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Re: [ontac-dev] Rules and classes

To: ONTAC Taxonomy-Ontology Development Discussion <ontac-dev@xxxxxxxxxxxxxx>
From: "Smith, Barry" <phismith@xxxxxxxxxxx>
Date: Wed, 18 Jan 2006 22:20:00 +0100
Message-id: <7.0.1.0.2.20060118221224.04802608@xxxxxxxxxxx>
At 07:52 PM 1/18/2006, you wrote:
>Chris and Barry,
>
>I was following Church's definition of a function as rule
>(see the excerpt in http://www.jfsowa.com/logic/alonzo.htm ).
>I consider a type to be of the same nature as a function,
>since one could consider a type to be a function from
>entities to truth values.
>
>JS>>  A _type_ t is a rule or specification for classifying entities,
> >>    concrete or abstract.  Any entity that has the characteristics
> >>    specified by the type t is called an _instance_ of t.    (01)


A dog is an instance of function from entities to truth values    (02)

Still does not sound right to me.    (03)



>I admit that my definition is as loosely stated as Church's,
>but I consider that at worst a venial sin, and it's certainly
>no disgrace to be lumped into the same group with Alonzo C.    (04)

Good to follow common sense, too, I think.    (05)

>BS> However, I think it wrong to coin a term 'relation type'. This
> > is because most of the relations which interest us here, e.g. is_a
> > (meaning: is subtype of), instance_of, part_of, etc., DO NOT HAVE
> > INSTANCES.
>
>Actually, they do.  If you consider the extension of a type to be
>a set of instances, the extension of a relation is a set of n-tuples,
>each of which may be called an instance of the relation.    (06)

You yourself have correctly been arguing that a type and its 
extension are two different entities. And now here too we see that 
there is a disanalogy between types and relations. The extension of a 
type is a set of instances of that type. Thus Fido instance_of the type dog.    (07)

The extension of a relation is a set of (ordered pairs of) instances 
of other quite different types.    (08)

We do not have instances of is_a, part_of.    (09)

For suppose that we did, e.g. the ordered pair <dog, animal> is an 
instance of the relation is_a.    (010)

Then this would mean that we would have to accept not merely the statement    (011)

dog is_a animal    (012)

but also the instantiation statemeno    (013)

dog <dog, animal> animal.    (014)

Put that in your pipe and smoke it.    (015)

BS     (016)



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