PatH –
Just two responses here – about whether the primitives
are necessary, and the question of whether 3D and 4D entities can live together
in a logically consistent ontology:
(1) [full preceding text is below, here just the last paragraphs]
[PH] > Well, now, this is certainly a reasonable grand
vision to guide future effort and research. What you describe here is
very similar to what John Sowa has described as a lattice of theories, and what
Cyc has implemented using its 'micro-theory' context mechanism. (Cyc actually
has the choice of modules semi-automated, as part of the overall Cyc ontology
is a fairly comprehensive ontology of contexts themselves, allowing the
inference engine to reason about what assemblages of micro-theories are most
suitable for various reasoning tasks or topic areas.)
> But allow me to suggest one small amendment. Given the
notions of being able to combine mutually consistent modules, why do we
need to have a single 'basic' FO at all? This combining-module idea does not
depend on there being a single central 'basic' module somewhere in the lattice,
or on all concepts being reducible to a smallish set of 'primitives'. It can be
a true catalog of various alternatives, with no single 'root', and still
provide the interoperability advantages. I have no problem with the lattice of
theories notion: it is this mythical single primitive core that is so
unconvincing: but your vision here does not seem to depend on that. For
example, for some purposes, a discrete time and a continuous space ontology
seems useful; for others, it is important to allow temporal limit points, but
spatial references can be minimal, and so on. Why do we need to decide which
combinations are more 'basic' than others, when it seems that all such
decisions will be largely matters of taste, and likely fraught with endless
controversy?
[PC] (1) Yes, it is true that different independent developers
could use different combinations of modules, provided that those modules were
known to be (or not disproven to be) logically consistent, and still achieve
optimal interoperability. But this still requires that the chosen modules have
all of the basic concepts that allow all of the newly created domain terms to
be ‘expressed in terms of’ (I am using your phrase) those
terms in the modules chosen. This means that *somewhere* in the
collection of mutually consistent modules there have to be enough of the basic
terms that are used to express the meanings of newly created domain terms, so
that any domain can be represented. That set of modules would then contain
what I think of as the minimum set of primitives, though the modules can also
have other ontology elements in them. It is not clear to me that we can have a
*stable* set of modules to serve the purpose of interoperability unless
we have some confidence that all or most of the terms needed to express the
meanings of domain terms are there at the start. The hypothesis of a finite
set of primitives (whether in a core ‘BaseKB’ or in a set of
consistent modules) provides a target number that is as small as possible, largely
**to make the task of agreement as easy as possible**.
If it turns out that there is no such thing as a finite set of primitives,
and it becomes necessary to continue adding new primitives indefinitely as new
domains are derived from the FO, then the FO will not be fully stable. It may
nevertheless be stable enough to achieve a practical level of semantic
interoperability. In any case, I expect that actively seeking out what look
like the basic semantic primitives will drive the FO to its most stable state
as quickly as possible.
In sum, I agree that the existence of a finite set of semantic primitives
is *not* a condition for success for a collaboratively developed
Foundation Ontology, but (a) if it does exist, the resulting ontology will be
more stable than one that starts out with fewer than the full number of primitives;
and (b) aiming to represent all the primitives is likely to make the FO as stable
as possible as quickly as possible.
That’s why I think that emphasizing the search for the
semantic primitives is a good approach. Of course, the most *essential* factor
is the collaborative development by a large consortium, to quickly create a
large user community.
(2) Concerning the question of whether 3D and 4D versions of an
Object can both exist in a logically consistent ontology:
[PH] > Before proceeding, please show us a sketch of
this part of the basic FO, containing both kinds of entity.
[PC] OK, first I will reproduce an email from PH dated March
20, 2008.
Note the phrase [PH]: “This is a 'unified'
ontology. But note, the result would not be acceptable to a confirmed 3D
modeler; it is for example incompatible with the OBO foundational ontologies or
DOLCE”
============ email from Pat Hayes 3-20-2008
========================
At 3:35 PM -0400 3/20/08, Patrick Cassidy wrote:
PatH,
There is an axiom provide by you during this thread which I would like
to
clarify:
>> (forall (x (t Time) P)(iff (P x t)(P (x during t))
))
[PC] >> I have not seen the two different syntactic expressions:
(P x t) and (P (x during t))
Used together before. The first suggests a 3D perspective, and the
second
suggests a 4D perspective.
Yes, exactly. Think of this as a 'bridging' axiom, part of a
translation specification, if you like.
OK, I'll come clean and tell you what I really think.
