Interpretations
> This section defines the basic notions of *simple* interpretation and truth for RDF
> graphs. All semantic extensions of any vocabulary or higher-level notation
> encoded in RDF MUST conform to these minimal truth conditions. Other
> semantic extensions may extend and add to these, but they MUST NOT modify or
> negate them. For example, because *simple* interpretations are mappings which apply
> to IRIs, a semantic extension cannot interpret different occurrences of a
> single IRI differently.
> The 2004 RDF 1.0 semantics defined *simple* interpretations relative to a vocabulary.
> *Simple* Interpretations are required to interpret all names, and are therefore
> infinite.
> The denotation of a ground RDF graph in an *simple* interpretation I is then given by
> the following rules, where the interpretation is also treated as a function
> from expressions (names, triples and graphs) to elements of the universe and
> truth values:
> Semantic extensions may impose further constraints upon interpretation
> mappings by requiring some IRIs to refer in particular ways. For example,
> D-interpretations, described below, require some IRIs, understood as
> identifying and referring to datatypes, to have a fixed *interpretation/denotation*.
> 5.1 Blank Nodes
> Suppose I is an *simple* interpretation and A is a mapping from a set of blank nodes
> to the universe IR of I.
> Mappings from blank nodes to referents are not part of the definition of an
> *simple* interpretation, since the truth condition refers only to some such mapping.
> Blank nodes themselves differ from other nodes in not being assigned a
> denotation by an *simple* interpretation, reflecting the intuition that they have no
> 'global' meaning.
> For example, consider
> the overlapping graphs and an *simple* interpretation I over the universe {Alice,
> Bob, Monica, Ruth} with: I(ex:Alice)=Alice, I(ex:Bob)=Bob,
> IEXT(I(ex:hasChild))={<Alice,Monica>,<Bob,Ruth> }
> 5.3 Simple Entailment
> Following standard terminology, we say that I satisfies E when I(E)=true,
> that E is *simply* satisfiable when an *simple* interpretation exists which satisfies it,
> (otherwise unsatisfiable), and that a graph G simply entails a graph E when
> every *simple* interpretation which satisfies G also satisfies E.
> In later sections these notions will be adapted to other classes of
> interpretations, but throughout this section 'entailment' should be
> interpreted as meaning simple entailment.
> 5.4 Properties of simple entailment (Informative)
> This does not hold for extended notions of interpretation. For example, a
> graph containing an ill-typed literal is D-unsatisfiable.
> 7. Literals and datatypes
> Datatypes are identified by IRIs. Interpretations will vary according to
> which IRIs they recognize as denoting datatypes. We describe this using a
> parameter D on *simple* interpretations. where D is the set of recognized datatype
> IRIs.
> In the 2004 RDF 1.0 specification, the semantics of datatypes referred to
> datatype maps. The current treatment subsumes datatype maps into the
> interpretation mapping on recognized IRIs.
> 7.1 D-interpretations
> [Before RDF interpretations are defined.]
> The *built-in RDF/special* datatype rdf:langString has no ill-typed literals. Any
> syntactically legal literal with this type will denote a value in every *RDF
> interpretation/D-interpretation where D includes rdf:langString*.
> 9. RDFS Interpretations
> Classes are defined to be things of type rdfs:Class, and the set
> of all classes in an *RDFS* interpretation will be called IC.
> Other triples which must be true in all *rdfs-interpretations/RDFS
> interpretations* include the following.
> A. Entailment rules (Informative)
> The semantics
> described in this document applies to the generalization without change, so
> that the notions of interpretation, satisfiability and entailment can be
> used freely.
> B. Finite interpretations (Informative)
> To keep the exposition simple, the RDF semantics has been phrased in a way
> which requires interpretations to be larger than absolutely necessary. For
> example, all interpretations are required to interpret the whole IRI
> vocabulary, and the universes of all D-interpretations *where D contains
> xsd:string* must contain all possible strings and therefore be infinite.
> Basically, it is only necessary for an interpretation structure to interpret
> the names actually used in the graphs whose entailment is being considered,
> and to consider interpretations whose universes are at most as big as the
> number of names and blank nodes in the graphs. More formally, we can define
> a pre-interpretation over a vocabulary V to be a structure I similar to a
> simple interpretation but with a mapping only from V to its universe
> IR. Then when determining whether G entails E, consider only
> pre-interpretations over the finite vocabulary of names actually used in G
> union E. The universe of such a pre-interpretation can be restricted to the
> cardinality N+B+1, where N is the size of the vocabulary and B is the number
> of blank nodes in the graphs. Any such pre-interpretation may be extended to
> simple interpretations, all of which which will give the same truth values
> for any triples in G or E. Satisfiability, entailment and so on can then be
> defined with respect to these finite pre-interpretations, and shown to be
> identical to the ideas defined in the body of the specification.
> C. Proofs of some results (Informative)
> The empty graph is true in all *simple* interpretations, so is entailed by any
> graph.  If G contains a triple <a b c>, then any *simple* interpretation I with
> IEXT(I(b))={ } makes G false; so the empty graph does not entail G. QED.
> If a subgraph E' of G is an instance of E then G entails E' which entails E,
> so G entails E. *NOw/Now* suppose G entails E, and consider the Herbrand
> interpretation I of G defined as follows.
> D.1 Reification
> For example, the triple might be part of an ontology describing animals,
> which could be satisfied by an interpretation in which the universe
> contained only animals, and in which a reification of it was therefore
> false.
> D.2 RDF containers
> However, these informal *interpretations/conditions* are not reflected in any formal RDF
> entailments.
> They may exclude interpretations of the collection vocabulary which violate
> the convention that the subject of a 'linked' collection of two-triple items
> of the form described above, ending with an item ending with rdf:nil,
> denotes a totally ordered sequence whose members are the denotations of the
> rdf:first values of the items, in the order got by tracing the rdf:rest
> properties from the subject to rdf:nil. This permits sequences which contain
> other sequences.

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Received on Sunday, 13 October 2013 05:23:08 UTC

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