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

Date: Thu, 24 Jul 2003 10:19:08 -0400 (EDT)

Message-Id: <20030724.101908.19673671.pfps@research.bell-labs.com>

To: jjc@hpl.hp.com

Cc: www-webont-wg@w3.org

Date: Thu, 24 Jul 2003 10:19:08 -0400 (EDT)

Message-Id: <20030724.101908.19673671.pfps@research.bell-labs.com>

To: jjc@hpl.hp.com

Cc: www-webont-wg@w3.org

From: Jeremy Carroll <jjc@hpl.hp.com> Subject: no explicit type on bnodes Date: Fri, 20 Jun 2003 13:53:09 +0300 > This is my final beer session action. > > The idea is to change the mapping rules, so that for any rule which introduces > a new blank node as its main node, then the explicit type triple in that rule > is made optional. We will continue to refer to this triple as the explicit > type triple (even though it is optional). > > This is a little too ambitious, (it does not work), and I suggest retaining > the restriction that unnamed ontologies must have an explicit type triple. > > Moreover, I need a small tweak to the OWL Full semantics concerning the > definition of the class extenstion of owl:DataRange. > Specifically any member of IDC that has a finite size is a member of the class > extension of owl:DataRange. Both of these make the change much less desirable in my eyes. Exceptions to ``all blank node typing is optional'' make it harder to determine just what needs to be typed. Changes to the semantics just to support this change impose a significant cost. > Observations: > > 1) With the new mapping rules, the direct semantics of an RDF graph G missing > one or more explicit type triples (for blank nodes) is the same as for the > same graph augmented by the explicit type triples. What is the direct semantics of an RDF graph? Do you mean that any ontology whose translation is G has the same meaning as any ontology whose translation is G plus the missing type triple? This is a large part of what needs to be shown. > 2) Under 1) the explicit type triples that must be added can be syntactically > computed from G, except, that there may be any number of > _:b rdf:type owl:Thing . > corresponding to facts of the form > individual() > 3) All missing explicit type triples are RDFS consequences of G. Not correct. The missing triples may be RDFS consequences of G plus a graph that carries some of the OWL semantic conditions, but they certainly are not RDFS consequences of G. > 4) Given 2 and 3 then the correspondence theorem continues to hold, because > given 2, and using the notation [G] to indicate the graph G with all missing > explicit type triples added we have: > > If G OWL-DL entails H > then > G RDFS entails [G] OWL-DL entails [H] > G RDFS entails [G] OWL-full entails [H} > G OWL-Full entails [H] > G OWL-Full entails H > > The inverse is not true, but then that seems to be the case anyway. The > inverse is only not true because: > a) [G] owl-DL entails [H] > does not follow from > [G] owl-full entails [H] > > b) _:b rdf:type owl:Thing . is always true in OWL Full > but > individual() is not always true in OWL DL This is Theorem 2 from S&AS, but Theorem 1 also needs to be demonstrated. > ================ > > I prove 2 and 3, and then have further discussion of facts > individual() > > ===== > 2) given a bnode b, from the mapping rules, then either there are no triples > involving b, If b is in the graph, then it is in some triple. > or one of the following is true. > > a) > b rdf:type owl:Ontology . is in G (*not* optional) > > and this is the explicit type triple. > > b) > b rdf:type blank . is in G > > and explicit type is present or owl:Thing. > > c) > b rdf:type classID . > classID rdf:type owl:Class . (or classID is a builtin class) > are in G > > and explicit type is present or owl:Thing. > > d) > b apID any . > apID rdf:type owl:AnnotationProperty . (or apID is a builtin annotation > property) > are in G > and > b rdf:type owl:Ontology . > is not in G > > and explicit type is present or owl:Thing. This introduces a form of non-monotonicity _:b <ex:ap> "1" . <ex:ap> rdf:type owl:AnnotationProperty . would entail _:b rdf:type owl:Thing . but _:b <ex:ap> "1" . <ex:ap> rdf:type owl:AnnotationProperty . _:b rdf:type owl:Ontology . would not. > e) > b owl:unionOf