Re: SUO: Re: More Terminology
> The way "relation" is defined in KIF certainly seems to
> me to be a parent class of "Class" as defined in KIF --
> relation -- a set of tuples
> class -- a set of tuples of length one.
In the IFF, morphisms are important. The term "class" is represented by the
IFF notion of *entity type*. The term "relation" is represented by either
the IFF notion of "relation type" or the IFF notion of "relation instance" =
"tuple". In the IFF, analogous to the well-known injection from a set A to
the set of strings A*, in the next version of the language namespace there
will be an injective function from the set of entity types to the set of
relation types. The corresponding monadic (unary) relation type is
equivalent to the entity type as far as extent is concerned. This has been
found necessary in order to define the notion of a *free model* over a
language and a *free logic* over a theory. Also in the IFF, there is a
function called *extent* from the set of relation types to the *power set*
of tuples. This is a special case of the extent function for any IFF
classification. All of these notions are components of (and thus
parameterized by) the IFF language in question.
Bottom line: Because of the new function representing entity types as
monadic (unary) relation types, we might view "relation" as a parent class
of "class". However, because of the extent function for relation types we
might view "relation" as a special kind of set. Morphisms (in this case,
functions) are important in the discussion.
PS: I back the idea of an SUO glossary, and in the structural part of this
glossary I could point to and comment on representative IFF terminology.
Robert E. Kent
rekent@ontologos.org