UKOLN 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.   Ci = Èall a Î Ci-1 [Ta,2 (Ci-1)]. (Note T is defined below, in terms of Ci-1).
  3.   There is a mapping prop(i) : Ci ® Nodes, s.t.
        (prop(i))(n) = { "property types" of n - certain semantically defined elements from atoms } for n Î Ci.

  4.   Define Pi := (prop(i)(Ci).
  5. `P = Èall i Pi.
  6.   Define the operator T:
        T (Ck, i) : Ck ® Pi ´ Ck ´ Ck, such that,
        T (Ck, i) = {(t1, t2, t3) | t1 ÎPi. t2 ÎCk, t3 ÎCk}.

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

  8.   Then Ta,j (Ck), a subset of T (Ck, k), is given by:
        Ta,j (Ck) = {(t1, t2, t3) | tj = a, (t1, t2, t3) Î T (Ck, k)},
        (if j = 1 then a Î Pk,
         if j = 2 or j = 3 then a Î Ck).
  9. `C = Èall i C i.

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

Tn,2 (`C).

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

Ta,k(Ck) Ì Ck + 1,

so that descriptions of a node from Ck are contained within Ck + 1, i.e.

Tn,2 : Ck ® Ck + 1.


A description of the resource n:
Tn,2 (C0)
A meta-description of the resource n:
T Tn,2 (C0) ,2 (C1),
which is equivalent to a description of the node Tn,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) : Pi ® Si.

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