Re: SUO: type equivalence

[apease <apease@teknowledge.com>]

Robert,
   This looks like a definition of "signature" that is similar to most 
programming languages.  Functions/Methods/Procedures are considered to have 
the same signature if they have the same parameter types and order.  This 
definition would be too impoverished to cover type equivalence I would 
think since two relations with the same signature can have very different 
axioms which define their semantics.

Adam

At 02:17 PM 11/2/2000 -0600, David Whitten wrote:

>  Robert E. Kent said:
> > I am currently contemplating quotients of "logical languages" via type
> > equivalence, and would be interested to know what has been done on this
> > subject. The central axiom would seem to be that relational type
> > equivalence implies the type equivalence of its signature. To wit: (
> > where == means type equivalence)
> >     if rho_1 == rho_2 then arity(rho_1) = arity(rho_2) and
> > sign(rho_1)(x) == sign(rho_2)(x) for all x in arity(rho_i), i = 1, 2.
> > This of course can easily be framed in KIF. Are there other obvious
> > axioms?
>
>I would like to know what you think a signature is.
>In my starter structural ontology, the distinction is made between
>the instance-of and the subclass-of relations on an argument to a
>relation.
>
>
>This means that if you know the argument to a relation is
>an instance of CLASS, you must further specify which class it is a
>subclass of.  I would also argue that you need to deal with
>inter-argument dependencies as well as only intra-argument definitions.
>
>A separate issue is specifying how propositions that use the relation
>are constrained.  For some relations, it doesn't make sense to have two
>propositions that are true at the same time.
>As an (admittedly flawed) example, if you had a 'COLOUR' relation
>which  related automobiles to a single member of the set {RED,YELLOW,BLUE},
>it would be a useful part of the signature/definition of the COLOR
>relation to say that if you have (COLOUR AUTO-9876 RED) that you
>cannot have (COLOUR AUTO-9876 BLUE) as well.
>
>These are some of the structural relations that I am trying to define
>for version 3 of the Starter Structural Ontology.
>
>David (whitten@lynx.eaze.net) (713) 791-1414 ext 6116
>

-----------------
Adam Pease
Teknowledge
(650) 424-0500 x571