Pat Hayes wrote: (01)
> Maybe this phrase has been unfortunate. By "in the head" I meant only
> that the commonality was identified using an intuition that the
> instances had something recognizably in common. For example, I can
> recognize a program as being an implementation of Quicksort because in
> have, in my head, an understanding of what constitutes Quicksort. Im
> quite happy to just say that Quicksort, the algorithm, is an
> abstraction, if you prefer that way of talking. We still need a way to
> refer to the 'abstract' version of an ontology, if we believe that such
> things exist: the thing that stands in the same relation to a number of
> formal ontologies that an 'abstract' algorithm stands in relation to any
> of its renderings as programs in a formal programming language. (02)
Being very careful, the notional QuickSort algorithm is itself based on
a set of assumed primitive functions (Turing's or whatever), which
effectively constitute the fundamental vocabulary of the language in
which the "algorithm" is "expressed" (even in your head). If you
express that algorithm in a communicable language that has those
functions, or has circumlocutions for them that neither lose nor gain
any significant meaning, then you clearly have another representation of
the same algorithm. (03)
The problem arises when the language in which you want to express your
algorithm doesn't have those functions, and the required circumlocutions
accrete noise -- unintended limitations, unintended generalizations,
etc. This expression is no longer quite the same algorithm. Is it
really an instance of the same abstraction? (04)
For programming languages we have fairly well established primitive
function vocabularies, common across many languages (although each
language may have additional gewgaws that don't get used in your
conceptual algorithm). For ontologies, it is not clear that we are in
an analogous situation. There is a collection of complete first-order
languages, and presumably the same ontology can be expressed in all of
them, where "same" means logical equivalence of the two theories as
expressed. But there is a large set of additional languages that are
slightly more than first-order or not quite first-order or intentionally
constrained (like OWL/DL and Horn clauses). Expressing your ontology in
one of those may give rise to loss, or to noisy circumlocution. And
unless two versions of the ontology are really logically equivalent, I
would be hesitant to agree that they are the "same ontology" in any
useful sense of "same". (05)
-Ed (06)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (07)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (08)
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