- From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
- Date: Tue, 20 Aug 2002 07:00:19 -0400
- To: phayes@ai.uwf.edu
- Cc: www-webont-wg@w3.org
From: pat hayes <phayes@ai.uwf.edu> Subject: revised version of semantics document Date: Tue, 20 Aug 2002 03:06:03 -0700 > I only just read Peter's comments, but I do not follow them. Both of > the entailments that he says are not present: > E1/ John in Student intersect Employee > entails > John in Employee intersect Student > E2/ John in atleast 2 friend > entails > John in atleast 1 friend > are in fact supported by the MT in the document, seems to me. Since > the basic semantic conditions are transcribed from his OWL MT this > should not be hard to see. If Im missing something, please tell me > what. Consider E1 in more detail. Its premise is John rdf:type _:x . _:x owl:intersectionOf _:l1 . _:l1 owl:first Student . _:l1 owl:rest _:l2 . _:l2 owl:first Employee . _:l2 owl:rest owl:nil. and its conclusion is John rdf:type _:y . _:y owl:intersectionOf _:l3 . _:l3 owl:first Student . _:l3 owl:rest _:l4 . _:l4 owl:first Employee . _:l4 owl:rest owl:nil. An interpretation of the premise above does not require the presence of the list in the conclusion. A GHOWL interpretation of the premise (ignoring some built-in stuff) is IR = { j, t, x, i, l1, l2, s, e, f, r, n } IS(John) = j IS(rdf:type) = t IS(owl:intersectionOf) = i IS(Student) = s IS(Employee) = e IS(owl:first) = f IS(owl:rest) = r IS(owl:nil) = n ICEXT(s) = { j } ICEXT(e) = { j } ICEXT(x) = { j } IEXT(j) = { } IEXT(t) = [see above] IEXT(x) = { } IEXT(i) = { <x,l1> } IEXT(l1) = { } IEXT(l2) = { } IEXT(s) = { } IEXT(f) = { } IEXT(f) = { <l1,s>, <l2,e> } IEXT(r) = { <l1,l2>, <l2,n> } IEXT(n) = { } This is not a GHOWL interpretation of the conclusion because there is no domain element related via I(owl:first) to I(Employee) and related via I(owl:rest) to I(owl:nil). QED My semantics has interpretations that are extensions of RDFS interpretations, but the abstract syntax on which my semantics works is not RDF graphs. Therefore there are no triples, and thus no RDFS semantic conditions on triples to block this kind of entailment. To make these sorts of entailments go through when using RDF graphs requires darkening a lot of triples. Peter F. Patel-Schneider Bell Labs Research
Received on Tuesday, 20 August 2002 07:00:28 UTC