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

Date: Mon, 22 Oct 2007 13:29:17 +0100

Message-ID: <471C979D.1060707@hpl.hp.com>

To: Ivan Herman <ivan@w3.org>

CC: public-owl-wg@w3.org

Date: Mon, 22 Oct 2007 13:29:17 +0100

Message-ID: <471C979D.1060707@hpl.hp.com>

To: Ivan Herman <ivan@w3.org>

CC: public-owl-wg@w3.org

Jeremy Carroll wrote: > I'll try again Monday. Sometimes I feel resentful when, over the weekend, I find that my mind is turning over the things that I am paid to think about from Monday to Friday ... I suppose I should try and complete work on Friday rather than leave such a dangling unfinished thought! So Friday's message was unsatisfactory in that while I claimed a semantic issue, I ended up with syntactic issues, which were essentially based on my view of the history of section 4 of the OWL 1.0 S&AS. In this message I will try again at item (b) >> 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 >>> reusing some of my text from my Friday with **** being used to emphasize important new/changed text > In this 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 in a later message). > > 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. > ***** A direct interpretation of trees I_t and an RDFS compatible interpretation of graphs I_g may be viewed (informally) as corresponding Such an informal view can be partially formalized by forming a bijection between a subset of the domain of discourse of I_t and a subset of the domain of discourse of I_g. For corresponding interpretations such subsets will include the interpretation of all normal terms, and the obvious identities will hold. ****** > 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 ****** Also any interpretation I_t1 of t1 corresponds to some interpretation I_g1 of g1, (and conversely ??? probably not) ****** > > 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. > ***** The role of the mapping rules is to allow interoperability between OWL DL and OWL Full - this is crucial in avoiding a schism in the semantic web. In my view an acceptable design has the following characteristics: OWL DL is largely a self-motivated design OWL Full is largely a self-motivated design Every AST in OWL DL is mapped into a graph in OWL Full with the 'same meaning'. Given a graph g in OWL Full, which has the same meaning as some AST in OWL DL, it is not too difficult to find a related graph g' for which there is some tree t' which maps to g'. There are some not too complicated rules of thumb that can be used when constructing such a g that ensure that g=g' nearly all of the time. ****** > 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. > The (informal) topology of the space of graphs is very different from that of the space of trees (with the topologies respecting semantic entailment). This seems to be most easily aligned with a many-to-many mapping. > > 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. > Enough on this for now. JeremyReceived on Monday, 22 October 2007 12:29:50 UTC

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