representation-relations in ontologies (Fritz Lehmann)
Date: Sat, 3 Jun 95 07:21:52 CDT
From: (Fritz Lehmann)
Message-id: <>
Subject: representation-relations in ontologies
Precedence: bulk

     Some moths ago Pat Hayes wrote the following, starting with
a quote from me.  I'm posting this to the srkb ontologies list since 
most ontologies will have to define a representation-relation (including
a notion of naming), to the peirce-l list to attract the expertise of some
Peirce scholars, and to the Conceptual Graphs cg list.  I conclude with
a remark that this issue has practical commercial consequences.
---------BEGIN HAYES QUOTE-----
FRITZ> . . .   BUT,
>would someone please propose the CENTRAL and BEST Peircean formal definition
>of the sign-relation.  Include any A. Necessary conditions true of any
>sign-relation, and B. Any sufficient conditions to determine that
>a given relation is in fact a sign relation, and C. Any necessary-
>and-sufficient conditions (pure logical "definition").
>     (Note that my allowing for A. and B. above, as opposed to C.,
>means that I'm not confining this to Ransdell's "mere stipulation"; the
>"definition" may be acknowledgedly incomplete and approximative,
>of something real in the world, but still a reliable formal
>constraint suitable for automated inference.)
Why do you say that such a definition is a FORMAL constraint? Because it is
to be expressed in a formal language? But a formal language can express
informal concepts. Watch: 'VeryFondOf(Jackie, Aielonwy)' asserts something
informal (ie not formally defined) but true about my wife and her cat. Its
informal becuase there is no formal defintion of 'VeryFondOf'. Thats OK:
all we need to be able to do is to write some axioms using it, and I just
did that. An axiomatisation (even in a formal language) isn't necessarily a

     The point is that I was not necessarily asking for a logical IFF
definition.  Merely some constraining axioms would help.  The Peirce
enthusiasts discuss signs endlessly, but it is hard to pin them down as to
what a sign-relation actually is; that's what I was hoping to do with
my request for something "formal".  "Clear" will do.  A mechanized ontology 
can't use mushy definitions.  Still I consider the Peircean theory of semiotics
to be by far the most likely valuable source of a useful and real ontology of
sign-relations.  There are three, then ten, then sixty-six, then maybe
111 different subclasses of sign-relations, built combinatorically from
fairly clear and solid elements; plus, there are further developments
by Robert Marty of "sign lattices".  The pictures are nice in his
"l'Algebre des Signes" but I don't speak French so I can't vouch for the

FRITZ>     We have a practical task which is to create a useful ontology
>for the real world (as part of the "CCAT" group of the "Peirce
>Software project" -- dealing with Conceptual Catalogues).  A major
>"core ontology" will be REPRESENTATION/SEMIOTIC which turns out to
>be required for most other subjects. We know that any sign-relation
>is triadic (a representamen A represents object B to interpretant C)

We do? I dont find this at all convincing: the relation seems essentially
binary to me. If you include 'interpretant', why stop there? Why not 'in
context D' and 'at time E' and 'for purpose F' and 'among socioeconomic
group G' etc etc. ?

     Heresy.  Now this is deemed a crucial point by Peirceans, and I
hope some will weigh in and correct you.  First of all, sign-relations
do not need to have any time, place, etc.  The Platonic tetrahedron
represents the element fire, with no commitment as to the time, place,
etc. of the tetrahedron nor the fire.  In contrast, what is it about the
tetrahedron that represents fire at all?  Nothing, if you confine yourself
to the inherent predicates true of a regular tetrahedron (4 faces, 6 edges,
etc.)  Also nothing if you confine yourself to the inherent relations
(dyadic ones) that exist between a regular tetrahedron and some fire.  It
is only the "interpretant" (an alchemist like Newton, say) that creates
the representation-relation between the tetrahedron and fire.  This third
element is essential, and failure to account for it has been shown to
underlie errors of many linguistic theories (e.g. Saussure et al. who grounded
all on a supposed dyadic sign-to-object relation).  Or consider my standard
example of the unexplored cave.  What "signs" are in there?  None; it is only
after some interpretants get in that the cave guide can inform me that
a particular stalagmite _represents_ "two fried eggs".  So, independent of
any monadic or dyadic relations which may additionally be required of the
participants, a sign relation requires at least the three participants:
the object (represented thing), the "representamen" (the sign, or
representing thing), and the "interpretant" (the thing to which the 
representamen represents the object).  I don't think you can correctly
concoct a true representation relation that omits the third participant
in the definition.

