Re: Roles, again

"Nicola Guarino" <>
Message-id: <guarino.1160950943A@>
Date: Fri, 8 Sep 95 13:28:23 +0100
From: "Nicola Guarino" <>
Subject: Re: Roles, again
To: "Pat Hayes" <>,,
Cc: "Pierdaniele Giaretta" <>,
        "Massimiliano Carrara" <>
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On 8 Sep 95 Pat Hayes wrote:

>>>On 28-AUG-1995 John Sowa wrote:
>>>Are Entity, Role, eventually Agent primitives? If not, what would
>>>be the definition of, say, Role?
>>>It seems to me that the above definition requires Entity an Role to have
>>>non-empty intersection (i.e. their common subtype must not be bottom).
>>John Sowa answered:
>>>Role is not a primitive in the logic, but in the ontology that I am
>>>suggesting (which, strictly speaking, is not part of the CG formalism,
>>>but of the top-level ontology that is optional) I have been following
>>>CG Peirce's categories of Firstness, Secondness, and Thirdness.  Since
>>>those labels sound strange to most people (and even to Peirce himself,
>>>who chose those labels precisely because they had no common associations),
>>>I have been using the type labels Form, Role, and Mediation.  Form is
>>>defined as the top (or Entity) with the differentia Firstness; Role is
>>>Entity with differentia Secondness; and Mediation is Entity with
>>>differentia Thirdness.
>Oh, thats a GREAT help. There were three incomprehensible words and now
>there are four. Could I put in a plea for good old Fregean extensionality
>here? In spite of its evident ability to intellectually seduce, I cant see
>a single practical reason why we should take any of this Peircian mysticism
>seriously: it belongs with Freemasonry.

I don't know whether it's Freemasonry, what is certainly true is that these
words are incomprehensible but at the same time stimulating. What is needed
is an effort for translating the relevant ideas (if any) into ordinary
logic, I agree with Pat on this point. Unfortunately, the sort of
"mysticism" which ssems to permeate John's words doesn't help too much.

However, I'm convinced that there *are* relevant ideas hidden behind this
mysticism. The notion which lies behind, as far as I have understood, is
that of *dependence* (to be more precise, "conceptual" or "notional"
dependence, as Peter Simons calls it in his book on parts [p. 297]). A
predicate like Mother, for instance, is dependent on Child if there cannot
be a mother without a child ("Secondness"). A predicate like Person, on the
other hand, can be conceived as indepedent if the fact that X is a Person
does not necessarily imply that somebody else is an instance of another
predicate ("Firstness"). Finally, if we have reified situations (or states
of affairs, eventualities, or whatever) in our domain, we can think that the
fact that X is a Mother implies the existence of a "Motherhood" situation

This notion of dependence is very akin to that of "Foundation", extensively
(but informally) discussed by Husserl in his "Logical Investigations". Its
rigorous formalization requires of course some care, but fortunately, there
are a couple of proposals around (Peter Simons, Kit Fine & Barry Smith)
which aim exactly to this purpose. In my papers, I have used an adaptation
of the modal formalization proposed by Peter Simons. 
>>This should answer - at least in part - the questions raised by Peter Clark
>>in a recent message:
>>On Aug 31, Peter Clark wrote:
>>>I'm worried (well, I always have been) about the distinction between roles
>>>and concepts, and also how things keep slipping betweeen the two -- eg. as
>>>reflected by often having relations and concepts with the same name 
>>>(Eg. [Person]->(MOTHER)->[Mother]). 
>>> - On the one hand: saying a concept C is in a role R isn't exactly 
>>>   the same as saying C isa R. An isa hierarchy gets messy with 
>>>   "concepts" in it like "Product", "Transportee", etc., which
>>>   happens if you write things like [Production]->(PRODUCT)->[Product] etc.
>>>   Often almost anything can fill these roles.
>>> - On the other hand: If a concept is playing some role R, then it
>>>   presumably should acquire some of information about the role. 
>>>   eg. if John's stomach is filling the role of container in eating (say),
>>>   then presumably we should be able to infer it's a concave structure,
>>>   has a boundary and free-space inside it, has a portal etc.
>>>   If a "role" is reduced to just being another relation then we 
>>>   lose any information about what that role *means*. Surely
>>>   by filling a role you aquire some properties (somehow) automatically???
>>>Maybe a role is a kind of "temporary isa link"? And when is something
>>>a role or a concept? Eg. "Agent", and "Mother" are perhaps roles rather
>>>concepts? (Or is everything a role)??
>Surely there is a well-known path through this tangle. The naming
>coincidence arises because in English we often use a relation name to
>indicate an individual (as in "Mother! You're safe!" where the full meaning
>is clearly "My Mother!..", rather than "A Mother!.." or "Motherhood!..").
>We shouldnt let this enthymematic elegance of our communication language
>confuse our conceptual language, but always clearly distinguish between the
>individual (my mom) from the relation (is-the-the-mother-of) it might have
>to another individual (me). If we do this, then to capture the linguistic
>regularity noted (that in certain
>cases the relation name can  be used to denote the property), we need to
>talk about the relations. Elegant and powerful notations already exist for
>doing this: in this case for example we could say 
> (lambda x)(x is-the-mother-of a) = (Mother a). 
>These notations can of course be strongly typed, if necessary.
>>I would say that, roughly, every unary predicate is either a concept or a
>>property: Mother, Pedestrian and Person are all concepts, while Red may be a
>>property (within a particular ontological commitment); the former two are
>>roles, accordinto the definitions above, but only Mother has a
>>corresponding *relational interpretation*, namely Has-Mother. 
>I suppose you mean that (Mother a) implies (exists x)(x is-the-mother-of
>a); or possibly (exists R)(exists x)(x R a).

