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RDF Terminology

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Gregg Kellogg edited this page Mar 18, 2023 · 2 revisions

RDF Terminology

Terms defined in RDF 1.1 Concepts:

Terms defined in RDF 1.1 Semantics:

  • class – It is convenient to state the RDFS semantics in terms of a new semantic construct, a class, i.e. a resource which represents a set of things in the universe which all have that class as a value of their rdf:type property.
  • D-entails – A graph is (simply) D-satisfiable or satisfiable recognizing D when it has the value true in some D-interpretation, and a graph S (simply) D-entails or entails recognizing D a graph G when every D-interpretation which satisfies S also D-satisfies G.
  • D-interpretation – A (simple) D-interpretation is a simple interpretation which satisfies the following conditions:
  • D-satisfiable – A graph is (simply) D-satisfiable or satisfiable recognizing D when it has the value true in some D-interpretation, and a graph S (simply) D-entails or entails recognizing D a graph G when every D-interpretation which satisfies S also D-satisfies G.
  • D-unsatisfiable – Unlike the case with simple interpretations, it is possible for a graph to have no satisfying D-interpretations i.e. to be D-unsatisfiable. RDF processors MAY treat an unsatisfiable graph as signaling an error condition, but this is not required.
  • Datatype map – The datatype map corresponding to the set D is the restriction of a D-interpretation to the set D.
  • Denotation – 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, itself called the denotation or referent.
  • Denotes – 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, itself called the denotation or referent.
  • Empty graph – The empty graph is the empty set of triples.
  • Entailment regime – Each semantic extension defines an entailment regime
  • Entail – Following standard terminology, we say that I (simply) satisfies E when I(E)=true, that E is (simply) satisfiable when a simple interpretation exists which satisfies it, otherwise (simply) unsatisfiable, and that a graph G simply entails a graph E when every interpretation which satisfies G also satisfies E.
  • Entails recognizing D – A graph is (simply) D-satisfiable or satisfiable recognizing D when it has the value true in some D-interpretation, and a graph S (simply) D-entails or entails recognizing D a graph G when every D-interpretation which satisfies S also D-satisfies G.
  • Equivalent – Following standard terminology, we say that I (simply) satisfies E when I(E)=true, that E is (simply) satisfiable when a simple interpretation exists which satisfies it, otherwise (simply) unsatisfiable, and that a graph G simply entails a graph E when every interpretation which satisfies G also satisfies E.
  • Extension – IEXT(x), called the extension of x, is a set of pairs which identify the arguments for which the property is true, that is, a binary relational extension.
  • Generalized RDF (RDFS) closure – Let S and E be RDF graphs. Define the generalized RDF (RDFS) closure of S towards E to be the set obtained by the following procedure.
  • GrdfD1 – G-RDF-D entailment pattern.
  • Ground – A ground RDF graph is one that contains no blank nodes.
  • Identify – 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.
  • Ill-typed – An ill-typed literal is one whose datatype IRI is recognized, but whose character string is assigned no value by the lexical-to-value mapping for that datatype.
  • Instance – Any graph obtained from a graph G by replacing some or all of the blank nodes N in G by M(N) is an instance of G.
  • Instance with respect to – An instance with respect to a vocabulary V is an instance in which all the names in the instance that were substituted for blank nodes in the original are names from V.
  • Interpolation – The interpolation lemma G simply entails a graph E if and only if a subgraph of G is an instance of E.
  • Interpretation – An interpretation is a mapping from IRIs and literals into a set, together with some constraints upon the set and the mapping.
  • Invalid – Any process which constructs a graph E from some other graph S is (simply) valid if S simply entails E in every case, otherwise invalid.
  • L2V – The function L2V maps datatypes to their lexical-to-value mapping.
  • Lean – An RDF graph is lean if it has no instance which is a proper subgraph of itself.
  • Merge – A related operation, called merging, takes the union after forcing any shared blank nodes, which occur in more than one graph, to be distinct in each graph. The resulting graph is called the merge. The merge of subgraphs of a graph may be larger than the original graph.
  • Merging – A related operation, called merging, takes the union after forcing any shared blank nodes, which occur in more than one graph, to be distinct in each graph. The resulting graph is called the merge. The merge of subgraphs of a graph may be larger than the original graph.
  • Monotonic – All entailment regimes MUST be monotonic extensions of the simple entailment regime described in the document, in the sense that if A simply entails B then A also entails B under any extended notion of entailment, provided that any syntactic conditions of the extension are also satisfied.
