RE: SUO: RE: SUMO - predicate vs relation
>
>>
>> In addition, under the "proposition-forming operator"
>> interpretation, a
>> binary predicate would correspond to a function of two
>> arguments, and would
>> thus be a ternary, not a binary, relation. So now you have this:
>>
>> (subclass BinaryPredicate TernaryRelation)
>
>Well, this sort of maneuver is possible in the case of any relation. For
>example, if one claims that fatherhood is a relation between two entities, a
>father and an offspring, someone can retort that there are actually three
>items here, the two original entities plus the relation of fatherhood. Once
>the three items are posited, someone is free to claim that there is actually
>a quaternary relation here, one specifying that fatherhood is the connection
>between the two original entities. Of course, this can go on ad infinitum,
>since it's always possible to objectify relations or, in Pierican terms, to
>transform secondness into thirdness.
>
>But really, I think all of this takes us far afield of my original,
>innocuous intention, which was just to have a means of distinguishing
>operators that result in sentences from those that result in terms. Surely,
>this isn't as controversial or as confusing as you make it out to be...
>
Ian, I suspect you are mixing different things together. There is no
maneuver in Bill's note, it's the simple difference between single-
and multiple-valued relations. If a relation is single-valued on its
range, you can take the last argument as implicit ('results in a
term' as you put it), therefore, a convention is made that a 'binary
function' is a way of expressing a 'ternary relation' with a
single-valued range.
On the other hand, your discussion on fatherhood concerns what entity
types are involved when one creates an axiom, and this is a
modeller's choice. If the modeller commits only to a universal
ranging over two kinds of particulars, (s)he may use: father(x,y), a
binary relation that in functional terms can be expressed by the
unary function: the-father(x) :-> y. If the commitment is more
complex, one may add new domains, but the distinction between
relational and functional views is kept.
Probably, you should have in mind an ontological distinction between
relations and functions: relations have instances constituted by
relationships between entities ('propositions'), while functions have
instances constituted by an unnamed concept. But you will not
implement this distinction by merging a set-theoretic convention
concerning the cardinality of relations, and a metaphysical
assumption. This move has in fact generated confusion in Bill's
cognitive processes ;-).
Moreover, I am not convinced about that metaphysical assumption ...
Cheers
Aldo
--
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Aldo Gangemi
Researcher
Ontology and Conceptual Modeling Group
ITBM-CNR (National Research Council)
Viale Marx 15, 00137
Roma Italy
+3906.86090249
+3906.8273665 (fax)
mailto://gangemi@acm.org
mailto://gangemi@saussure.irmkant.rm.cnr.it
http://saussure.irmkant.rm.cnr.it