Yes, exactly. By the way, you exchanged x with a: it should be (Mother a)
implies (exists x)(a is-the-mother-of x).

>If so, you can 'define' being
>an attribute thus:
>(forall A) (Attribute A) iff 
>    (forall x)((A x) implies (exists R)(exists x)(x R a) )
>Of course if you want uniqueness conditions, etc., these can all be
>asserted as needed. (By the way, this is all essentially first-order...if
>you give it the right (Henkin) semantics.)

I agree it is essentially first-order, however the definition you propose is
too weak, since if you have in your knowledge something like "every Person
loves some Person":

(forall x) ((Person x) implies (exists y) (x Loves y))

then it turns out that Person is an attribute.

The definition I have used in my DKE92 paper goes as follows:

A unary predicate A is an attribute iff:

1) there exists another unary predicate B such that A is conceptually dependent 
   on B;

2) there exists a binary relation R such that its domain is subsumed by B and
   its range is subsumed by A.

A predicate A is conceptually dependent on B iff:

   necessarily, (A x) implies (exists y) ( (B y) and not (y Part-of x) ).

The proviso concerning part-of (amended wrt the published version) is
required in order to consider a predicate like Person as indepedent even if
each person has some parts (this version of dependence may be called "strong
conceptual dependence").

Finally, notice that the definition above only holds for what I have called
"relational attributes" (like Mother), while it doesn't work for
part-denoting attributes like Wheel (of a Car, for instance). In this case
we may require a Part-of relation such that its domain intersects Wheel, but
this is another story...

>>A final comment deserves Peter's concern regarding the proliferation of
>>concepts: one of the advantages of a clean distinction between types and
>>roles is the possibility to superimpose a "skeleton" of types on a huge
>>network of concepts: such a skeleton (which in most cases turns to be a
>>tree) would help a lot for indexing purposes.
>Types are indeed an excellent idea for this reason, but they can get a bit
>complicated if you want to utilise them fully, as for example in
>unification. (See for example Tony Cohn's doctoral thesis.)

I agree.

>By the way, interesting 'sort' structures are not then usually trees. For
>example, consider the relation of being-a-boundary-of. This can hold
>between a line and a surface or a surface and a volume, but not between a
>line and a volume. Or for a more mundane example, consider
>being-married-to, which can hold between a male and a female or vice versa,
>but not between two males or two females. In cases like these there isnt
>any way to make the sortal structure tree-like: there isnt any sort above
>Male and Female which one can assign to the arguments of the
>being-married-to relation which captures the needed constraint.

These examples don't actually involve the sort structure itself (which in
the last example is just a tree, i.e. Person with Male and Female as
children), but the attempt to express the necessary conditions for some
relations by means of sortal restrictions only: of course this is almost
impossible to obtain, in general. When I was speaking of trees, I intended
to underline the fact that types *tend* to form a tree, while roles do not.

-- Nicola


Nicola Guarino
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