SUO: Re: nature of organisation
Adam --
Four related points here in response to your note:
(1) Can an organization have no members?
(2) CYC #$Group vs. SUMO &%Collection,
(3) Set vs. Class -- what is a Class?
(4) Axioms relating to Organization
(1) You believe that an organization cannot exist without members:
> Another issue which is on my mind because of discussions with Chris
> Welty is the essential property of an Organization. An Organization is not
> an Organziation without people but may still be one without anything other
> than it's members.
As I understand corporation law, a legal corporation is a Legal
Person
that does indeed exist as an entity on its own, related to its members,
but not depending on them for its existence (I'm not well-versed in
Law, someone who is should have the definitive opinion -- I
thought that dissociating the identity of a Corporation from its
members was one of the points of incorporation, which creates
a new legal person). The point I made is that the last member
of a corporation may die or leave, and the Organization as
a legal Person can still have assets and debts -- it still exists.
If that happens, a court may appoint an executor to liquidate
the assets, pay the debts, dissolve the corporation, and figure
out who gets any leftovers. This is probably a rare condition, but
it illustrates that Corporations, at least, may exist without members.
Probably most organizations we deal with do exist only while the
members exists, but I can think of other scenarios when an
organization may temporarily have no members.
Not quite on point, but related, is an incident when one
church group decided to merge with another, and arranged for
all it members to resign and then join the other church and
transfer their remaining property to the other church.
However, some members decided not to resign, and
after the majority did, the residuals claimed the assets as
belonging to them as the remaining members of the
original corporation -- and the court agreed. The
mistake was not to transfer the assets *before* resigning.
One can imagine a similar situation when they *did* all
resign -- the original corporation would exist without
any members, and it would be even more of a legal mess.
Even without the law, it seems reasonable to distinguish
an Organization as a group of people bound by some set of rules,
in which case it is *more* than just a group of people. If there
are no organizational rules (at least tacit or informal) ,
I think it would then be just a group of
people and not an Organization.
==========================================
(2)
My interpretation of the meaning of the CYC #$Group is
not based on the name, but on the documentation, to wit:
--------------
(from the Public CYC)
;;; #$Group
(#$isa #$Group #$ObjectType)
(#$genls #$Group #$TemporalThing)
(#$genls #$Group #$Individual)
(#$genls #$Group #$Situation)
(#$comment #$Group "A collection of objects. Each element of #$Group is
a composite object, made up of individual members which may be either
events or objects. A group is related to its members by the predicate
#$groupMembers (q.v.). Note that elements of #$Group are NOT
collections; consider: a group has temporal extent and may have spatial
extent and location, while a collection is timeless and abstract.
Nonetheless, it is possible to define a collection parallel to any
group, so that the #$groupMembers of that group are also instances
(#$isa's) of the correlated collection; e.g., each toe on my left foot
is both an element of the collection of my left toes and a member of the
group of toes on my left foot. But that group (of my left toes) is a
spatiotemporal thing, while the correlated collection (of my left toes)
is NOT. Another example: if I consider a certain flock of pigeons as
having a location, a spatial extent, and a time of existence, then I am
considering (the pigeon flock) a group and NOT a collection. As a
default, a group whose #$groupMembers are elements of
#$SomethingExisting is itself an element of #$SomethingExisting; and a
group whose #$groupMembers are elements of #$Event is itself an element
of #$Event. Finally, unlike a collection, a group cannot be empty; a
group must have some #$groupMembers, or there is no group (at that point
in time). Examples of #$Group: #$QueensGuard, #$ThreeWiseMen,
#$SantasReindeer, #$InternationalCommunity.")
--------------------
Of course, without the axioms and examples of useage we can't
know for sure the details of what a reasoning process may do
with such a concept. I presume that the individuals writing that
documentation and the subsumption of #$Organization under #$Group
never considered the possibility of an #$Organization
persisting without members.
One of the objectives, I would hope, for the
SUO effort is to look critically at what has been
done before and try to avoid what appear to be
mistakes. The CYC usage appears to me to be a mistake,
and the present SUMO usage looks similar.
In SUMO 1.17, the definition of &%Collection
appears to have a similar intention to the CYC
#$Group, though the documentation in SUMO isn't as
detailed, and the axioms are insufficient to
make a distinction. A &%Group is a subclass of
&%Collection, so it should have similar properties.
Sumo definitions:
----------------
Group:
(subclass Group Collection)
(subclass Group Agent)
(documentation Group "A &%Collection of &%Animals or &%Humans, e.g. a
flock of sheep, a herd of goats, or the local Boy Scout troop.")