  • Name – A name is any IRI or literal.
  • Pre-interpretation – 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.
  • Proper instance – A proper instance of a graph is an instance in which a blank node has been replaced by a name, or two blank nodes in the graph have been mapped into the same node in the instance.
  • Proper subgraph – A proper subgraph is a proper subset of the triples in the graph.
  • RDF entail – S RDF entails E recognizing D when every RDF interpretation recognizing D which satisfies S also satisfies E.
  • RDF interpretation – An RDF interpretation recognizing D is a D-interpretation I where D includes rdf:langString and xsd:string, and which satisfies:
  • RDF unsatisfiable – E is RDF unsatisfiable (recognizing D) when it has no satisfying RDF interpretation (recognizing D).
  • rdfD1 – The RDF entailment pattern.
  • rdfD2 – Additional RDF entailment pattern.
  • RDFS entails – S RDFS entails E recognizing D when every RDFS interpretation recognizing D which satisfies S also satisfies E.
  • RDFS interpretation – An RDFS interpretation (recognizing D) is an RDF interpretation (recognizing D) I which satisfies the semantic conditions in the following table, and all the triples in the subsequent table of RDFS axiomatic triples.
  • RDFS vocabulary – The RDFS vocabulary.
  • rdfs1 – An RDFS entailment pattern.
  • rdfs2 – An RDFS entailment pattern.
  • rdfs3 – An RDFS entailment pattern.
  • rdfs4a – An RDFS entailment pattern.
  • rdfs4b – An RDFS entailment pattern.
  • rdfs5 – An RDFS entailment pattern.
  • rdfs6 – An RDFS entailment pattern.
  • rdfs7 – An RDFS entailment pattern.
  • rdfs8 – An RDFS entailment pattern.
  • rdfs9 – An RDFS entailment pattern.
  • rdfs10 – An RDFS entailment pattern.
  • rdfs11 – An RDFS entailment pattern.
  • rdfs12 – An RDFS entailment pattern.
  • rdfs13 – An RDFS entailment pattern.
  • Recognize – Datatypes are identified by IRIs. Interpretations will vary according to which IRIs are recognized as denoting datatypes. We describe this using a parameter D on simple interpretations, where D is the set of recognized datatype IRIs.
  • Referent – 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, itself called the denotation or referent.
  • Refers to – 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, itself called the denotation or referent.
  • Reification – Assuming that the IRI can be used to refer to the triple, then the reification vocabulary allows us to describe the first graph in another graph. The second graph is called a reification of the triple in the first graph.
  • Satisfiable – Following standard terminology, we say that I (simply) satisfies E when I(E)=true, that E is (simply) satisfiable when a simple interpretation exists which satisfies it, otherwise (simply) unsatisfiable, and that a graph G simply entails a graph E when every interpretation which satisfies G also satisfies E.
  • Satisfiable recognizing D – A graph is (simply) D-satisfiable or satisfiable recognizing D when it has the value true in some D-interpretation, and a graph S (simply) D-entails or entails recognizing D a graph G when every D-interpretation which satisfies S also D-satisfies G.
  • Satisfies – Following standard terminology, we say that I (simply) satisfies E when I(E)=true, that E is (simply) satisfiable when a simple interpretation exists which satisfies it, otherwise (simply) unsatisfiable, and that a graph G simply entails a graph E when every interpretation which satisfies G also satisfies E.
  • Semantic extension – A particular such set of semantic assumptions is called a semantic extension.
  • Simple interpretation – A simple interpretation I is a structure consisting of: 1) A non-empty set IR of resources, called the domain or universe of I. 2) A set IP, called the set of properties of I. 3) A mapping IEXT from IP into the powerset of IR x IR i.e. the set of sets of pairs < x, y > with x and y in IR . 4) A mapping IS from IRIs into (IR union IP), and 5) A partial mapping IL from literals into IR.
  • Skolemization – Skolemization is a transformation on RDF graphs which eliminates blank nodes by replacing them with "new" IRIs, which means IRIs which are coined for this purpose and are therefore guaranteed to not occur in any other RDF graph (at the time of creation).
  • Standardize – When graphs are formed by combining RDF from multiple sources, it may be necessary to standardize apart the blank node identifiers by replacing them by others which do not occur in the other document(s).
  • Subgraph – A subgraph of an RDF graph is a subset of the triples in the graph.
  • Unsatisfiable – Following standard terminology, we say that I (simply) satisfies E when I(E)=true, that E is (simply) satisfiable when a simple interpretation exists which satisfies it, otherwise (simply) unsatisfiable, and that a graph G simply entails a graph E when every interpretation which satisfies G also satisfies E.
  • Valid – Any process which constructs a graph E from some other graph S is (simply) valid if S simply entails E in every case, otherwise invalid.
  • Value space – The value space of a datatype is the range of the lexical-to-value mapping.
  • Vocabulary – A vocabulary is a set of names.
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