Re: [ontolog-forum] Foundation ontology, CYC, and Mapping

[Gary Berg-Cross <gbergcross@xxxxxxxxx>]

I have a small question to wedge into this discussion on whether the meaning of Primitives in a Foundation Ontology change (or may change) as we add axionms.

 

Patrick Cassidy  describd this as a 

  >disconnect between PatH's view of "meaning" and mine is that he is
>content to believe that the meanings of the elements used in programs,
>databases, ontologies (e.g. time, distance, physical object, dollar, person)
>all change every time we add a new assertion about unicorns, and I am not.
>IMNSHO, this is not a useful interpretation of "meaning" for practical
>programming purposes.
 

Eearlier John Sowa expressed his objection to using 'primitives' as a foundation is that

 

"the meaning of a primitive changes with each theory in which it occurs.
 For example, the term 'point' is a 'primitive' in cand
various non-Euclidean geometries.  But the meaning of the term 'point' is
specified by axioms that are different in each of those theories."
 (and in another note)  "As soon as you add more axioms to a theory, the "meaning" of the
  so-called "primitives" changes.'

 

Since Euclidean geometry, an axiomitized systems, was mentioned it reminded me of Euclid's first 4 postulates (axioms) which involve primitives like point.  When a 5th axioms is added it didn't seem like the primitives changed and that any conclusion just using the first 4 axioms would be the same.  If the 5ht axioms is involved then new conclusions are reached.  On the face of it this seems to be the an intuition that supports  (in part) what Pat C was saying.

 

Can our formalists help out on this question?

 

Gary Berg-Cross,Ph.D.
gbergcross@xxxxxxxxx      http://ontolog.cim3.net/cgi-bin/wiki.pl?GaryBergCross
SOCoP Executive Secretary
Knowledge Strategies
Semantic Technology
Potomac, MD
240-426-0770

 

On Thu, Feb 25, 2010 at 12:18 PM, Patrick Cassidy <pat@xxxxxxxxx> wrote:

John,
  The disconnect between PatH's view of "meaning" and mine is that he is
content to believe that the meanings of the elements used in programs,
databases, ontologies (e.g. time, distance, physical object, dollar, person)
all change every time we add a new assertion about unicorns, and I am not.
IMNSHO, this is not a useful interpretation of "meaning" for practical
programming purposes.
  I am well aware that for each new axiom added to an ontology, some
logical inferences derived from input assertions will change.  But in my
view there are some elements - specifically the primitives - whose
interpretation by programmers, database developers, and domain ontologists
*must* not change when remotely related elements are added, and they will
still be used in the same way in programs and still give **the same
answers** to queries that are of practical importance to the programs they
are used in - even if they may give different answers to bizarre test
queries that force reasoning to reach the remote parts of the ontology that
have changed.  Semantic interoperability is a practical problem that has
been addressed in the past by local agreements on interpretation of data
elements without resort to Model theoretic/Tarskian theories, and the FO is
merely a practical tactic to extend the ability to forge useful and
practical agreements on meaning among a much wider community than is
possible through local agreements. In spite of the admitted beauty and power
of model theory, if in fact it forces the conclusion that all meanings
change when a new axiom is added, then it is not a proper formalization of
what "meaning" has to mean in a computational ontology.
  One way that the apparent problem might be addressed is to recognize that
programs have some expected behavior for their data elements, and this can
be tested with test suites.  If some change to an FO causes a change in the
usage of data elements that are not intended to be changed, then either (1)
that change is inconsistent and has to be rescinded or somehow modified so
that the proper usage of other data elements is not affected; or (2)
programs that are affected by a change in the FO have to use the old FO, and
if they need to interoperate with programs that use the new FO they will
have to take precautions against the undesirable changes.
  But these problems affect interoperability primarily if there are changes
in the FO.  The problem of changes to the FO is precisely why I have
suggested that it is important to identify at the earliest stage as many as
possible of the primitives that will be used for translating among multiple
domain ontologies. That will keep the need for changes to an FO to the
minimum that is practical.

  Another comment from PatH that is puzzling:
> [PC] > > Perhaps future objections could focus on genuine technical

> problems
> > (not analogies with human language), and better yet suggest
> > alternatives to solving the problem at hand: not just *some* level
> > of interoperability, but accurate interoperability that would let
> > people rely on the inferences drawn by the computer.  If not a common
FO, then what?
>

> [PH] > Nothing. This is not a viable goal to seek. It is a fantasy, a

dream.
> One does not seek alternative ways to achieve a fantasy.