(=>
(and
(instance ?GROUP Group)
(member ?MEMB ?GROUP))
(instance ?MEMB Animal))
(subclass GroupOfPeople Group)
(documentation GroupOfPeople "A &%Group consisting exclusively of
&%Humans.")
(=>
(and
(instance ?GROUP GroupOfPeople)
(member ?MEMB ?GROUP))
(instance ?MEMB Human))
----------------
Collection:
(subclass Collection Object)
(documentation Collection "Collections have &%members like &%Classes,
but,
unlike &%Classes, they have a position in space-time and &%members can
be
added and subtracted without thereby changing the identity of the
&%Collection. Some examples are toolkits, football teams, and flocks
of sheep.")
(=>
(instance ?COLL Collection)
(exists (?OBJ)
(member ?OBJ ?COLL)))
==================================
-----------------------------
(3) Question:
Set vs. Class
A related question I have asked and do not yet know the answer
to is why a "Set" in SUMO is a subclass of "Class" when in most
theories the opposite is true. The definitions below
say that a Set, "unlike &%Classes generally", does not
have "an associated condition" (i.e. the standard interpretation
of Class), but if Classes all had "an associated condition", then
with the subclass relation in SUMO this would
appear to violate the principle of inheritance of attributes;
whereas, if the subclass/set order were reversed, the comment
would be correct, but then Class would no longer be a
generalization of Set.
This would not be a contradiction if in fact Classes
generally were not *required* to have an associated
memership condition, but this would then differ from the usual
interpretation of "Class" as it is used in ontologies
(e.g. in the Ontolingua Frame Ontology, a Class is a subclass of
Set; a Class is distinguished from a unary predicate only by
a second-order predicate.) I can understand why one might
want to define a "generalization" of Set so that it is
not extensional, but I could not find defining axioms for
"Set" or "Class" (except the extensionality axiom for &%Set),
and from the definitions below I am not sure whether these
two concepts actually serve their intended pupose.
In the documentation, a distinction is drawn between
Class and Collection that a collection can change
members without changing the identity of the collection
(a typical criterion for *intensional* definiton):
"Collections have &%members like &%Classes, but,
unlike &%Classes, they have a position in space-time and &%members can
be
added and subtracted without thereby changing the identity of the
&%Collection."
. . . but the documentation for &%Class specifically says that
Classes are *not* defined extensionally, which is
also what is implied for &%Collection by the documentation for
&%Collection. Can you clarify this?
Question: Is it *required* that a Class have an
assocated membership condition (predicate)? If not, is there
any concept that serves as an intensionally defined Set,
like the "Class" of the Ontolingua Frame Ontology?
If a &%Collection retains its idenity in spite of membership
changes, does this not mean it is *necessarily* defined
intensionally (by a defining predicate)?
I think it's a good idea that the highest levels of the
ontology should have the clearest and least
ambiguous definitions.
--------------------
From SUMO 1.17
(subclass Set Class)
(documentation Set "A &%Class that satisfies extensionality as well as
other conditions specified by some choice of set theory. Unlike
&%Classes generally, &%Sets need not have an associated condition that
determines their membership. Rather, they are thought of metaphorically
as `built up' from some initial stock of objects by means of certain
constructive operations (such as the pairing or power set operations).
Note that extensionality alone is not sufficient for identifying
&%Classes with &%Sets, since some &%Classes (e.g. &%Entity) cannot be
assumed to be &%Sets without contradiction.")
(subclass Class Abstract)
(documentation Class "&%Class generalizes that &%Set. &%Classes, like
&%Sets, are collections of things. Accordingly, the notion of
membership
is generalized as well - a member of a &%Class is an &%instance the
&%Class. &%Classes can differ from &%Sets in two important respects.
First, &%Classes that are not explicitly identified as &%Sets are not
assumed
to be extensional. That is, distinct &%Classes might well have exactly
the
same instances. Second, &%Classes typically have an associated
`condition'
that determines the instances of the &%Class. So, for example, the
condition `human' determines the &%Class of &%Humans. Note that some
&%Classes might satisfy their own condition (e.g., the &%Class of
&%Abstract
things is &%Abstract) and hence be instances of themselves.")