There are a variety of notational options in combining a simple timeless
assertion with a temporal parameter. One is to treat the time as a context, in
effect attaching it to the entire sentence (or in IKL, proposition):
(ist t (P x y))
(ist t (that (P x y)))
another is as an extra relational argument, giving the
'fluent' style which goes naturally with continuants:
(P x y t)
and a third is to connect it to the object(s) being related,
the relation then being naturally understood as a relation between time-slices:
(P (x at t)(y at t))
But in fact, these are really all just notational variations
on a single theme. They amount to choosing where in the parse tree of the
simple _expression_ to attach the parameter, is all. If we simply FORGET the
philosophy for a second, then we can treat this as an arbitrary conventional
choice, and think of them as all meaning exactly the same thing, and therefore
equivalent. Then it makes literally no difference if you say "At t, its
true that P holds between x and y" or "P is true of x and y and
t" or "P holds between the t-slices of x and y" , as these all
mean the same. As to what exactly x and y are in this, I don't really care what
your favorite philosophical answer is. Choose the philosophy you like best: but
then be prepared to have your head exploded by some of the things that you
might have to read. Maybe this is what you meant by 'dimension neutral', but I
don't like that way of describing it, as I see them myself as inherently 4-D.
Attaching the temporal parameter 'higher up' the tree is just a handy shorthand
convention useful at times; but there are some things
(Q (x at t)(y at t'))
that just cannot be said any other way. So we have to have
the 4D picture as a kind of base case; and once we have that, we really don't
need the others (all of which are based on highly questionable philosophical
foundations in any case. Trying to make actual physical sense of the notion of
'continuant' is just about impossible.)
This is a 'unified' ontology. But note, the result would
not be acceptable to a confirmed 3D modeler; it is for example incompatible
with the OBO foundational ontologies or DOLCE.
[PC] >> How would you describe the type that
"x" belongs to?
Type?? Do you mean, what kind of thing is it supposed to
denote? Anything with an extension in space and time. This seems to me
to be a basic ontological category. I'd say that if you are a 3D man, think of
it as the union of continuants and occurrents; if a 4D man, think of it as a 4D
'worm' or history.
[pc] >> The way it is used in those expressions,
it looks a lot like the
"dimension neutral object" that I suggested as a way of providing
both 3D
and 4D perspectives in the same ontology.
Possibly.
[PC] >> In my case, however, I did not
use the (x during t) _expression_, but created a type "TimeSlice" so
that
time-slices (any temporal length) of 4D objects could be expressed in an OWL
formalism.
Oh sure, any 2-argument function is basically trinary, so
has to be re-manipulated to get it into a binary language like OWL.
[PC] >> Is there a documentation
somewhere that additionally explains the
intended meaning and use of that type (of which "x" is an instance)?
See above.
PatH
--
============================== end email from PatH
=============================
A fragment of an ontology where 3D and 4D versions of
entities live peacefully together:
[[ notation: (iff {X rel Y @Z}
(rel X Y @Z))
The notation (x during t), is introduced by PH (above) , and
used here for further illustration:
[PH] >> (forall (x (t Time)
P)(iff (P x t)(P (x during t)) ))
My idea of a
‘unified’ 3D-4D ontology would permit (among other things) the
assertions (I hope the meaning is clear from the labels):
{PH isanInstanceOf Object}
{PH4D isanInstanceOf Object4D}
{t1 isanInstanceOf TimePoint}
{t2 isanInstanceOf TimePoint}
{t1t2 isanInstanceOf TimeInterval}
{t1t2 hasStartingTimePoint t1}
{t1t2 hasEndingTimePoint t2}
{PH4D isTheWholeLife4dVersionOf PH}
{PHt1t2 isaTimeSliceOf PH4D from t1 to t2}
If I included a ‘during’ similar to the one PH
uses, it might look like:
{(PH during t1t2) isIdenticalTo PHt1t2}
{{PH isLocatedAt IHMC from t1 to t2} iff {PHt1t2
isLocatedAt IHMC}}
And, redundantly, given the above:
{{PH isLocatedAt IHMC from t1 to t2} iff {(PH during t1t2}
isLocatedAt IHMC}
The above explicitly has a 4D entity PH4D as
TheWholeLife4dVersionOf the ‘dimension neutral’ object PH.
The syntactic structures using an instance of
‘dimension neutral’ Object are identical to those of a 3D object.
