- From: Peter F. Patel-Schneider <pfpschneider@gmail.com>
- Date: Sat, 12 Oct 2013 06:05:03 -0700
- To: Pat Hayes <phayes@ihmc.us>
- CC: RDF Working Group <public-rdf-wg@w3.org>
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.
Received on Saturday, 12 October 2013 13:05:39 UTC