  I had thought that general accurate semantic interoperability (not
"perfect" interoperability) was the goal of the "Semantic Web", and it seems
that PatH's comment therefore includes the SW in the realm of "fantasy".
Since PatH is a Semantic Web enthusiast, I doubt that was his intention, but
it would seem that some clarification is required.

Pat

Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx


> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa

> Sent: Thursday, February 25, 2010 8:47 AM
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] Foundation ontology, CYC, and Mapping
>

> Pat C, Pat H, and Ron,
>
> RW> [Pat H's reply to Pat C] does look like some things worth keeping
>  > for more than the time it takes to read an e-mail and press delete.
>
> I agree.  I'd just like to summarize and emphasize a few points.
> In the following summary, the quoted sentences are by Pat H, and
> the unquoted sentences are by me.
>
>   1. "Tarskian semantics... is a very general theory of meaning, one
>      that can be applied to a wide range of languages and notations."
>
>      Yes indeed.  In fact, *every* theory of formal ontology that
> anyone
>      has proposed in the past half century is based on a Tarski-style
>      semantics.  That includes Cyc, SUMO, BFO, Dolce, etc., etc., etc.
>      It also includes the semantics for every digital system (hardware
>      or software) that has ever been designed and built since the 1940s
>      -- including those for which the designers had no idea what a
>      formal semantics is or might be.
>
>   2. "It is just wrong to draw the contrast between the natural things,
>      on the one hand, and the account provided of those things by a
>      theory of them, on the other, as a difference of **kind**."
>
>      Yes.  Every statement in logic is absolutely precise.  The common
>      words used to define the subject in Longman's dictionary (or any
>      other dictionary written by lexicographers for human readers) are
>      usually rather vague and shift their meanings slightly from one
>      definition to the next.  But that vague cloud of meaning
> *includes*
>      the formally defined meaning.  The vague meaning covers more cases
>      and it has a fuzzier boundary, but each precise meaning contained
>      in the could is just one very sharply defined sense of the same
>      nature as any other word sense in the cloud.
>
>   3. "Computational ontologies are artifacts, written in formal logical
>      notations."
>
>      Although I agree with that statement, I suspect that Pat C was
>      claiming that programs have some meaning other than what is
>      captured in a formal logic.  But it is important to distinguish
>      a declarative statement (in a usual logic) from an imperative
>      statement, such as a command or a machine instruction.  But every
>      machine instruction and every program written for a digital
>      computer can be completely defined in the following form:
>
>          Preconditions, Action, Postconditions.
>
>      The preconditions and postconditions are statements in logic,
>      which can be formally defined by a Tarski-style semantics.
>      The preconditions describe the state of the computer system
>      before the action, which may be a single machine instruction
>      or an arbitrarily large program composed of many instructions.
>      And the postconditions define the state after the action.
>
>      The action itself has no meaning outside what can be described in
>      the logic used to state the preconditions and the postconditions.
>      The human commentary may explain what the programmer or designer
>      had intended, but if there is any discrepancy between the comments
>      and the program, there is a bug (or *issue* as MSFT calls it).
>
> Pat C has repeatedly made the following claim to justify his search
> for primitives:
>
> PC>> So, if we want the meanings of terms in an ontology to remain
>  >> stable, and **don't** want the meanings to change any time some
>  >> remotely related type appears in a new axiom...
>
> PH> But we DO want this! Surely that is the very point of changing
>  > and adding axioms. If meanings are stable across theories, then
>  > what is the point of adding axioms to capture more meaning?
>
> I'd like to clarify the kind of change that occurs when more axioms
> are added.  Each addition of an axiom to a theory is a specialization.
> The change it makes *narrows* the meaning of the terms in it.  For
> example, the term 'Animal' is very broad.  By adding more qualifiers
> (axioms), the meaning can be specialized to 'Dog'.  Further axioms
> can narrow it to 'Poodle'.
>
> Those are certainly changes, but they don't go outside the cloud
> of meaning of the original term.  In fact, every dictionary written
> for human consumption uses such definitions.
>
> John
>
>
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