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Re: Comments on informal meaning of the RDFS vocabulary

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 3 Feb 2003 09:11:46 -0800
Message-Id: <p05111b05ba644d3343d6@[10.0.100.86]>
To: w3c-rdfcore-wg@w3.org

Concerning the notion of 'well-formed' lists, there is a 
characterization of the RDF graphs which describe such lists in the 
relevant section of the semantics document.  Here is a more exact and 
careful statement of that characterization.

Define a 'link' in a graph G to be a subgraph consisting of two 
triples of the form

aaa rdf:first bbb .
aaa rdf:rest ccc .

where ccc may be rdf:nil, but otherwise aaa and ccc are bnodes or 
urirefs which are not in the RDFS namespace. Call aaa the *addr* of 
the link, bbb the *head* of the link, and ccc the *tail* of the link. 
Define a 'line' in G to be a finite subgraph of G consisting of links 
and satisfying the following conditions: exactly one link in the line 
has rdf:nil as its tail; otherwise, every link's tail is the addr of 
exactly one other link in G; one link in the line has an addr which 
is not a tail of any other link - call this the *addr of the line* - 
and otherwise, the addr of every link in the line is the tail of 
exactly one other link in G; and no addr or tail (except rdf:nil) in 
the line occurs as the subject or object of rdf:first or rdf:rest 
elsewhere in G.

Given any line, the sequence of denotations of the heads of links 
obtained by starting with the addr of the line and following the 
tails in order, is the *list denoted by the line*. Semantic 
extensions of RDF may well want to require that addrs of lines denote 
the list denoted by the line.

This allows the heads of links to be the addrs of other lines, so it 
allows arbitrary S-expressions, in LISP parlance. To restrict oneself 
to 'linear' lists, add the condition that no head of any link in the 
line occur as the subject of any rdf collection property in G.

Pat

PS. I have not sent this directly to rdf:comments, but feel free to 
do so, Brian.

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Received on Monday, 3 February 2003 12:10:06 EST

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