[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Jawit Kien
Sent: Tuesday, February 02, 2010 11:11 AM
To: ian@xxxxxxxxxxxxxxxx; [ontolog-forum]
Subject: Re: [ontolog-forum] Foundation Ontology Primitives
On Tue, Feb 2, 2010 at 3:53 AM, Ian Bailey <ian@xxxxxxxxxxxxxxxx> wrote:
Hi Pat (I won't qualify which
Pat, as I'm pretty sure the other one has me
on his filter list),
In the thread that's been running, you indicate that you believe there are
some common ontic primitives that can be shared across multiple ontologies -
e.g. as a foundation. Do you have a clear idea of what these might be ?
(some examples would really help my understanding).
If I have an issue with this idea, it is one of pragmatism. As an
aspiration, a common foundation ontology is something I would really
support. There seems to me to be a couple of practical problems:
* Reaching consensus - ontology is a topic that attracts people with strong
opinions. Consensus requires compromise, and I don't see much of that going
on in this community. In my experience of developing ISO standards, it
usually requires a commercial reward to ensure true consensus is met - i.e.
they all (well, most) stop bickering if they can see some profitability in
not bickering. I don't think ontology is at the maturity level where huge
sums of money depend on its success or failure, so I fear consensus is going
to be nigh impossible.
* Metaphysical choices - most serious ontologists are aware of the
metaphysical choices (i.e. the ground rules) of their ontology. This
involves questions of how time is managed (3D, 4D Endurant, 4D Perdurant,
etc.), whether the ontology is extensional or intensional (both for class
membership, and how spatial/temporal extents are handled), and whether the
ontology is first order or higher order.
The first problem may be overcome by shear will - if enough people take a
positive approach and really want to get it done, it might happen. The
second issue is much more thorny, and that's why I asked what you thought
the primitives were. I once suggested a set of ontic categories on this
forum and was soundly thrashed for it, so I'd understand if you want to send
them off-list. Also, getting a clearer idea of what choices all the major
ontologies took might give us a better idea what common primitives are
possible. Again, if folks want to send that to me off-list, I'll collate it
all anonymously and post it back. God forbid we should actually use the
forum to discuss any real ontologies.
In the hope that we can
actually discuss some details about ontologies and
useful primitives, I submit the following table:
1. Current set of semantic relation types in MindNet
This is from:
MindNet: acquiring and
information from text
Stephen D. Richardson, William B. Dolan, Lucy
One Microsoft Way
is in a file: tr-98-23.doc which I downloaded from http://research.microsoft.com
some trail that John Sowa started me following recently.
is related to MNEX at http://stratus.research.microsoft.com/mnex/Main.aspx
the page http://stratus.research.microsoft.com/mnex/MnexHelp.aspx
probably be useful to someone looking to get more information.
note that Pat Cassidy has a list of "connectives" at http://micra.com/dictionary/tagset.txt
realistically, making a list of connectors is not the the interesting issue, in
you focus on making this list, as your first problem, you lose sight of the
is more interesting on this list i.e.: what axioms/true statements/rules exist
I mean is, can we create a list of axioms for Color, or Purpose similar to the
which are mentioned on the page: http://en.wikipedia.org/wiki/Mereology#Axioms_and_primitive_notions
(stealing from that page)
Axioms and primitive notions
It is possible to formulate a "naive mereology" analogous to naive
set theory. Doing so gives rise to paradoxes analogous to Russell's paradox. Let there be an object O
such that every object that is not a proper part of itself is a proper part of O.
Is O a proper part of itself? No, because no object is a proper part of
itself; and yes, because it meets the specified requirement for inclusion as a
proper part of O. (Every object is, of course, an improper part
of itself. Another, though differently structured, paradox can be made using improper
part instead of proper part; and another using improper or proper
part.) Hence mereology requires an axiomatic
A mereological "system" is a first-order
theory (with identity) whose universe of discourse consists of wholes and
their respective parts, collectively called objects. Mereology is a
collection of nested and non-nested axiomatic
systems, not unlike the case with modal logic.
The treatment, terminology, and hierarchical organization below follow
Casati and Varzi (1999: chpt. 3) closely. For a more recent treatment,
correcting certain misconceptions, see Hovda (2008). Lower-case letters denote
variables ranging over objects. Following each symbolic axiom or definition is
the number of the corresponding formula in Casati and Varzi, written in bold.
A mereological system requires at least one primitive binary
predicate). The most conventional choice for such
a relation is Parthood (also called "inclusion"), "x
is a part of y", written Pxy. Nearly all systems
require that Parthood partially order the universe. The following defined
relations, required for the axioms below, follow immediately from Parthood
object lacking proper parts is an atom. The mereological universe consists of all objects we wish to
think about, and all of their proper parts:
- Overlap: x and y overlap, written Oxy,
if there exists an object z such that Pzx and Pzy
parts of z, the "overlap" or "product" of x
and y, are precisely those objects that are parts of both x and y.
- Underlap: x and y underlap, written Uxy,
if there exists an object z such that x and y are
both parts of z.
Overlap and Underlap are reflexive, symmetric, and intransitive.
Systems vary in what relations they take as primitive and as defined. For
example, in extensional mereologies (defined below), Parthood can be
defined from Overlap as follows:
The axioms are:
M1, Reflexive: An object is a part of itself.
M2, Antisymmetric: If Pxy and Pyx
both hold, then x and y are the same object.
M3, Transitive: If Pxy and Pyz,
- M4, Weak
Supplementation: If PPxy holds, there exists a z such
that Pzy holds but Ozx does not.
- M5, Strong
Supplementation: Replace "PPxy holds" in M4 with
"Pyx does not hold".
- M5', Atomistic
Supplementation: If Pxy does not hold, then there exists an
atom z such that Pzx holds but Ozy does not.
- Top: There exists a "universal object",
designated W, such that PxW holds for any x.
is a theorem if M8 holds.
- Bottom: There exists an atomic "null object",
designated N, such that PNx holds for any x.
- M6, Sum:
If Uxy holds, there exists a z, called the "sum"
or "fusion" of x and y, such that the objects overlapping
of z are just those objects which overlap either x or
- M7, Product:
If Oxy holds, there exists a z, called the
"product" of x and y, such that the parts of z
are just those objects which are parts of both x and y.
does not hold, x and y have no parts in common, and the product
of x and y is undefined.
- M8, Unrestricted
Fusion: Let φ(x) be a first-order formula in which x is a free
variable. Then the fusion of all objects satisfying φ exists.
is also called "General Sum Principle", "Unrestricted
Mereological Composition", or "Universalism". M8 corresponds to
the principle of unrestricted comprehension of naive
set theory, which gives rise to Russell's paradox. There is no mereological
counterpart to this paradox simply because Parthood, unlike set
membership, is reflexive.
- M8', Unique
Fusion: The fusions whose existence M8 asserts are also unique. P.8'
- M9, Atomicity:
All objects are either atoms or fusions of atoms.