ontolog-forum
[Top] [All Lists]

Re: [ontolog-forum] Truth

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>, David Price <dprice@xxxxxxxxxxxxxxx>
From: "Obrst, Leo J." <lobrst@xxxxxxxxx>
Date: Sun, 8 Jul 2012 18:46:01 +0000
Message-id: <FDFBC56B2482EE48850DB651ADF7FEB01934084A@xxxxxxxxxxxxxxxxxx>
Pat,    (01)

So if I understand your statements correctly, two OWL classes EveningStar and 
MorningStar will be equal if their extensions are the same, i.e., {venus}, or:
EveningStar = MorningStar. And that this holds of OWL-DL, but not of OWL-Full, 
correct? In OWL-Full, EveningStar \= MorningStar, even if they have the same 
extension (apparently because OWL-Full allows classes to be instances, and that 
therefore, one does not know if the extension of a given class includes the 
instance or the class).     (02)

Thanks,
Leo    (03)

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx 
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
Sent: Sunday, July 08, 2012 11:12 AM
To: [ontolog-forum] ; David Price
Subject: Re: [ontolog-forum] Truth    (04)


On Jul 8, 2012, at 8:34 AM, David Price wrote:    (05)

> 
> On 8 Jul 2012, at 03:52, Pat Hayes wrote:
> 
>> 
>> On Jul 7, 2012, at 12:54 PM, Chris Mungall wrote:
>> 
>>> 
>>> On Jul 6, 2012, at 7:08 PM, Pat Hayes wrote:
>>> 
>>>> 
>>>> On Jul 6, 2012, at 4:25 PM, Chris Menzel wrote:
>>>> 
>>>>> On Fri, Jul 6, 2012 at 4:05 PM, Michael Brunnbauer <brunni@xxxxxxxxxxxx> 
>wrote:
>>>>> 
>>>>> Hello Matthew,
>>>>> 
>>>>> On Fri, Jul 06, 2012 at 09:35:02PM +0100, Matthew West wrote:
>>>>>> CM> ... classes are extensional in OWL.
>>>>>> Is that extensional in that the extension is the members declared in the 
>OWL ontology, or is that extensional in the sense that the members define the 
>class, but I might not know about all of them?
>>>>> 
>>>>> I think it's extensional in the sense that classes are not first class 
>entities
>>>>> but defined via the extension of the rdf:type property.
>>>>> 
>>>>> http://www.w3.org/TR/rdf-mt/#sinterp
>>>>> 
>>>>> Actually, yes, there is an RDF-compatible semantics for OWL I'd forgotten 
>about where OWL classes are simply entities that are assigned sets of 
>individuals as their extensions. In this semantics, distinct classes can have 
>the same "members". But IIRC in both the W3C "direct" semantics for OWL and 
>the "model theoretic" semantics, OWL classes are simply sets of individuals.
>>>>> 
>>>>> Pat will probably jump in here and straighten me out...
>>>> 
>>>> (Back from being a builder of kitchens, Pat reads lots of emails...)
>>>> 
>>>> FIrst, there are several OWLs. OWL-Full is the most RDF-compatible, with 
>very few restrictions on what can be said in it, but has no complete reasoners 
>so isn't very widely used. OWL-DL has many restrictions. OWL-Full follows RDF 
>and RDFS in treating classes as first-class (sorry about the pun) entities and 
>intensional, not extensional (in the sense that classes are not identified 
>with sets, so it is consistent for two classes to have exactly the same 
>members but still be distinct classes.) OWL-DL is quite different: it does not 
>allow classes to be first-class entities, and it assumes that classes are 
>defined extensionally, i.e. are sets, ie defined by their membership. So, to 
>sum up:
>>>> extensional = classes are identified with the sets of their members.
>>>> intensional = not extensional, so having the same members does not 
>guarantee identity of classes. (Put another way, classes have 'robust 
>identity' which is independent of their membership.)
>>>> 
>>>> OWL-Full: classes are individuals, just as in RDF and RDFS and Common 
>Logic. Classes are intensional.
>>>> OWL-DL: classes are not individuals, and  properties (binary relations) 
>only relate individuals, not classes. In the language of the ISO Common Logic 
>specs, OWL-DL is a segregated dialect. Classes are extensional. 
>>> 
>>> To be pedantic - in OWL-DL there are object properties (individual to 
>individual), data properties (individuals to literals) and annotation 
>properties (these are invisible in the direct semantics, but in practical 
>terms these can link classes, provided you don't need inferences from them)
>>> 
>>> Regarding classes being the same as their extents in OWL: I don't think 
>this view is universally shared.
>> 
>> Well, I havnt checked the OWL2 specs in detail, I confess, but it is 
>certainly true in the original OWL-DL, stated quite explicitly in the 
>semantics. Mathematical statements in a normative specification are, 
>fortunately, not "views" to be shared or not, at will.
> 
> 
> The OWL 1 Language Reference says:    (06)

