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RE: Xtreme Punning

From: Pat Hayes <phayes@ihmc.us>
Date: Fri, 11 Jan 2008 09:39:42 -0800
Message-Id: <p06230905c3ad574329d7@[]>
To: "Gerd Wagner" <wagnerg@tu-cottbus.de>
Cc: "'Denny Vrandecic'" <dvr@aifb.uni-karlsruhe.de>, "'Jeremy Carroll'" <jjc@hpl.hp.com>, "'Owl Dev'" <public-owl-dev@w3.org>

At 1:09 PM +0100 1/11/08, Gerd Wagner wrote:
>  > I think this kind of punning comes very natural.
>>  Snoopy a Dog.
>>  Dog a Species.
>>  Charlie_Brown Dog Snoopy.
>>  All of them feel right, and are also allowed in both RDF and OWL with
>>  punning.
>>  Father rdfs:range Father.
>>  Anakin a Father.
>>  Luke Father Anakin.
>OK, but there is an important difference between these
>two cases.
>In the first case, the thing denoted by the first occurrence
>of Dog is the same thing as the thing denoted by the second
>occurrence of Dog, namely the class Dog, which happens to be
>an instance (not really an "individual" in the strict sense
>of a thing that has no instances/extension).
>In the second case, the thing denoted by the first occurrence
>of Father is a property, while the thing denoted by the second
>occurrence of Father is a (role) class. Clearly, these two
>things are closely related to each other, but they are not
>the same.

In the RDF/RDFS/OWL1.0Full/CommonLogic/Hilog semantics, they are the 
same 'thing'. That is, there is one thing denoted by the name, which 
has both a class and a property extension. The two extensions are 
distinct mathematical entities, of course, but the semantics insists 
that each name denote a unique entity. This preserves the meaning of 
equality, avoids the oddities of punning (where two occurrences of a 
given name may or may not co-denote), and has the nice side-effect of 
allowing a more natural (non-extensional) identity criterion for 
classes and properties. It also has a more tractable logic, by the 
way: but that should not, of course, be the governing criterion for 
choosing a SWeb language. (It also is usefully extendable: in IKL, 
for example, propositions are another kind of name extension.)

>Another important case of the same thing appearing in two
>different forms (or sntactical categories) are functional
>properties which can appear both as property predicates and
>as function symbols (though not in OWL).

Ah, now there I disagree. KIF used this, but we abandoned it in CL. 
The problem is that in order to use it, a convention has to be 
adopted (and built into the syntax) about which relational argument 
is the 'value' of the function. This amounts to an arbitrary 
non-logical convention being made part of the logic, which invariably 
causes confusion: and indeed, there are systems out there already 
using both conventions (value first/value last). Also, speaking 
strictly, a function is not actually *identical* with a functional 
relation. So in CL we left the relationship between R with two 
arguments and R with one argument entirely open, and require users to 
axiomatize their preferences explicitly, for example

(forall (r)(iff (FunctionalBinaryRelation R)(forall (x)(R x (R x))) ))

>However, it seems that this difference in using the same
>name for different syntactic categories once denoting the
>same thing and once denoting distinct things, cannot be
>captured by OWL 1.1 punning, where they are always denoting
>different things.

The essence of punning is that each occurrence of the name denotes 
one thing, chosen in essence by the syntactic context of the 
occurrence, but that different occurrences can denote different 
things. I see no reason this canot apply to this case also.


>Gerd Wagner
>Email: G.Wagner@tu-cottbus.de

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Received on Friday, 11 January 2008 17:39:55 UTC

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