It just isn’t labeled as ‘3D’ – though the label
shouldn’t matter. The way I use these, there cannot be a ‘disjoint’
axiom between the dimension-neutral ‘Object’ and
‘Object4D’ (instances of ‘Object’ can have time slices,
in the OWL version, to allow time to be used in binary relations - a syntactic
convenience).. Although the ‘dimension-neutral’ Object is not
explicitly 3D, it behaves syntactically like a 3D object. I think in this
case there are actually two types of entities, not just syntactic variations on
a single inherently 4D entity. Perhaps, if one wants to stick to solely 4D
entities, it *might* be possible to equate PH with PH4D, and allow both
syntactical forms (P x t1 t2) and (P xt1t2) but I haven’t tried to work
through whether the domain restrictions would then become inconsistent (is this
what you have already done?). I prefer to keep around something that looks
like a 3D Object, not confused with the 4D, to make translation to pure 3D ontologies
easier. The 3D ‘Object’ behaves a lot like other 3D ontologies, except
that it is not disjoint with Object4D.
You say that the ‘unified ontology’ that uses
such structures would be incompatible with OBO or DOLCE. I haven’t
looked at them to check that. Could you cite specifically the axioms that
would create that incompatibility if ‘Object’ was a subtype of
‘Continuant’ and ‘Object4D’ a subtype of Occurrent?
I am assuming that the syntax of OBO or DOLCE might require
some translation of axioms to achieve logical consistency, and it is logical
consistency after/modulo translation that I am concerned about.
Final question: I interpreted your comment that the axioms
you gave are part of a ‘unified’ ontology – which I took to
mean, containing 3D-like and 4D-like entities. The axioms seemed to be consistent
with that, though the (x during t) structure was not repeated in the later
axiom set. Perhaps you meant something else by ‘unified’?
PatC
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx
======================= original note from PH Thursday, January
08, 2009 ==========================
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
Sent: Thursday, January 08, 2009 6:11 PM
To: [ontolog-forum] ; Patrick Cassidy
Subject: Re: [ontolog-forum] FW: Next steps in using ontologies as standards
On Jan 8, 2009, at 4:02 PM, Patrick Cassidy wrote:
A few points are selected that seem most
productive:
(1) [pc] >>
Alternative theories can be represented in extensions to the
>> foundation ontology
[PH] > That is extremely
unlikely, for two reasons. First, no such foundation is likely to exist;
second, even if it did, the
extensions to it would be mutually inconsistent with one another,
so would not all together
form a coherent single ontology.
We may be using “extension” in a different sense.
Extensions in the sense I intend do not have to be logically consistent
with each other.
Hmm. OK, then, in what sense is
this resulting, er, structure of extensions an ontology? And why are you not
just being vacuous here, and urging that there should be many alternative,
mutually inconsistent, ontologies? We can arrange for that with a very low cost
to the government.
[[PC]] The base FO plus extensions would form a hierarchy
of possible ontologies and ontology modules from which parts could be taken for
specific applications. Each extension would have to be logically consistent
with the sum of modules of which it is a submodule. It will be
essential to specify which branches of the hierarchy are logically inconsistent
with which others. Having done that, it will be possible to take and
combine modules with some confidence that the whole will be logically
consistent. Proving consistency among specific modules may well be
intractable, but some degree of certainty may be derived by running a
consistency checker for some time (or, being open-source, having everyone
interested run a consistency checker on the parts of interest to them, perhaps
using SETI-like system for distribution of tasks and receipt of results)
. Such a hierarchy will allow a much higher level of confidence in
the consistency of any given collection of modules than an unregulated
collection.
Any two collections of
modules known to be consistent, or not proven to be inconsistent, should then
be able to be automatically merged into a common ontology that should also be
consistent, and able to produce the same inferences form the same data as the
individual collections used locally. Using this hierarchy (and creating
any local extensions desired, based on the terms in the extracted modules)
would provide what I would consider a higher level of interoperability
than any I have seen suggested by any technique other than everyone using the
same ontology.
Not every ontology
describable using the terms of the FO would necessarily be consistent with the
FO (one only has to assert (not P) for some P in the FO), and therefore would
not be part of this hierarchy. Ontologies described in terms of, but
inconsistent with, the base FO might be maintained in a separate
registry. That will be an issue for decision by the committee maintaining
the FO.
Well, now, this is certainly a reasonable grand vision to
guide future effort and research. What you describe here is very similar
to what John Sowa has described as a lattice of theories, and what Cyc has
implemented using its 'micro-theory' context mechanism. (Cyc actually has the
choice of modules semi-automated, as part of the overall Cyc ontology is a
fairly comprehensive ontology of contexts themselves, allowing the inference
engine to reason about what assemblages of micro-theories are most suitable for
various reasoning tasks or topic areas.)
