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Re: [ACTION-78] What it means to define OWL-1.1-Full as a "delta" to OWL-1.0-Full

From: Jim Hendler <hendler@cs.rpi.edu>
Date: Tue, 12 Feb 2008 11:17:31 -0500
Cc: Michael Schneider <schneid@fzi.de>, <public-owl-wg@w3.org>
Message-Id: <D35C3F66-A4FB-4628-A457-3C80FFCC5FAB@cs.rpi.edu>
To: Jim Hendler <hendler@cs.rpi.edu>

obviously there is a "o" missing in the below, please don't beat me  
up...

On Feb 12, 2008, at 10:43 AM, Jim Hendler wrote:

>
> Just to be clear where I stand - I have no objection to us doing a  
> formal semantics for OWL 1.1 Full, and Michael's approach would be  
> the one that makes most sense.  However, I also believe we would  
> need to provide an explanation that is more "human  
> readable" (operational or axiomatic semantcs or a god reference)  
> because most Web App developers I know have told me they don't  
> really understand the model theory stuff (which isn't that  
> surprising, because after 30 years as an AI professor, I admit that  
> I don't fully understand all the details)
> -JH
> p.s. again, to be clear, this is my "druthers"
>
>
> On Feb 12, 2008, at 10:12 AM, Michael Schneider wrote:
>
>> Hello WG!
>>
>> My ACTION-78 [0] is to explain what it means to define OWL-1.1-Full  
>> as a
>> "delta" to OWL-1.0-Full. There was a straw poll about this question  
>> at the
>> last telecon, but some people asked what this actually means. Here  
>> is my
>> understanding of it.
>>
>> In short, the idea is to take the current OWL-1.0-Full semantics  
>> [1] as a
>> base, and to add semantics for each of the new language constructs in
>> OWL-1.1 (e.g. QCRs). This "adding" of semantics would be performed by
>> defining a set of "semantic conditions" to treat the new OWL-1.1  
>> vocabulary,
>> and to add these semantic conditions to those which already exist for
>> OWL-1.0-Full. By this, one would follow the same approach which was  
>> taken
>> for defining OWL-1.0-Full as a "delta" to RDFS semantics. This  
>> approach
>> would automatically maintain backwards compatibility to OWL-1.0- 
>> Full and
>> RDF(S) in the sense that every entailment of RDF(S) and OWL-1.0- 
>> Full is also
>> an entailment of OWL-1.1-Full.
>>
>> I am going to elaborate on this idea now. I will first talk about  
>> what it
>> means that OWL-Full is a "semantic extention of RDFS". I will then  
>> point to
>> the observation that OWL-Full semantics is organized in a "layered"  
>> style.
>> Based on this, I will argue that a "delta" just means an additional  
>> semantic
>> layer for OWL-1.1-Full. There will also be an example for a "semantic
>> condition", which is the basic building block of a semantic layer.
>>
>> == 1. OWL-Full as a "semantic extention of RDF(S)" ==
>>
>> The OWL-1.0-Full spec [1] calls OWL-Full a "semantic extention of  
>> RDF[S]" in
>> its first sentence, and points to the RDF semantics spec [2] for a
>> definition of this term [3]. What this means is the following:
>>
>> The semantics of RDF(S) is a model theoretic semantics, which is  
>> presented
>> in the form of a set of "semantic conditions". These semantic  
>> conditions are
>> "IF->THEN" rules, which map one or more RDF triples in an RDF graph  
>> to their
>> respective mathematical meaning (see the example of such a semantic
>> condition below). OWL-Full only adds additional semantic conditions  
>> to the
>> existing semantic conditions of RDFS.
>>
>> These additional semantic conditions of OWL-Full are primarily  
>> intended to
>> deal with the specific OWL vocabulary (e.g. 'owl:disjointWith').  
>> There are
>> also a few additional semantic conditions which extend the  
>> semantics for the
>> RDFS vocabulary (e.g. 'rdfs:subClassOf', see the example below).  
>> But most of
>> the semantics for RDFS vocabulary is already specified by RDFS  
>> itself. So
>> OWL-Full simply "inherits" parts of its semantics from RDFS, and  
>> augments it
>> with own semantic conditions.
>>
>> == 2. The layered architecture of OWL-Full semantics ===
>>
>> OWL-Full does not only inherit parts of its semantics from RDFS,  
>> but it also
>> copycats RDFS in defining the /style/ how the semantics are  
>> presented. RDFS
