RE: ISSUE-3 and RDF simple entailment

Hi David!

You wrote:

>Hi Michael,
>
>I'm not sure I understand your comment.  Are you saying that 
>OWL already does not claim to satisfy the monotonicity 
>requirement of RDF semantics, and therefore OWL 1.1 DL also 
>does not need to satisfy it?
>
>The normative OWL semantics document begins by saying:
>http://www.w3.org/TR/owl-semantics/rdfs.html#5
>"This model-theoretic semantics for OWL is an extension of the 
>semantics defined in the RDF semantics [RDF Semantics], and 
>defines the OWL semantic extension of RDF."

Chapter 5 of the OWL AS&S, which you refer to above, is the specification of OWL-/Full/. Indeed, for OWL-Full it *is* necessary to satisfy the monotonicity requirement of RDF semantics, since, according to the citation you give above, OWL-Full claims to be a semantic extention of RDF(S). Remember that I wrote in my mail:

    "and both OWL-1.0-Full and pD* 
    are semantic extentions to RDFS."

But this is *not* the case for OWL-/DL/, which is specified in the other chapters of the AS&S (however, see below!). OWL-DL doesn't claim to be a semantic extention of RDFS, and it would not be adequate to do so. 

Note that OWL-DL, as described in chapters 2, 3 and 4 of the AS&S, does /not/ allow assigning a semantic interpretation to /every/ RDF graph. This means that some RDF graphs are /syntactically/ invalid ontologies in OWL-DL. But in RDFS /every/ RDF graph is a syntactically valid ontology, and can therefore be interpreted semantically.

Note further, that the semantics of RDFS give the interpreted universe a specific structure. For example, in RDFS every class and every property is also an individual. The semantics of OWL-DL does not enforce such a semantical structure of the OWL universe. OWL-DL is based on a description logic. AFAIK, description logics typically start from a domain D, which contains all individuals, and the classes are subsets of D, while the properties are subsets of the cartesian product DxD. And AFAIK, it is normally not assumed (at least not explicitly required) that the classes and properties in description logics are themselves elements of the domain D. But in order to be RDFS compatible, this would have to be necessarily the case for OWL-DL.

You might have observed that chapter 5 of the AS&S also contains a characterization of OWL-DL. This alternative definition of OWL-DL, unlike the version given in the rest of the AS&S spec, actually allows semantic interpretations for /every/ RDF graph. However, this version of OWL-DL is *not* an RDFS extention, since section 5.4 explicitly states that the different parts of the OWL universe (e.g. individuals, classes, properties, datatypes, data values) have to be /mutually disjoint/ (see first line of the table given in this section). This is not compatible with RDFS, in which the axiom

  rdfs:Class rdf:type rdfs:Class

is true, i.e. the entity denoted by the URI 'rdfs:Class' is both a class and an individual.

Best regards,
Michael


>David Booth, Ph.D.
>HP Software
>+1 617 629 8881 office  |  dbooth@hp.com
>http://www.hp.com/go/software
>
>Opinions expressed herein are those of the author and do not 
>represent the official views of HP unless explicitly stated otherwise.
>
>
>> From: Michael Schneider [mailto:schneid@fzi.de]
>>
>> Jeremy Carroll wrote on Friday, February 29, 2008:
>>
>> >One question that came up in HP discussion was whether the proposed
>> >resolution to ISSUE-3 would break the monotonicity requirement for
>> >semantic extensions
>> >http://www.w3.org/TR/rdf-mt/#MonSemExt
>> >
>> >I suggested that the proposal does break this requirement.
>>
>> AFAICT, this topic is only relevant for languages which claim
>> to be "semantic extentions" as defined by [10].
>> In this way,
>> RDF semantics is a semantic extention to Simple Entailment,
>> RDFS to RDF, and both OWL-1.0-Full and pD* are semantic
>> extentions to RDFS. This is the "layered" approach which I
>> described in [20]. In fact, the "delta to OWL-1.0-Full idea",
>> which we discussed in an earlier telco, would mean that
>> OWL-1.1-Full is becoming a semantic extention to OWL-1.0-Full.
>>
>> But neither OWL-1.0-DL nor OWL-1.1-DL claim to be such a kind
>> of semantic extention to RDFS. So you cannot reasonably apply
>> the "General monotonicity lemma" from the RDF(S) semantics spec
>> to them, where you have to "Suppose that Y indicates a semantic
>> extension of X".
>> [ . . . ]
>
>
>

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
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Email: Michael.Schneider@fzi.de
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