RDF Layer 0-1

Layer 0

Definitions

• atoms Ì {alphabet defined by ISO/IEC 10646}*.
• Nodes = { semantically defined elements from atoms & constructions of these elements }.
• PropertyTypes = { semantically defined elemets from atoms } Ì Nodes.
• Triples = {(t₁,t₂,t₃) | t₁ Î PropertyTypes, t₂Î Nodes, t₃Î Nodes È {atoms}}.

Notes on definitions

• atoms defines a language consisting of the RDF string values.
• Nodes contains some representations of semantically defined "resources".
• atoms is a subset of Nodes.
• A triple from Triples represents "knowledge" about a node.

Development

Define-

T_a,j := {(t₁,t₂,t₃) | t_j = a for (t₁,t₂,t₃) Î Triples} for j = 1, 2, 3,
(if j = 1 then a ÎPropertyTypes,
 if j = 2 then a ÎNodes,
 if j = 3 then a ÎNodes È {atoms}).

Then the description of a node n is defined to be T_n,2.

A description is a node, i.e.T_n,2 Î Nodes " n Î Nodes.

There is a (partial) function that defines the pair (p_i, S_i), where p _i Î {t₁ | (t₁,t₂,t₃) Î T_n,2} Ì PropertyTypes. S_i is the (only) schema corresponding to p_i. Note that the p_i are the property types of the description of node n.

A schema is identified by a URI [ !the mapping is not specified ?! ]

Layer 1

Definitions

• {RDF:InstanceOf, RDF:PropName, RDF:PropObj, RDF:Value} Ì PropertyTypes.
• {RDF:Property, RDF:Seq, RDF:Bag, RDF:Alt} Ì Nodes \ PropertyTypes.
• Ord := {RDF:N, N Î (1,2,3, ...)} Ì PropertyTypes.

Development

In layer 1 we work within a subset Tr of Triples:

Tr = T_{RDF:InstanceOf, 1} \ T_{atoms},3,
where T_{atoms},3 := È_{aÎ {atoms}} T_a,3.

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

È	(Ti,1 Ç Tn,2 Ç Tj,3),
i = RDF:PropName, j = t1 i = RDF:PropObj, j = t2 i = RDF:PropValue, j = t3 i = RDF:InstanceOf, j = t4.

Collections of nodes N = (n₁, n₂, ..., n_k) are modelled as a description, C Ì T_n,2, of an arbitrary node n.

There is an injection, m: N ® Ord È {undef} (for undef Î Nodes).

C is then defined:

C := {(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 },

where (RDF:1, n, n₁) Î C Û C ' (RDF:Alt, n, a).