Abstract model of RDF layer 0

There is a set called atoms:

atoms Ì {alphabet defined by ISO/IEC 10646}*.

The alphabet defines a language - the RDF string values.

There is a set called Nodes:

Nodes = `C È`P.

The following steps result in a definition of `C and `P.

Note that "resources" and "property types" have to be semantically defined.

1.   C₀ = { "resources" - certain semantically defined elements from atoms }.
2.   C_i = È_{all a Î Ci-1} [T_a,2 (C_i-1)]. (Note T is defined below, in terms of C_i-1).
3.   There is a mapping prop(i) : C_i ® Nodes, s.t.
       (prop(i))(n) = { "property types" of n - certain semantically defined elements from atoms } for n Î C_i.
   
   
4.   Define P_i := (prop(i)(C_i).
5. `P = È_{all i} P_i.
6.   Define the operator T:
       T (C_k, i) : C_k ® P_i ´ C_k ´ C_k, such that,
       T (C_k, i) = {(t₁, t₂, t₃) | t₁ ÎP_i. t₂ ÎC_k, t₃ ÎC_k}.

   Note that for any (k,i) pair, T maps to a partial function. This function maps onto sets of triples.


7.   Then T_a,j (C_k), a subset of T (C_k, k), is given by:
       T_a,j (C_k) = {(t₁, t₂, t₃) | t_j = a, (t₁, t₂, t₃) Î T (C_k, k)},
       (if j = 1 then a Î P_k,
        if j = 2 or j = 3 then a Î C_k).
   
8. `C = È_{all i} C _i.

A description of a node n, a special case of T_n,a (`C), is defined to be:

T_n,2 (`C).

Note that substituting k := i - 1 in point 2 implies:

T_a,k(C_k) Ì C_{k + 1},

so that descriptions of a node from C_k are contained within C_{k + 1}, i.e.

T_n,2 : C_k ® C_{k + 1}.

---

Example:

A description of the resource n:

T_n,2 (C₀)

A meta-description of the resource n:

T _{Tn,2 (C0) ,2} (C₁),

which is equivalent to a description of the node T_n,2 (C₀).

In the above C₀ and C₁ may be replaced by `C. As is, the notation reflects that only resources will be contained within C₀ and descriptions (not meta-descriptions) within C₁.

---

Let S be the set of schemas.

For each i > 0 there is a surjective function schema(i), that is an instance of the operator schema that maps onto S, i.e. schema(i) : P_i ® S_i.

This defines the pair (p_i, s_i), i.e. each property of a (possibly multi-level) description corresponds to exactly one schema.