On Fri, Jan 30, 2009 at 10:20 AM, Pat Hayes <phayes@xxxxxxx> wrote:
> On Jan 29, 2009, at 11:13 PM, John F. Sowa wrote:
>
>> I just want to point out an important class of common triads.
>>
>>> Examination of the dependencies in a ternary or quaternary
>>> relationship often reveals an intermediate object that has
>>> semantics and should actually be called out in creating
>>> a strong ontology for the domain in question.
>>
>> All the basic arithmetic operators, + - * /, take two inputs
>> and generate one output. Trying to represent simple arithmetic
>> expressions with only dyadic relations creates very awkward,
>> unnatural and unreadable statements.
>>
>
> Agreed, but the main problem there is treating these as relations at
> all. They are functions. In passing defense of the unary/binary OWL,
> no sane person would suggest using OWL properties to represent
> arithmetic functions. (01)
That's because there is a much better representation/inference
mechanism for arithmetic already implemented (any computer's CPU). (02)
>> There are many other examples, but these are the most obvious. (03)
- Any (relational) database schema describes a set of relations/an
ontology and most are extremely multi-ary. (04)
- The examples of addition or betweenness do look intuitively
essentially more than binary, but because of the -very- simple
reduction of multi-ary to binary, one can think of multi-ary relations
as 'syntactic sugar', a convenience. (05)
So maybe triples (binary relations) or OWL are the way to go as far as
efficiency or interoperability, but it might be nice for humans to
encode things directly in the arity that is most salient, then
'compile' to the appropriate formalization. (06)
--
Mitch Harris (07)
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