But allow me to suggest one small amendment. Given the
notions of being able to combine mutually consistent modules, why do we
need to have a single 'basic' FO at all? This combining-module idea does not
depend on there being a single central 'basic' module somewhere in the lattice,
or on all concepts being reducible to a smallish set of 'primitives'. It can be
a true catalog of various alternatives, with no single 'root', and still
provide the interoperability advantages. I have no problem with the lattice of
theories notion: it is this mythical single primitive core that is so
unconvincing: but your vision here does not seem to depend on that. For
example, for some purposes, a discrete time and a continuous space ontology
seems useful; for others, it is important to allow temporal limit points, but
spatial references can be minimal, and so on. Why do we need to decide which
combinations are more 'basic' than others, when it seems that all such
decisions will be largely matters of taste, and likely fraught with endless
controversy?
(3) [PH]> >> This seems vanishingly unlikely. This first requirement forces
this common theory
>> to be as small as
possible, but you believe that it will be as large as any theory
>> every conceived by the
human mind.
[PC] >> No, the theory encoded by the FO is only as
large as the number of primitives and their deductive closure. But
extensions can be infinitely large, since there is no limit to the number of
complex concept representations that can be constructed as combinations of the
primitive concept representations.
[PH] > Since these complex
concepts are all defined, they are all eliminable. The extensions have the same
expressive power as the FO. So the FO itself already has the expressive power
of every other theory.
[[PC]] Well, if “largeness” is the same as
“expressive power” in your terminology, then, yes. I am
accustomed to thinking of size as something different.
The point is that this single theory has to be both small,
and expressive enough to define all concepts adequate for human thought. There
is no reason to suppose that such a theory exists, and many reasons to suggest
otherwise. And, perhaps more to the current point, its not even clear
that it would be very much use even if it did exist, cf. above.
(4) [PC] >> I
recall that PH and I had a long exchange last year or so at the end of which I
thought that we agreed that 4D and 3D assertions could be translated into each
other. Did I get a wrong impression, or is PH misinterpreting what I am
saying?
[PH] > You got a wrong
impression. But the point is not just about translation. I recently had a
discussion with Barry Smith about this. Barry's view of the way to reconcile
3-D with 4-D (apologies for the terminology) is that the 4D perspective simply
classifies everything as an occurrent. That is the most natural way to express
it from his perspective, and it is in a sense accurate. For Barry, people are
continuants, and the 4D-ers say they are occurrents: a simple difference
of ontological opinion, like me saying I'm Irish and Barry saying I'm American.
> That would be one way to
reconcile the two point of view, but it has the demerit that if the basic
ontology accepts the distinction, there have to be two 'me's: the occurrent and
the continuant. And this is a problem for the 4Ders such as myself, because
from our point of view, this bifurcation of entities into two halves is an
ontological mistake. From this point of view, there simply is no meaningful distinction to be
made between continuants and
occurrents; that all the so-called continuants are in fact
occurrents. From this point of view, there is no disagreement between Barry
saying I am a continuant and me saying I am an occurrent; we aren't disagreeing
about any matter of fact, or indeed about anything.
> The problem lies higher up
the classification chain: it is the notion, fundamental to Barry, that the
occurrent/continuant distinction is basic ("upper") and also sharply
dichotomous, so that nothing can possibly be in both categories. To me, in
contrast, the distinction is vacuous or, at most, amounts merely to a syntactic
preference for writing certain time-dependent facts in one style rather than
another.
> Now, it is possible to
translate between these points of view, but not to reduce them to a single one.
They are not two branches extending from a common trunk: they are more like two
completely separate plants which are about the same height. They give different accounts of Pat Hayes the person: in one
viewpoint, there are two of me: me the continuant and me (my lifespan) the
occurrent, and all the vocabulary for talking about me has to be duplicated.
One cannot simply say that the 4D perspective is got by equating these (though
that would be intuitively correct) as the ontology itself would prohibit this
equation.
[PC] >> If some person PH is classified in one ontology as
4D and in another as 3D, clearly the ontologies cannot be combined under the
assumption that the label PH applies to the same thing in the two cases.
It isn’t.
[PH] > Ah, but you see, it IS.
That is the critical point. Lets agree that I am what I am, the facts of my
life are what they are, and so on. Nobody will dispute any of this, let’s
suppose. Still, two philosophers can disagree about how all this stuff should
be encoded in an ontology. But they are both talking about the same person, the
actual Pat Hayes in the actual world. (If they aren't, there is something badly
wrong with their ontologies.) The two ontologies conceptualize me differently,
but it is simply factually wrong to claim that I am two persons, just because
two philosophers disagree about how best to describe me. Everyone agrees that I
last for a time and occupy space and have properties which vary with time, and
so on. They just disagree about how to formulate this in a logic. But neither
of them thinks that there are two Pat Hayeses, and any ontology which says
there are is just flat wrong. http://www.ihmc.us/users/phayes/PatHayes denotes me, the actual me, here in the
actual world.