any . > is in G > > and explicit type is owl:Class > > f) > b owl:intersectionOf any . > is in G > > and explicit type is owl:Class > > > g) > > b owl:complementOf any . > is in G > > and explicit type is owl:Class > > h) > > b owl:oneOf any . > is in G > and > exists dpID such that > dpID rdf:type owl:DatatypeProperty . > is in G > (or dpID is a builtin datatypeproperty) > such that > either > h.1) > dpID range b . > is in G > or > h.2) > there is another blank node c with > c owl:onProperty dpID > in G > and either > c owl:allValuesFrom b . > or > c owl:someValuesFrom b . > in G > > and explicit type is owl:DataRange > > i) > > b owl:oneOf any . > is in G > and > h) does not apply > > and explicit type is owl:Class > > j) > b owl:onProperty any . > is in G > > and explicit type is owl:Restriction > > k) > b rdf:first any . > is in G > > and explicit type is rdf:List . > > > That is an exhaustive analysis of the mapping rules, except > for the new rule (in red in the current editors draft) which > maps > individual() to > b rdf:type owl:Thing . > > If this is a top-level fact then this may result in no triple > in the graph, since the explicit type triple is optional. > > Otherwise we have either: > > l) > any apID b . > apID rdf:type owl:AnnotationProperty . > (or apID is a builtin annotationproperty) > are in G > > and explicit type of b is owl:Thing > > or > > m) > any opID b . > opID rdf:type owl:ObjectProperty . > (or opID is a builtin individual valued property) > are in G > > and explicit type of b is owl:Thing . > > Since the options a) through m) are mututally exclusive except for those that > result in explicit type of owl:Thing; and moreover options a) through m) are > an exhaustive analysis of the mapping rules, we have that any missing > explicit type triple of blank nodes (other than owl:Ontology) can be deduced > by syntactic analyis of G, or they are triples of the form > b rdf:type owl:Thing . > where b does not occur elsewhere in G. > > > 3) analysing the cases above we see: > > the empty ontology OWL Full entails > > b rdf:type owl:Thing > > (owl:Thing rdf:type owl:Class and > owl:Class rdfs:subClassOf rdfs:Resource > and > rdfs:Resource owl:equivalentClass owl:Thing > are all trivial) > > The cases > > e) > b owl:unionOf any . > f) > b owl:intersectionOf any . > g) > b owl:complementOf any . > i) > b owl:oneOf any . > is in G > and > h) does not apply > > and explicit type is owl:Class > > j) > b owl:onProperty any . > k) > > all follow by considering the rdfs:domain of the predicate of the given > triple. > > Case > > a) > b rdf:type owl:Ontology . > > is trivial, since the explicit type triple is not optional. > > Cases > > b) > b rdf:type blank . is in G > c) > b rdf:type classID . > d) > b apID any . > l) > any apID b . > m) > any opID b . > > all have explicit type owl:Thing, which is trivially OWL Full entailed for any > node. > > Which leaves only case h). > > [[ > b owl:oneOf any . > is in G > and > exists dpID such that > dpID rdf:type owl:DatatypeProperty . > is in G > (or dpID is a builtin datatypeproperty) > such that > either > h.1) > dpID range b . > is in G > or > h.2) > there is another blank node c with > c owl:onProperty dpID > in G > and either > c owl:allValuesFrom b . > or > c owl:someValuesFrom b . > in G > > and explicit type is owl:DataRange > ]] > > This case follows because by the syntax of G the triple > b owl:oneOf any . > has object which is a (possibly empty) well-formed list of data literals, and > from OWL Full semantics we have > if there exisits: > l, a sequence of x1,…,xn over LVI > then there exisits > y in IDC, <y,l> in EXTI(SI(owl:oneOf)) > > since this is finite, then y is also in the class extention of owl:DataRange, > by the proposed tweak to OWL Full semantics. > > Finished. I don't see how this second half demonstrates 3). > ++++ > > I've j[us]t discovered this msg sitting on my desktop - I think it's finished, > if not I guess someone will point it out. I'm not sure if you got around to > [...], and then have further discussion of facts > individual() > Jeremy peterReceived on Thursday, 24 July 2003 10:19:25 GMT

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