========================================
(4). Axiomatization of Organization:
(using SUMO terminology:
This isn't carefully checked -- it may have errors, but this is
the
general idea)
Relevant Hierarchy fragment:
------------------
Agent
Organization
NormativeProposition
Rule
Set
Membership
RuleSet
OrganizationRules
Collection
OrganizationMembers
------------------------
((1)) (subclass Organization Agent)
((2)) (subclass Rule NormativeProposition)
(I can't easily axiomatize this because our discussions of
Rules and Authorities
and consequences of infringement never reached a
conclusion)
((3)) "RuleSet is a Class each instance of which is a non-empty Set,
all of whose elements are Rules"
(subclass RuleSet Set)
(forall ?RS
(=>
(instance ?RS RuleSet)
(and
(exists ?y
(and
(element ?y ?RS)
(instance ?y Rule))
(forall ?z
(=>
(element ?z ?RS)
(instance ?z Rule)))
)))
((4)) " Organizational Rules are a RuleSet"
(subclass OrganizationRules RuleSet)
" OrganizationRules and the Membership are proper parts of an
organization:"
(subclass Membership Set)
(properPart OrganizationRules Organization)
(properPart Membership Organization)
" All elements of Membership are Agents"
(as does CYC, we leave open the possiblity that a "member" of an
Organization
may be another organization (e.g. as with the UN, or a
Chamber of Commerce))
(forall (?MBSHP)
(=>
(instance ?MBSHP Membership)
(forall ?MEMBR
(=>
(element ?MEMBR ?MBSHP)
(instance ?MEMBR Agent) ))
))
To allow empty sets of organization members, it
is possible to define a set all of whose members (if
they exist) are also members of an associated
"OrganizationMembers" (this is one way to allow
null membership -- another way is to allow a Collection
to have null membership)
((5))" The group of OrganizationMembers is a Collection (because it
may include other groups, not only individual people)"
(subclass OrganizationMembers Collection)
((6)) "The Membership of an organization is a
(possibly empty) set, all elements of
which are also members of some instance of
OrganizationMembers; for
every non-null Set in Membership there is an associated
Collection in OrganizationMembers"
(subclass Membership Set)
(forall (?MEMB ?MSHP)
(=>
(and
(instance ?MSHP Membership)
(element ?MEMB ?MSHP))
(exists (?OM ?ORG )
(and
(instance ?ORG Organization)
(instance ?OM OrganizationMembers)
(properPart ?MSHP ?ORG)
(member ?MEMB ?OM)))
))
------------------
Pat Cassidy
======================
Adam Pease wrote:
>
> Pat,
> We should be a little careful here because it sounds like you may be
> reading a bit into the names of terms - especially for Cyc since the axioms
> aren't public.
> Another issue which is on my mind because of discussions with Chris
> Welty is the essential property of an Organization. An Organization is not
> an Organziation without people but may still be one without anything other
> than it's members.
> But, overall, I think you're bringing up excellent issues. Could you
> recommend a change in the axioms to accommodate these issues?
>
> Adam
>
> At 02:40 PM 8/24/2001 -0400, Patrick Cassidy wrote:
>
> >Concerning organizations:
> > In the SUMO and also in the CYC, Organization is a
> >subclass of Group, which is some assemblage of
> >entities -- distinguished from a Set, which is
> >considered "timeless an abstract". This
> >distinction can be useful, but since groups of
> >physical objects can then be considered as physical
> >objects, it seems inappropriate to classify an
> >organization as a subclass of Group. The members
> >of an Organization form part of the Organization,
> >but not the whole part. The rules creating the
> >organization and defining the relations of members
> >to each other and to the group are an essential
> >part of an organization -- that's why it is
> >"organized". I would prefer to see an
> >Organization defined as an agent that has
> >a set of operating rules and a group of people
> >as a *Part* of the organization. A lot
> >of "organizations" have only one person as
> >a member (e.g. sole proprietarship corporations
> >with no employees other than the owner).
> >Consider a legal organization -- it is possible
> >for the sole member to die, but for the
> >organization to continue as a legal entity,
> >e.g. if it has property and debts
> >(the heirs might have to clean up the mess).
> >In CYC, a Group must have at least one member.
> >This situation would create a contradiction,
> >unless one were to specify that every owner is
> >de facto a member, and even then there could be
> >an ownerless corporation whose affairs are
> >terminated by some appointeee of the courts.
> > To clarify the distinction, we could consider
> >a mob or a crowd as consisting solely of
> >its members. A mob or a crowd, then, could be
> >an Agent that *is* a subtype of Group. The useful
> >(I think) distinction would be to consider an
> >Organization as an Agent that has a Group as a part.
> > The way to specify roles in an organization
> >is a different issue.
> >
> > Pat Cassidy
> >
> >===========================================
> >
>
> Adam Pease
> Teknowledge
> (650) 424-0500 x571
--
=============================================
Patrick Cassidy
MICRA, Inc. || (908) 561-3416
735 Belvidere Ave. || (908) 668-5252 (if no answer)
Plainfield, NJ 07062-2054 || (908) 668-5904 (fax)
internet: cassidy@micra.com
=============================================