graph ::= *(triple)
triple ::= no-lit-term iri term
no-lit-term ::= iri | bnode | quoted-triple-term
term ::= no-lit-term | literal
quoted-triple-term ::= CG-qtt | CG-TEP-qtt | ASS-qtt
CG-qtt ::= no-lit-term iri term
CG-TEP-qtt ::= no-lit-term iri term
ASS-qtt ::= no-lit-term iri term

Terms are denoted by r, triples by t, and graphs by g.
Given a triple or quoted triple term a, we denote the subject, predicate, and object of a as a.s, a.p, and a.o, respectively.

• CG quoted triple terms have opaque IRIs and Literals, transparent BNodes, and opaque properties:

  << dbr:Linköping dbo:populationTotal "104232"^^xsd::nonNegativeInteger >>
      :type rdf-star:triple ;
      :source <https://dbpedia.org/data/Linköping.ttl> .
  

• CG-TEP quoted triple terms have transparent IRIs, Literals, and BNodes, and opaque properties:

  rdf:type rdf:type rdf-star:TransparencyEnablingProperty .
  :measuredOn rdf:type rdf-star:TransparencyEnablingProperty .
  << dbr:Linköping dbo:populationTotal "104232"^^xsd::nonNegativeInteger >>
      :type rdf-star:statement ;
      :measuredOn "2010-12-31"^^xsd:date .
  

• ASS quoted triple terms have transparent IRIs, BNodes, and Literals, and transparent properties - this captures the representation of events and of n-ary relations:

  <<< :john :teaches :cs101 >>> 
       rdf:type rdf-star:event ; 
       rdf:type :teaching ; 
       dct:Location dbr:Stanford_University .
  

An RDF-star interpretation I is a structure:

< < IR, IP, ISASS, ILASS, IEXTASS >, ITASS ,
    < IR, IP, ISCG, ILCG, IEXTCG >, ITCG ,
    < IR, IP, ISCG-TEP, ILCG-TEP, IEXTCG-TEP >, ITCG-TEP >

such that (with i ∈ {ASS,CG,CG-TEP}):

• Each < IR, IP, ISi, ILi, IEXTi > is a RDF 1.1 simple interpretation.
  
• The interpretation of a graph without quoted triple terms is reduced to the RDF 1.1 simple interpretation:
       < IR, IP, ISASS, ILASS, IEXTASS >.
  
• Each ITi interprets quoted triple terms as resources,
      namely it is a mapping from IRxIPxIR to IR, satisfying in addition:
      ∀ <x,y,z> ∈ dom(ITi). <x,z> ∈ IEXTi(y).
  
• IRIs and literals are transparent in CG-TEP quoted triple terms_, namely:
      ISCG-TEP = ISASS and ILCG-TEP = ILASS.

• A is (the only) mapping from blank nodes to IR;
      therefore blank nodes are transparent in quoted triple terms.
  

Given I and A, the function [Ii+A](.) is defined over terms, triples, and graphs as follows.

• [Ii+A](r) = ILi(r) if r is a literal
  
• [Ii+A](r) = ISi(r) if r is a IRI
  
• [Ii+A](r) = A(r) if r is a blank node
  
• [Ii+A](r) = ITCG(<[ICG+A](r.s),[ICG+A](r.p),[ICG+A](r.o)>)
      if r is a CG quoted triple term
  
• [Ii+A](r) = ITCG-TEP(<[ICG-TEP+A](r.s),[ICG-TEP+A](r.p),[ICG-TEP+A](r.o)>)
      if r is a CG-TEP quoted triple term_
  
• [Ii+A](r) = ITASS(<[IASS+A](r.s),[IASS+A](r.p),[IASS+A](r.o)>)
      if r is an ASS quoted triple term
  

• [IASS+A](t) = TRUE if and only if <[IASS+A](t.s),[IASS+A](t.o)> ∈ IEXTASS(ISASS(t.p))
  

• [IASS+A](g) = TRUE if and only if ∀ t ∈ g . [IASS+A](t) = TRUE
  

An interpretation I is called a model for g if there exists A such that [IASS+A](g) = TRUE.

Simple entailment: g ⊨ g' if and only if models(g) ⊆ models(g').

( A review of the standard semantics of RDF 1.0: semantics of RDF.pdf ).