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Re: [ontolog-forum] Logic, Datalog and SQL

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Sun, 11 Feb 2007 13:47:35 -0600
Message-id: <096ECA4B-45C4-419E-A1AB-CB2A46A84E98@xxxxxxxx>
On 11 Feb, at 1:08 , John F. Sowa wrote:
> ...
> The definition I proposed on January 30 includes everything
> you've requested so far:
>      A formal ontology consists of a theory T stated in some
>      version of logic and a nonempty vocabulary V.  The
>      vocabulary V is a subset of the names of types and relations
>      used in T.    (01)

John, I think I might agree with you that something along these lines  
is a better definition of "formal ontology" than mine (via., that  
"formal ontology = logical theory").  It does seem to capture  
something important about proposed ontologies that is missing from  
many logical theories.  However, it needs a bit of work.  First, you  
say that T is stated in terms of a nonempty vocabulary V; then you  
suggest that V is only a subset of the type and relation names in T.   
But you have identified V as T's vocabulary; how could it *fail* to  
be anything other than the type and relation names used in T?  In  
fact, V could well contain vocabulary not used in T (perhaps the  
developer intends to extend T or something).  So, if anything, it  
seems to me that "subset" there should be "superset" (where superset  
is taken to be reflexive).    (02)

Note however that, even with this revision, there is still the  
possibility of "vacuous" ontologies; imagine, e.g., a theory whose  
only axiom is "Every loopyletter is a loopyletter".  This seems to me  
to meet your definition.  Hence, you might consider adding that T  
must contain at least one axiom that is not a logical truth.   
However, because logical truth is only semi-decidable, adding that  
qualification now makes it the case that there is no general  
procedure for determining whether or not any particular logical  
theory is *really* an ontology.  (This is one of the reasons I simply  
opted for allowing any logical theory to be considered a formal  
ontology.)  However, in practice it will probably always be the case  
that one can demonstrate that at least one of the axioms of a  
proposed ontology is not a logical truth.  (This is easy to do for,  
e.g., PSL.)  So maybe the qualification is innocuous; it's  
*possible*, but really unlikely, that anyone would attempt to develop  
an ontology that turned out to be logically vacuous.  At the least,  
it seems reasonable that the risk of a subtly vacuous logical theory  
being counted as an ontology (and really, *who cares* if that ever  
happens?) is greatly outweighed by the benefits of being able to  
exclude obviously vacuous logical theories from being considered  
genuine ontologies.    (03)

Chris Menzel    (04)

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