On Jan 29, 2009, at 2:11 PM, Mike Bennett wrote: (01)
> 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. (02)
I don't think this is a very productive argument to be having, largely
because its already been hashed, many many times in many many forums,
for at least 20 years. But to set the record straight. (03)
First, its not so much a mathematical solution as a linguistic one.
Linguists prefer the so-called 'case-role' representation style rather
than the many-argument one, on the grounds that it makes the
ontological (though they tend not to use that word) structure more
visible. Many domain experts report a similar effect: its often very
hard to recall, given a many-argument relation, which argument is
supposed to be which (was that B between A and C, or A between B and
C?) whereas when the arguments are explicitly labelled by role names,
things are a lot easier. Even binary relations without role names can
give trouble, c.f. the ongoing debates about the use of names in OWL/
RDF: do want to say (Bill isFatherOf Joe) or (Joe hasFather Bill)? For
sure, better not just say (Bill Father Joe) as we then have no idea
which way round it should be read. Several rule languages and some
versions of Prolog use case-role notation for similar reasons. On the
other hand, one of the tricks we have found useful in CL is to allow
very long argument sequences when these are all being treated in some
common way, eg a variadic 'not-equal' which might be used with ten
arguments to say they are all distinct. (04)
The moral I draw from this is that it is very hard, next to
impossible, to predict ahead of time what "domain experts" will or
will not prefer. And the process of designing intuitive interfaces for
experts to use to interface with formal ontology content is an art and
a science in itself, one that we would best keep apart from ontology
engineering as far as possible. I don't mean because its not important
- it is - but because the constraints of being readable, intuitive,
easy to edit, etc., are different from the those which make a formal
ontology easy to manipulate by formal means. For example, XML makes
everything much worse for readability but is crucial for many
applications. Since the different styles of multi-argument relations
are so well understood and so easy to translate between, we should
allow various applications to use whatever form they find most useful,
rather than debate the merits and demerits of the various alternatives. (05)
Pat H (06)
>
>
> Mike
>
> •`'·.¸(`'·.¸(•)¸.·'´)¸.·'´• 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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>
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