- From: Sergey Melnik <melnik@db.stanford.edu>
- Date: Wed, 30 May 2001 19:15:09 -0700
- To: www-rdf-logic@w3.org
- CC: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, connolly@w3.org
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