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Re: [ontolog-forum] Is there something I missed?

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Mike Bennett <mbennett@xxxxxxxxxxxxxxx>
Date: Thu, 29 Jan 2009 20:11:52 +0000
Message-id: <49820D88.1060403@xxxxxxxxxxxxxxx>
 From the point of view of having something that can be put in front of 
domain experts for review, I would rather have a ternary relation than 
the mathematical solution to the problem of reducing it to binary 
relations. It's one thing, as John says, that OWL falls down on.    (01)

Mike    (02)

`'.(`'.().').' wrote:
> John and Pat,
>
> While I realize that it is possible to reduce many higher valence 
> expressions to those with lower arity, it is unclear to me why we 
> would force this on people.
>
> As John illustrated below, it /is /possible to capture "+" as a series 
> of binary and unary relations, though the syntax and articulation of 
> this idea seems rather unnatural and unintuitive.
>
> Off the top of my head, my location seems like a quaternary relation 
> (location Ali, x, ,y ,z) in 3D space. Or by GPS, it'd be at least a 
> ternary relation. Similarly, if i wanted a time stamp associated 
> /within/ a relation (as opposed to a conjunction with another 
> relation), i'd want potentially higher arity relations.
>
> To use an analogy, while i might be able to reconstruct a 
> multi-variable derivative by taking partial derivatives and then 
> taking a series, it seems like an awkward workaround to express what 
> would otherwise be a straightforward oncept.
>
> Given that this discussion is ostensibly concerned with
>
> Is there something I missed? (and What is an Ontology)
>
> Might you tell me what the advantage of restricting vocabularies to 
> unary and binary predicates are?
>
> This seems to be steering the discussion to the question of "what 
> constitutes a '/good/' axiom?"
>
> //
>
> Indeed, it seems to me that the greatest difficulty in the creation of 
> ontologies is the paucity of guidelines as to what constitutes a 
> "good" axiom or ontology. Michael Uschold and Michael Gruninger wrote 
> a paper briefly touching this topic in 1996, though i'm not sure how 
> much of an impact it had (277 citations). They appealed to the notion 
> of /competency questions/ to guage whether the ontology you have 
> developed is addressing its purported function.
>
> Extending this idea, if an ontology is a coherent account of what 
> (relevantly) is, in some formal language, we should be concerned with 
> capturing that knowledge in a direct way. If we so desire, we may then 
> use projection to reduce the arity of the relation (and perhaps create 
> contexts), but to /a priori/ restrict expression and understanding of 
> ontologies to this particular mode of representation seem odd to me, 
> unless of course, i'm missing something :P.
>
> Ali
>
> -- 
> Ref - Uschold & Gruninger 1996) M. Uschold and M. Gruninger. 
> "Ontologies: Principles, methods and applications." Knowledge 
> Engineering Review vol. 11, pages 93-196, 1996.
>
> On Thu, Jan 29, 2009 at 12:48 PM, John F. Sowa <sowa@xxxxxxxxxxx 
> <mailto:sowa@xxxxxxxxxxx>> wrote:
>
>     Ali and Pat,
>
>     I agree with Pat's comments on this topic, but I'd like to
>     add a few.
>
>     Nicola G> This set of assumptions has usually the form of a
>      > first-order logical theory, where vocabulary words appear as
>      > unary or binary predicate names, respectively called concepts
>      > and relations.
>
>     AH> Though i'm not sure why vocabulary words are restricted to
>      > unary or binary predicate names
>
>     PH> Me neither. Writing in 2008, Nicola was probably intending to
>      > make a nod at the prevailing widespread use of description
>      > logics, which are restricted to the unary/binary case.
>
>     As an example, the English word 'add' maps to the mathematical '+',
>     which represents a function with two inputs and one output.
>
>     It is possible to represent such things with a concept type Add
>     that represents an add operation, which is linked to three dyadic
>     relations:
>
>      1. Arg1 links the Add concept to the first argument.
>
>      2. Arg2 links Add to the second argument.
>
>      3. Rslt links Add to the result.
>
>     PH> In practice, there seems to far more unary/binary than anything
>      > else, and one can routinely encode an n-ary relation is a
>      > conjunction of binary ones.
>
>     Yes.  And it's desirable to use a logic that can relate the different
>     representations by if-then rules, such as
>
>        (forall (x y z w)
>           (if (and (Add w) (Arg1 w x) (Arg2 w y) (Rslt w z))
>               (= z (Sum x y)) ))
>
>     PH> Most ontologies are built on a skeleton of taxonomy, or at least
>      > a subclass hierarchy. Its hard to avoid having such a structure
>      > somewhere in any large ontology, in fact.
>
>     Yes.  That has been common practice since Aristotle.  In fact, many
>     of the ontologies that are written in OWL don't use anything beyond
>     Aristotle's subset.
>
>     John Sowa
>
>
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>
>
> -- 
> (`'.(`'.().').') .,.,
> ------------------------------------------------------------------------
>
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>      (03)


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