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Re: no explicit type on bnodes

From: Jeremy Carroll <jjc@hplb.hpl.hp.com>
Date: Thu, 24 Jul 2003 16:31:38 +0100
Message-ID: <3F1FFBDA.5080106@hplb.hpl.hp.com>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
CC: jjc@hpl.hp.com, www-webont-wg@w3.org


Peter

I agree this was somewhat less than we hoped for.
Since you were the main proponent of trying to do more than the simplest 
change in response to the RDF Core decision on rdf:List, and on seeing the 
details, no longer wish to pursue it, I am not too unhappy just to let it 
drop. Making that simple triple optional is clearly enough.

This was more complicated than I had imagined, and even though I think it 
allows a slightly more elegant statement of OWL DL syntax, it is a 
distinctly more fragile one. I have a weak preference for making the bigger 
change, but doubt I could persuade many people.

Jeremy




Peter F. Patel-Schneider wrote:

> 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,‚EUR¶,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
>>
> 
> peter
> 
> 
> 
Received on Thursday, 24 July 2003 11:32:53 GMT

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