Abstract model of RDF layer 1

Layer 1 theory assigns meaning to the atoms contained within the following subsets:

• P₀ É {RDF:InstanceOf, RDF:PropName, RDF:PropObj, RDF:Value}.
• P₀ É Ord := {RDF:N, N =1, 2, 3, ...}.
• C₀ É {RDF:Property, RDF:Seq, RDF:Bag, RDF:Alt}.

Reification

Define a set Triples that is the union of T(`C, i) for all i:

Triples := T(`C, N) where N is the set of natural numbers.

The reification of a triple t = (t₁, t₂, t₃) Î Triples is a description of some node n given by:

È	(Ti,1(`C, N ) Ç Tn,2(`C, N ) Ç Tj,3(`C, N )),
i = RDF:PropName, j = t1 i = RDF:PropObj, j = t2 i = RDF:PropValue, j = t3 i = RDF:InstanceOf, j = t4, and N is the set of natural numbers.

Collections of nodes

A collection of nodes list = (n₁, n₂, n₃, ..., n_k) is modelled as a description of an arbitrary node n. Call this description collection, then:

collection Ì T_{n, 2} (`C).

There is an injection, m: N ® Ord È {undef} (for undef Î atoms) and collection is defined:

collection := {(RDF:InstanceOf, n, a), a Î {RDF:Seq, RDF:Bag, RDF:Alt}} È {(m (n_i), n, n_i), 1 £ i £ k, m (n_i) ¹ undef },

and (RDF:1, n, n₁) Î C if and only if C ' (RDF:Alt, n, a).