From: Ivan Herman <ivan@w3.org>

Date: Mon, 22 Oct 2007 13:35:20 +0200

Message-ID: <471C8AF8.4090704@w3.org>

To: Jeremy Carroll <jjc@hpl.hp.com>

CC: public-owl-wg@w3.org

Date: Mon, 22 Oct 2007 13:35:20 +0200

Message-ID: <471C8AF8.4090704@w3.org>

To: Jeremy Carroll <jjc@hpl.hp.com>

CC: public-owl-wg@w3.org

Jeremy, thanks. I now understand what you mean by non-deterministic but (bear with me:-), can you give an example on: [[[ The non-determinism that was gradually introduced during the OWL 1.0 development, while being horrible from some point of view, fixed the underlying granularity problem, because the non-determistic rules are about aligning equivalence classes of trees with equivalence classes of graphs, rather than individual trees with individual graphs. ]]] That would help in understanding the issue for more specific cases... Thanks a lot Ivan Jeremy Carroll wrote: > > Ivan Herman wrote: >> Jeremy, >> >> I am not ashamed to acknowledge my own missing technical knowledge...:-) >> could you explain (or give specific references) to your points (b) and >> (c) below? >> > > I've been struggling to articulate point (b) to myself today, this is > where I've got to. I'll try and articulate better on Monday, and also > address (c) next week. > > I am having to think quite hard to justify the concern - so this is a > first attempt. > > In this first attempt I will pretend that the resolution of webont issue > 5.3 was iff rather than the actual if-then. > http://www.w3.org/2001/sw/WebOnt/webont-issues.html#I5.3-Semantic-Layering > > I will use iff* for a pretend iff, that refers back to this point, etc. > > (More on this point next week I guess). > > > >> Thanks >> >> Ivan >> >> Jeremy Carroll wrote: >>> >>> b) In OWL 1.0, the tension between the OWL Full semantics and the direct >>> semantics is resolved in cleverly non-deterministic mapping rules >>> > > The OWL DL vs OWL Full issue in v 1.0 is resolved in the following way: > > There is an OWL DL syntax and semantics: abstract syntax trees (AST) and > the direct semantics. > > There is an OWL Full syntax and semantics: graphs and the RDFS > compatible semantics. > > For each of these, we can form equivalence classes of ontologies that > have the same meaning: > > i.e. > > ASTs t1 and t2 are equivalent if t1 entails t2 and t2 entails t1 under > the direct semantics > > Graphs g1 and g2 are equivalent if g1 entails g2 and g2 entails g1 under > the RDFS compatible semantics. > > The mapping rules relate ASTs with Graphs in a way that aligns the > semantics. So if > t1 m g1 > and > t3 m g3 > then > t1 direct-entails t3 iff* g1 full-entails g3 > > Overall we get a relationship between the equivalence relationships over > ASTs and over graphs, via the mapping rules. > > i.e. If > > g1 m t1 > > g2 m t2 > > then > > { > > t1 ~ t2 > > iff > > g1 ~ g2 > > } > > [I still need to think through the iff* issue here] > > Thus any subset of an equivalence class of trees is mapped to a subset > of equivelance class of graphs, and conversely. > > Some of the equivalent ASTs will be equivalent becasue of syntactic > variation in trees that does not correspond to a syntactic variation of > graphs. > > Some of the equivalent graphs will be equivalent becasue of syntactic > variation in graphs that does not correspond to a syntactic variation of > trees. > > Some of the equivalent graphs will have corresponding equivalent trees > in which the syntactic variations are similar. > > If the mapping rules are too strict then each graph and each tree will > map to only a small number (e.g. 0, 1 or 2) of trees or graphs. > If the mapping rules are looser (non-deterministic) then much of the > equivalence relationships are built into the mapping rules. > > > With strict (deterministic) rules, the following are likely: > a) large numbers of graphs which have no equivalent trees > b) no easy to articulate rationale for which graphs have trees and which > don't > c) unnecessary algorithmic complexity in determining whether a > particular graph does or does not have a tree representation > > > All three of these issues arose in OWL 1.0 development, and in my > opinion, they all are derivative from the overall problem framework, and > are symptons of trying to align the trees and graphs in too fine grain a > fashion. The non-determinism that was gradually introduced during the > OWL 1.0 development, while being horrible from some point of view, fixed > the underlying granularity problem, because the non-determistic rules > are about aligning equivalence classes of trees with equivalence classes > of graphs, rather than individual trees with individual graphs. > > Hmmmm - that's where I've got to today, but it doesn't feel like what I > wanted to say at all! I've moved from semantic articulation to the > syntactic .... > > I'll try again Monday. > > Jeremy > > > > > > > > > > > > > -- Ivan Herman, W3C Semantic Web Activity Lead Home: http://www.w3.org/People/Ivan/ PGP Key: http://www.ivan-herman.net/pgpkey.html FOAF: http://www.ivan-herman.net/foaf.rdfReceived on Monday, 22 October 2007 11:35:23 UTC

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