>> itself is a semantic extention to RDF. RDFS augments the existing  
>> semantic
>> conditions of RDF by own semantic conditions for the specific RDFS
>> vocabulary (e.g. 'rdfs:Class'). And even RDF is a semantic  
>> extention to so
>> called "Simple" semantics. This will also be demonstrated in the  
>> example
>> below.
>>
>> With other words, the semantics for OWL-Full is presented in a  
>> "layered"
>> style: Each layer (1 "Simple", 2 RDF, 3 RDFS, 4 OWL-Full) just adds  
>> new
>> semantic conditions to the previous layer's set of semantic  
>> conditions. This
>> happens primarily in order to provide additional semantics to the  
>> layer's
>> specific vocabulary, and sometimes also in order to enrich the  
>> semantics of
>> the vocabulary from lower layers. *Never* is semantics from lower  
>> layers
>> canceled out by higher layers. All semantic conditions from lower  
>> layers
>> also exist in the higher layers.
>>
>> This approach has the advantage that higher layer languages are  
>> always
>> automatically downwards compatible to all of its lower layer  
>> languages (for
>> example, OWL-Full is downwards compatible with RDFS). This means  
>> that if
>> there is some RDF graph G, all entailed triples produced from G by  
>> the lower
>> layer language are also entailed by the higher layer language. The  
>> reason
>> for this is that the higher layer language uses all the semantic  
>> conditions
>> of the lower one, and if some triple is already entailed by a  
>> subset of
>> semantic conditions, then it is entailed by a superset of semantic
>> conditions, too.
>>
>> == 3. What does the "delta" mean? ==
>>
>> I interpret saying that OWL-1.1-Full is a "delta" to OWL-1.0-Full  
>> to mean
>> that OWL-1.1-Full is specified by just another layer of semantic  
>> conditions
>> on top of OWL-1.0-Full (layer 5). This means that there will be  
>> dedicated
>> semantic conditions for the new OWL-1.1 vocabulary, like e.g.  
>> vocabulary
>> related to QCRs, sub property chains, and the new property  
>> characteristics.
>> Everything else is inherited from OWL-1.0-Full, and by this  
>> transitively
>> from the lower layers, like RDFS.
>>
>> Note that this is an assertion about both the semantics for OWL-1.1- 
>> Full
>> itself AND the style how this semantics is organised. So if one  
>> asks only
>> for the semantics of OWL-1.1-Full, it would be sufficient to  
>> present the
>> same semantics in another style, perhaps a more "direct", non- 
>> layered style.
>>
>> == 4. An example of a semantic condition ==
>>
>> Here is an example for how the layered approach works. The  
>> semantics for
>> subclassing axioms in RDFS and OWL-Full is discussed by looking at  
>> the
>> respective semantic conditions involved. The following semantic  
>> condition is
>> given in the RDFS semantics spec [4]:
>>
>> (SC-SUBCLASS)
>>
>> IF
>>     <x,y> is in IEXT(I(rdfs:subClassOf))
>> THEN
>>     x and y are in IC
>>   AND
>>     ICEXT(x) is a subset of ICEXT(y)
>>
>> This semantic condition has the form of a rule. It "fires" its  
>> "THEN" part,
>> whenever there is some triple of the form "x rdfs:subClassOf y" in  
>> the
>> regarded RDF graph, or when such a triple can be entailed by  
>> applying other
>> semantic conditions from RDFS semantics.
>>
>> Actually, the "IF" part specifies a slightly different (and more  
>> complicated
>> looking) condition: It demands that the tuple <x,y>, consisting of  
>> resources
>> x and y, is contained in the "property extention" IEXT(.) of the  
>> property
>> denoted by 'rdfs:subClassOf'. This is in fact a statement about the
>> interpreted domain, not about the RDF graph itself (remember that  
>> RDFS
>> semantics is a model theoretic semantics!). But this doesn't matter  
>> here
>> much, since it is essentially what the existence of a triple "x
>> rdfs:subClassOf y" means.
>>
>> Now if this semantic condition fires, we get some new information:
>>
>> (1) The not further specified resources x and y are determined to  
>> be in
>> fact /class/ resources. This is expressed by "x in IC", where "IC"  
>> is that
>> part of the RDFS universe, which contains exactly all class  
>> resources. A
