- From: Paul Gearon <gearon@itee.uq.edu.au>
- Date: Thu, 7 Apr 2005 10:11:54 +1000
- To: www-rdf-logic@w3.org
I need to respond to what everyone has said about cardinality (thanks for the responses!), but I thought I'd better write up something on the approach that I've been taking. That may help me clear up some of my fundamental misconceptions, and ease the rest of my process of understanding. I'll confess that my terminology may not always be appropriate. Terminology can be confusing, as different sources define certain concepts with subtle differences. For instance, one source I have defines consistent expressions as being true under at least one interpretation, while another source defines it as "Having no contradictions." These end up being equivalent for most systems, but there are subtle differences (according to one professor I know), that I only have a vague grasp of. My other problem is relating statements in an RDF database to predicate logic. Again different people have subtly different ways of doing this mapping. The standard meaning of "interpretation" is substituting values into each variable of a set of formulae (this assumes you accept a specified meaning for the operations, and you don't have to interpret them as well). Since a database contains statements without variables, then perhaps it is inappropriate to refer to an "interpretation" in this context? In what I wrote last time, I chose to use "interpretation" to mean: "The entire sum of RDF statements which exist in the real world". Hence, if the model in the database was the single statement: <ns:entity_1> <owl:sameAs> <ns:entity_2> Then in one interpretation, a statement might exist in the real world which says: <ns:entity_1> <owl:differentFrom> <ns:entity_2> Of course, this "interpretation" contains a contradiction, and so it is inconsistent. A consistent "real world" could not contain this extra expression, and so I ignore those interpretations. I only consider the interpretations which hold consistent statements. Of course, there are an infinite number of such interpretations, though the possibilities are diminished as I put more data into the database. In response to some questions that I've been given I'm thinking that I should not have used "interpretation" for this. Instead, I should probably re-orient the question to refer to consistent and "unknown" conditions, instead of an infinite set of statements which when combined (say with ⋀) evaluate to true or false. Comments appreciated. Regards, Paul Gearon
Received on Thursday, 7 April 2005 00:12:19 UTC