From: Dan Connolly <connolly@w3.org>

Date: Thu, 27 Sep 2001 10:40:57 -0500

Message-ID: <3BB34889.C4A0063E@w3.org>

To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>

CC: phayes@ai.uwf.edu, www-rdf-logic@w3.org

Date: Thu, 27 Sep 2001 10:40:57 -0500

Message-ID: <3BB34889.C4A0063E@w3.org>

To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>

CC: phayes@ai.uwf.edu, www-rdf-logic@w3.org

"Peter F. Patel-Schneider" wrote: [...] > Syntax: > > URI is the collection of URI names, i.e., some collection of strings > > [NB: This ignores all aspects of the structure of URIs.] > > L is the collection of literals, i.e., some collection of strings, > disjoint from URI I think the mention of "string" here is a misnomer/red-herring, no? i.e. take the string "http://example/". It's a URI, and you say URIs are disjoint from literals... hence it's not a literal. But it's a perfectly legal property value in RDF: <rdf:Description rdf:about="#something"> <dc:identifier>http://example/</dc:identifier> </rdf:Description> I think if you just say URI and L are disjoint, denumerable sets, you've said what you need to say. > [NB: This ignores non-string literals, but they wouldn't cause > any more problems.] > Literal Values: > > LV is a non-empty set, currently the set of strings. again, why bother mentioning "strings"? > XL : L -> LV, giving meaning to literals > > [NB: This ignores many aspects of the intended meaning of strings, > such as whether the mapping is surjective or injective.] > > Interpretations: > > Let V be a subset of URI. > > [NB: Does V have to be non-empty, does it have to be finite? So far > there are no such requirements, but we have to be careful that this > is OK, and that we don't make unnecessary requirements on V.] > > An interpretation, I, on a vocabulary V, is a four-tuple < IR, IP, IEXT, IS> > where IR is a non-empty set, called resources > IP <= IR, called properties > IEXT : IP -> powerset ( IR x (IR u LV) ) > IS : V -> IR > > [NB: There is no requirement that IR and LV be disjoint nor is there any > requirement that they be subsets of one another. We have to be > careful that this is OK, and that we don't accidentally disturb this > (non-)relationship.] > > Interpretations of ground basic untidy RDF graphs: > > Let R = < N, E, LN, LE > be a ground basic untidy RDF graph. > > [NB: There appears to be no harm in allowing untidy graphs here, but this > could easily be restricted to tidy graphs.] restricting to tidy graphs would be my preference. I'm not sure exactly why just now... > An interpretation I on the vocabulary V with > { LN(n) | n in N } ^ URI <= V > { LN(e) | e in E } <= V > is extended to R as follows > > [NB: I am being a bit vague here in just what is the domain of I.] > > [NB: It is explicit here that the vocabulary of the interpretation can > have ``names'' that do not appear in the graph. Pat's theory is > vague on this point.] > > 1. if LN(n) is defined and in L then I(n) = XL(LN(n)) > > 2. if LN(n) is defined and in V then I(n) = IS(LN(n)) > > [NB: These two give an interpretation for all nodes in R.] > [NB: The ``defined'' part is used later.] > > 3. if <f,g> is in E > then I(E) = true you mean I(<f,g>) rather than I(E), no? > if IS(LE(<f,g>)) in IP and <I(f),I(g)> in IEXT(IS(LE(<f,g>))), > I(E) = false otherwise > > [NB: This cleans up the meaning of edges whose labels are not mapped to > properties. Ah! now I understand your earlier comment about that. > It might also be possible to make graphs with such > edges ill-formed in some way.] > > 4. I(R) = false if I(e) = false for some e in E, > I(R) = true otherwise > > Interpretations of basic untidy RDF graphs: > > [NB: I'm writing out extended interpretations completely for purposes of > being completely pedantic. > > An extended interpretation on a vocabularly V is a two-tuple > <<IR,IP,IEXT,IS>,A'> > where <IR,IP,IEXT,IS> is an interpretation on V > and A' is a mapping to IR. > > [NB: This means that unnamed nodes have to be resources, not literals > that are not resources. This may have consequences!] > > Let R = < N, E, LN, LE > be a basic untidy RDF graph and > let U = { n in N | LN(n) is not defined } > > An extended interpretation I = <<IR,IP,IEXT,IS>,A'> on the vocabulary V with > { LN(n) | n in N } ^ URI <= V > { LN(e) | e in E } <= V > and the domain of A' = U > is extended to R as follows > > 0. if LN(n) is not defined I(n) = A'(n) > > 1. if LN(n) is defined and in L then I(n) = XL(LN(n)) > > 2. if LN(n) is defined and in V then I(n) = IS(LN(n)) > > 3. if <f,g> is in E > then I(E) = true if IS(LE(<f,g>)) in IP and <I(f),I(g)> in IEXT(IS(LE(<f,g>))), > I(E) = false otherwise > > 4. I(R) = false if I(e) = false for some e in E, > I(R) = true otherwise > > Let R = < N, E, LN, LE > be a basic untidy RDF graph and > let U = { n in N | LN(n) is not defined } > > An interpretation I = <IR,IP,IEXT,IS> on the vocabulary V with > { LN(n) | n in N } ^ URI <= V > { LN(e) | e in E } <= V > is extended to R as follows: > > I(R) = true if there is some mapping A' from U to IR such that <I,A'>(R) = true, > I(R) = false otherwise > > An interpretation I with vocabulary V is called a model of a > basic untidy RDF graph R = <N,E,LN,LE> iff > 1. { LN(n) | n in N } ^ URI <= V > { LN(e) | e in E } <= V, and > 2. I(R) = true > > Taking care of rdf:type: > > A core RDF interpretation, i.e., RDF without reification or containers, is > an interpretation over a vocabularly that includes rdf:type with the > following extra conditions > > 1. IS(rdf:type) is in IP > 2. IEXT(IS(rdf:type)) <= IR x IR > > Now for the claims: > > All these sorts of claims have to be backed up with theorems and lemmas > like the ones that Pat has. I would go even further than Pat has, > extending to RDF query languages, at least whenever such become > well-defined. > > Claim 1: > > A core RDF interpretation that is a model of a basic untidy RDF graph R > contains everything (and more) that is in the intended core RDF (i.e., RDF > without reification or containers) meaning of R. In other words, a model > contains all the information implicitly (or explicity) in the graph, and > maybe more, and contradicts nothing that is implicitly (or explicitly) in > the graph. Hmm... at this point, the formality fails me. I would need an example to provide intiutions about whether I believe this or not. > Claim 2: > > A core RDF interpretation that is not a model of a basic untidy RDF graph R > has something that is not compatible the intended core RDF meaning of R. > In other words, a non-model is missing or incorrect on something that is > implicitly (or explicitly) in the graph. That makes sense relative to claim 1 (though I don't have a good feel for claim 1 itself). > Claim 3: > > For every basic untidy RDF graph R there is a core RDF interpretation that > captures exactly the closure of the intended core RDF meaning of R and that > is a model for R. That is, roughly, that there is a model that makes > everything implicitly (or explicitly) in the graph true, and everything > else false. I have no idea what the significance of this claim is, let alone any sense of whether I agree or disagree with it. > [NB: This claim is not true for more-powerful representation systems.] -- Dan Connolly, W3C http://www.w3.org/People/Connolly/Received on Thursday, 27 September 2001 11:41:08 UTC

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