>> class resource x is a resource, which additionally owns a "class  
>> extention",
>> i.e. the set of all resources z with "z rdf:type x".
>>
>> (2) The class extention of x, named "ICEXT(x)", is a subset of  
>> ICEXT(y),
>> which is the class extention of y. This is, of course, what one  
>> actually
>> intends to express by specifying a subclass axiom.
>>
>>> From what I have said above about the layered approach to specify  
>>> semantics
>> for RDFS, the semantic condition SC-SUBCLASS is not yet the full  
>> story. The
>> RDFS semantics for 'rdfs:subClassOf' is given not only by this RDFS- 
>> specific
>> semantic condition, but also by the respective semantic conditions  
>> for
>> "Simple" semantics and RDF semantics. The semantics of  
>> 'rdfs:subClassOf' is
>> thus "cumulative".
>>
>> * Layer 1: From "Simple" semantics one can conclude that the  
>> statements
>>
>>     _:u rdfs:subClassOf y
>>     x rdfs:subClassOf _:w
>>     _:u rdfs:subClassOf _:w
>>
>> are all true, where "_:u" and "_:w" are bNodes, which are  
>> existentially
>> interpreted. So, e.g., from knowing that x is a rdfs:subClassOf y,  
>> one also
>> learns that there /exists/ some subClassOf y.
>>
>> * Layer 2: From RDF semantics one can conclude that the statement
>>
>>     rdfs:subClassOf rdf:type rdf:Property
>>
>> is true, i.e. 'rdfs:subClassOf' denotes some property in the RDF  
>> universe.
>>
>> * Layer 4: OWL-Full additionally specifies the semantic condition
>> SC-SUBCLASS to be an IF-AND-ONLY-IF condition (in RDFS it is only a
>> "IF-THEN" condition). So if one happens to find two class resources  
>> x and y,
>> and their class extentions ICEXT(x) and ICEXT(x) occur in a subset
>> relationship, then the statement "x rdfs:subClassOf y" can be  
>> deduced to be
>> true.
>>
>> The first two layers (Simple and RDF semantics) can IMHO be  
>> regarded to
>> create a "semantic foundation" for RDF graphs. The entailed triples  
>> itemized
>> above result from /every/ triple within an RDF graph, not only from
>> 'rdfs:subClassOf' triples.
>>
>> The fourth layer from OWL-Full allows in certain situations to  
>> directly
>> derive new triples from existing ones. For example, if one has the  
>> triples
>> 'x rdfs:subClassOf y' and 'y rdfs:subClassOf z' in an OWL-Full  
>> ontology, one
>> can, via the additional transitivity semantic condition of RDFS on
>> 'rdfs:subClassOf', entail the triple 'x rdfs:subClassOf z'. The  
>> semantic
>> condition SC-SUBCLASS of RDFS semantics alone only provides the
>> "mathematical meaning" of such an additional rdfs:subClassOf  
>> triple, not the
>> triple itself.
>>
>> Regards,
>> Michael
>>
>>
>> [0] http://www.w3.org/2007/OWL/tracker/actions/78
>> [1] http://www.w3.org/TR/owl-semantics/rdfs.html
>> [2] http://www.w3.org/TR/rdf-mt/
>> [3] http://www.w3.org/TR/rdf-mt/#DefSemanticExtension
>> [4] http://www.w3.org/TR/rdf-mt/#RDFSINTERP
>>
>> --
>> Dipl.-Inform. Michael Schneider
>> FZI Forschungszentrum Informatik Karlsruhe
>> Abtl. Information Process Engineering (IPE)
>> Tel  : +49-721-9654-726
>> Fax  : +49-721-9654-727
>> Email: Michael.Schneider@fzi.de
>> Web  : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555
>>
>> FZI Forschungszentrum Informatik an der Universität Karlsruhe
>> Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe
>> Tel.: +49-721-9654-0, Fax: +49-721-9654-959
>> Stiftung des bürgerlichen Rechts
>> Az: 14-0563.1 Regierungspräsidium Karlsruhe
>> Vorstand: Rüdiger Dillmann, Michael Flor, Jivka Ovtcharova, Rudi  
>> Studer
>> Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus
>
> "If we knew what we were doing, it wouldn't be called research,  
> would it?." - Albert Einstein
>
> Prof James Hendler				http://www.cs.rpi.edu/~hendler
> Tetherless World Constellation Chair
> Computer Science Dept
> Rensselaer Polytechnic Institute, Troy NY 12180
>
>
>
>
>

"If we knew what we were doing, it wouldn't be called research, would  
it?." - Albert Einstein

Prof James Hendler				http://www.cs.rpi.edu/~hendler
Tetherless World Constellation Chair
Computer Science Dept
Rensselaer Polytechnic Institute, Troy NY 12180
Received on Tuesday, 12 February 2008 16:17:48 GMT

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