FRITZ>and inherently causal (the relations of A to B, and of A to C,
>_cause_ a relation to arise between B and C),

You just indicated why the relations involved are binary.

     No.  If it were only R1(A,B) causes R3(B,C), or else only R2(A,C)
causes R3(B,C), then this would be a second-order dyadic (binary) relation, 
as you suggest, but that's not the case.  Nor is it a mere happenstance
conjunction of these dyadic second-order relations; it is a genuine
first-order triadic relation among A, B and C; if any one is
missing, the derived dyadic relation between the other two evaporates.

---------RESUME HAYES QUOTE-------
If you mean eg that "cat" meaning cat (your A) causes my thinking of cats
when I see or hear "cat" (your B), then I think theres a problem. Its not a
relationship between "cat" and cats which causes me to think of anything,
its a relation between "cat" and complicated aspects of my psychological
state, including my knowledge of English. I don't think the denotation
relation can possibly cause anything, in fact.
--------PAUSE HAYES QUOTE------

     Say A is "cat", B is the cat, and C is Pat.  You have hit the nail on
the head: the "denotation relation" (a dyadic relation between A and B)
does not exist without C; it does not cause anything.  It is _your_
relation to "cat" (C to B) which _with_the_sign_triad_ causes you to come
into a relation with the cat (C to A); the "denotation" relation 
inherently involves you.  Now when you bring in psychological states,
and English, that complicates things a bit because we get into
intersubjective consensus when more than one "interpretant" is involved.
But the essential sign relation does not change.  Without the sign-relation
triad, hearing "cat" would no more remind you of a cat than "splat" does.

>but that is still too
>general to capture what is meant by sign-relation or representation.
>     Any takers?
Heres a suggestion, which Ive made before. Dont start by trying to write
definitions. Rather, try to write down facts about the subject-matter,
using the best vocabulary youve got, and try to sharpen up the vocabulary
while sorting the facts out. That way you might discover some definitions:
but to try to make definitions first is bound to lose. Similar things have
been said (and done) by many others, maybe including Peirce.

     I agree.  Facts first, definitions later.  Among facts, consider
all the borderline cases you can think of.

Eg think about an act of representing, ie what happens when a
representational token is used in a representational way. Ask what can
count as such a token; and the answer is just about anything, which
suggests that attempting to give a general definition of your A might be a
mistake, since it is pretty much the universal relation. ("Let this
sugar-cube represent the Russian cavalry...")
------END HAYES QUOTE------

     Exactly!  It is _not_ a defining feature of "a sign" that we are
looking for.  It is a defining feature of a _sign_relation_ (including
the interpretant) that we need.  Anything can be used as a sign 
(representamen).  "This pineapple here is me."  We are not trying to
define what can or cannot be "a sign".

HAYES>Pat Hayes

     I want to say to practical-minded people on these lists that
this business of representation is something that needs to be
understood well.  In data sharing applications (such as EDI - Electronic
Data Interchange - commercial transactions between trading partners)
there are multiple ways of "naming" the same concept.  The identity
of a company, for example, may be denoted using the company name (full
legal name, customary name, acronym, alias, etc.), by a description (e.g. by
role), or by reference to some code authority (say, the DUNS number).  Careful
ontologizing requires accounting for certain facts, such as the possibility
that one company has many names, many companies have one name, companies
can split and merge, different authorities may have different encodings
of the same company, etc.  The DUNS number of a company may change.  Most
companies in the world have no DUNS number.  Etc.   When some "sign" is
used to represent a company, it should be clear just on what basis that
sign represents the company, and what entity is represented.  To some extent
this involves matters of law.  Those of us concerned with careful grounding
of complex concepts in terms of more primitive concepts will be interested
in defining these pragmatic commercial representations with basic "sign-
relation" concepts which underlie them.

     Specifically for conceptual graphs, the sign-relation is, I believe,
a necessary part of any supposed "co-reference" between an individual inside
an intensional cotext (say, a belief context) and the "corresponding"
individual outside the context.  They are not the same individual.  Your
mental notion of the Suez Canal cannot be _identified_ with the Suez
Canal.  There is a semiotic chain of triadic sign-relations from one to the
other, however.

                          Yours truly,   Fritz Lehmann

GRANDAI Software, 4282 Sandburg Way, Irvine, CA 92715, U.S.A.
Tel:(714)-733-0566  Fax:(714)-733-0506