Re: The Mel99 semantics for RDF

Dan:

thanks for bringing up the issues dealing with the algebraic spec. I
think the algebraic interpretation has a certain value in that it lowers
the expectations ;)

Peter:

I appreciate your comments. In fact, I do like your et al spec at

	http://www.daml.org/2001/03/model-theoretic-semantics.html

It is definitely more powerful in explaining things than the algebraic
spec. However, as indicated in my previous posting, I still wonder
whether it is possible to interpret classes as individuals rather than
sets of individuals.

Sergey


"Peter F. Patel-Schneider" wrote:
> 
> I have a number of problems with your summarization of Melnik's interesting
> algebraic specification for RDF.
> 
> I think that your summarization has a lot more in it that Melnik's
> specification does.  Melnik does not mention URI's at all.  Melnik does not
> talk about variables, existentially quantified or otherwise.
> 
> Melnik's algebraic structure is, in essence, a set of statements, and is
> not a graph of any shape or form.
> 
> Melnik distinguishes between resources and literals in many places.  The
> distinction forms a major portion of his algebraic specification.
> 
> Melnik has a PARTIAL map from statements to their reification, not a total
> map.
> 
> Melnik's specification is an algebraic specification.  In general this
> implies that a KB (or whatever you want to call it) maps to a specific
> structure, namely the one that has the statements from the KB.  On the
> other hand, model theoretic semantics generally have a many-to-many
> satisfaction relationship between KBs and semantic structures.  It makes
> sense in model-theoretic semantics to talk about interpretations satisfying
> different KBS, and thus makes sense to talk about the ``principle of
> erasure'' or monotonicity.  Such notions are harder to define in algebraic
> specifications---you have to talk about an algebraic structure having more
> information than another.
> 
> In general, algebraic specification can be used to provide meaning for
> logics.  However, for logics that have non-trivial inference, algebraic
> specification begins to look a lot like axiomatic specification.  (You need
> to talk about something like saturated sets of statements, i.e., sets of
> statements that contain all their conclusions.)  For this, and other,
> reasons I prefer model-theoretic semantics.
> 
> Peter Patel-Schneider
> Bell Labs Research

Received on Wednesday, 30 May 2001 21:49:47 UTC