[PC] >> In one case, it is a 4D entity whose lifetime is
PH4D and in the other case it is a 4D entity whose lifetime is PH4D, where the
‘lifetime’ is in the FO even if that concept is not in the 3D
ontology (actually, I use a “dimension-neutral object” to relate
the two). When the ontologies are translated or merged
[PH] > If you merge them, they
will be inconsistent. I agree that in many cases one can translate between the
two points of view, but its not easy and not always possible at all. I've never
seen a program that can do it.
[PC] >> , the different entities PH3D and PH4D are both
present, and assertions about the properties of one in 3D-speak can be
translated into assertions about the properties of the other in 4D-speak.
[PH] > Yes, though not always
in the other direction.
[PC] >> The problem here again appears (from
the description) to be an attempt to use the same term to refer to 2 different
entities –a terminology clash.
[PC] well, my point is that a 3D
entity and it corresponding 4D entity are truly different though intimately
related things, though they are labeled by the same term by different
people.
The problem goes deeper than this. The things which some
philosophers call 'continuants' are not either 3-d or 4-d when viewed from a
4-d perspective; they are simply impossible. They have to be
3-dimensional but also persist through time, which is logically incoherent in a
4-d ontological perspective. (Continuants aren't the 3-d slices of the 4-d
thing; those are different at different times, but continuants retain their
identity through time.) Its not just a matter of terminology. One perspective
insists that things exist which are provably impossible when seen from
the other perspective. It is possible for a broad-minded 4-d thinker to take
what the other guys say and make a kind of sense of it (I speak here from
personal experience) but only by 'translating' it a way that the other guys
insist isn't acceptable, by denying a basic assumption of their universe.
One philosopher may insist
that only 4D entities exist, and another philosopher may insist that only 3D
entities exist. These are different **belief systems** about their real
world. As far as an ontological engineer should be concerned, what
“exists” is only what is or can be represented in an ontology, and
ontologically speaking, both 3D and 4D entities exist in that sense.
But not in the same ontology. There is no single consistent
ontology that admits both continuants and 4-d histories.
We can model the belief systems of
those ontologists, by asserting the “non-existence” in the sense
that the philosophers are using, and since both of those belief systems assert
the non-existence of something that is in the ontology, then whether these
belief systems are or are not inconsistent with the base FO (which has both
kinds of entities)
Before proceeding, please show us a sketch of this part of
the basic FO, containing both kinds of entity.
depends on how one interprets the
philosophers’ view of “exist”. If it is identical
to the logical “exists’ applying to axioms in the ontology, there
would be an inconsistency, and both belief systems would be inconsistent
– moved into a module in the “inconsistent” set. The
ontology would still be able to express assertions about the 3D and 4D
entities. IF the ontologists’ “exists” is something
different – existence in the real world, or in some ideal world, then
both theories individually would be consistent with the base FO, though
inconsistent with each other. Then they could be put into different
logically inconsistent extensions of the FO.
It all sounds very nice, but it doesn't actually work out
this way. Just try it and you will find out why.
[PH] > But my point is that
there is only one entity, in fact. And it is important for an ontology to be
able to say this, and clearly draw appropriate conclusions. If I am in a room
and nobody else is in it, there is one person in the room. Not two people, one
of them 4-d and one of them 3-d.
From an ontological point of view,
I would say there are at least two entities: a PH3D and a time-slice of
PH4D.
And how do they differ? Which of them has my social security
number? Can one of them be hungry and the other not, a the same time? (Why
not?)
In fact, there are an infinite
number of time slices of PH4D, though one is likely to be concerned only with
one of them.
(5) [PC] >> , The FO needs to be
permissive to serve its purpose of translation. Where there are
logical inconsistencies, one or both of the candidate entities needs to be
moved to an extension (which can be logically incompatible with other
extensions). This decision would be taken by a vote of the executive
committee for the FO project.
[PH] > I cant help expressing
my amusement at the naiveity of this casual remark. Patrick, have you ever been
on a standards working group?
I have attended
meetings of some groups, and am aware of the difficulty of finding
consensus. But a practical project of this kind cannot depend on
consensus, there has to be a simple majority up-or-down vote on issues of
controversy, and very quickly. Anyone who cannot bear to participate
under such conditions doesn’t have to – that will be clear before
any organization work gets under way. I expect there will be enough
people oriented toward a practical solution to form the large community that is
required for this project. If not, the project will never start –
no harm done. This isn’t naïve, it’s practical and realistic.
I hope you will agree to be the chairman.
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