Yes, this is for all the OWLs, so to speak, as a general statement.  OWL Full 
does indeed treat classes intensionally.  OWL-DL, however, treats them 
extensionally. See the 'direct semantics' (which is normative) for OWL-DL in 
http://www.w3.org/TR/owl-semantics/direct.html, where the interpretation of a 
class name is simply a subset of the universe. That is an extensional meaning 
for classes. RDFS and the RDF-based semantics for OWL both distinguish between 
the class itself  I(<name>)  and the class extension CEXT(I(<name>)), which 
distinction allows for an intensional interpretation.     (07)

Pat    (08)


> 3. Classes
> 
> Classes provide an abstraction mechanism for grouping resources with similar 
>characteristics. Like RDF classes, every OWL class is associated with a set of 
>individuals, called the class extension. The individuals in the class 
>extension are called the instances of the class. A class has an intensional 
>meaning (the underlying concept) which is related but not equal to its class 
>extension. Thus, two classes may have the same class extension, but still be 
>different classes.
> 
> So, if "Classes are extensional" means two OWL 1 classes with the same extent 
>are the same class, then clearly OWL 1 classes, while having extents, are not 
>extensional - or else this paragraph in the OWL 1 LR is wrong. FWIW I checked 
>the errata and this paragraph is not mentioned so it seems to stand as-is. 
> 
> The OWL 2 new features document claims "More importantly, backwards 
>compatibility with OWL 1 is complete, both syntactically and semantically." 
>even though I can't find any mention of the intensional meaning vs. class 
>extension relationship in any of the OWL 2 documents. So what does Pat's 
>"assumption of extensionality" mean wrt OWL 1 and OWL 2 and the question of 
>whether two classes with the same extent are the same class?
> 
> Cheers,
> David
> 
>> 
>> The "argument" given in the blog cited below is completely spurious: it is 
>based on a common misunderstanding about model theory, that the individuals in 
>models are "mathematical" entities rather than real things in the world, which 
>is complete nonsense. It (the cited blog) also confuses extensionality with 
>the idea of knowing or explicitly listing the elements of a set.
>> 
>> Pat
>> 
>> 
>>> In fact, one of the authors of the OWL2 direct semantics specification 
>states otherwise here:
>>> http://ontogenesis.knowledgeblog.org/1004
>>> 
>>>> The OWL specs give a 'direct' semantics for OWL-DL (which was the only OWL 
>that many of the WG cared about, those people also being not particularly 
>interested in RDF) whlie allowing OWL-Full to simply be an RDF extension. This 
>makes for confusing reading, and is the primary reason the specs are so hard 
>to follow..
>>> 
>>> Indeed!
>>> 
>>>> (There is also the newer standard OWL2-DL, which relaxes the syntax to 
>apparently allow classes to contain other classes, just as in OWL-Full, but in 
>fact it does this by a mechanism called 'punning' which keeps the underlying 
>segregation in the semantics. And it also assumes extensionality.)
>>>> 
>>>> Hope this helps.
>>>> 
>>>> Pat
>>>> 
>>>> 
>>>>> 
>>>>> -chris
>>>>> 
>>>>> 
>>>>> _________________________________________________________________
>>>>> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
>>>>> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
>>>>> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>>>>> Shared Files: http://ontolog.cim3.net/file/
>>>>> Community Wiki: http://ontolog.cim3.net/wiki/ 
>>>>> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>>>> 
>>>> ------------------------------------------------------------
>>>> IHMC                                     (850)434 8903 or (650)494 3973   
>>>> 40 South Alcaniz St.           (850)202 4416   office
>>>> Pensacola                            (850)202 4440   fax
>>>> FL 32502                              (850)291 0667   mobile
>>>> phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes
>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>>> _________________________________________________________________
>>>> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
>>>> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
>>>> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>>>> Shared Files: http://ontolog.cim3.net/file/
>>>> Community Wiki: http://ontolog.cim3.net/wiki/ 
>>>> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>>>> 
>>> 
>>> 
>>> _________________________________________________________________
>>> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
>>> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
>>> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>>> Shared Files: http://ontolog.cim3.net/file/
>>> Community Wiki: http://ontolog.cim3.net/wiki/ 
>>> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>>> 
>>> 
>> 
>> ------------------------------------------------------------
>> IHMC                                     (850)434 8903 or (650)494 3973   
>> 40 South Alcaniz St.           (850)202 4416   office
>> Pensacola                            (850)202 4440   fax
>> FL 32502                              (850)291 0667   mobile
>> phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes
>> 
>> 
>> 
>> 
>> 
>> 
>> _________________________________________________________________
>> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
>> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
>> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
>> Shared Files: http://ontolog.cim3.net/file/
>> Community Wiki: http://ontolog.cim3.net/wiki/ 
>> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
>> 
> 
> 
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/ 
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (09)

------------------------------------------------------------
IHMC                                     (850)434 8903 or (650)494 3973   
40 South Alcaniz St.           (850)202 4416   office
Pensacola                            (850)202 4440   fax
FL 32502                              (850)291 0667   mobile
phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes    (010)






_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (011)


_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J    (012)

<Prev in Thread] Current Thread [Next in Thread>