On Jan 7, 2009, at 9:49 PM, Patrick Cassidy wrote: Responses to a few points from Pat Hayes: [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] (1) different models.
>> Consider Newtonian and Einsteinian space.
>> For simplicity let us say per Newton "space is flat(Euclidian)"
>> And per Einstein "space is curved" [PH] >But this begs the question. Calling Newtonian space "flat" is only meaningful Ø from Einstein's viewpoint. In Newton's ontology, space isn't either flat or curved. Ø The idea of its having these attributes is (literally) meaningless.
No, “space is flat” is meaningful from Euclid’s postulates, which is why I appended “(Euclidean)”.
In Newton's physics, space has no 'shape' at all. The idea isn't meaningful. In fact, it isn't meaningful in any physics: what Einstein's general relativity provides is a curved space-time; and Newton's entire framework doesn't even mention the notion of space-time. Until the late 19th century, no human mind had ever even conceived of space-time as a meaningful notion.
With the benefit of hindsight, we can now characterize the abstract product of Newtonian space with Newtonian time as 'flat', but my point is that this hindsight is only available because we are already within the post-Einsteinian (actually post-Minkowskian) world in which this way of talking and thinking makes sense. No pre-1850 ontology, no matter how sophisticated, would have mentioned a flat space-time coordinate system.
[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.
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.
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.
[PH] >> This may be true in many cases, but it is most definitely not true in the hard cases that cause the most grief, such as the notion of a 'continuant' which underlies the BOF and DOLCE ontologies. In a 4-d ontology, being a continuant isn't a missing attribute: its impossible. So here is DOLCE which says that people are continuants, and here is EPISTLE which says they are 4-d. So what am I, in this combined ontology? I can't be what DOLCE says I am, in EPISTLE, since in EPISTLE it is fairly easy to show that none of those things can possibly exist. The DOLCE view is that EPISTLE has me mis-classified as an occurrent. The EPISTLE view is that everything in space and time - every physical thing - has the attributes that DOLCE restricts to events. 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?
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 ontoilogical mistake. From this point if 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.
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.
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, lets 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 tI 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. 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
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. , 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.
Yes, though not always in the other direction.
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.
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.
There is a point, though about BFO. BFO is a single-inheritance ontology, with partitions. It is not clear that this ontology can be reconciled with multiple-inheritance ontologies. It depends on whether the restriction on multiple inheritance also forbids the inferences regarding subtype relations that can be generated from inference as with a DL reasoner. I am not certain that BFO assertions can be translated into other ontology representations, though I suspect they can. The general principle that I think is needed is that although the general principle is that every logically consistent view should be represented – in the FO or some extension - no one can *forbid* (veto) the inclusion of something they don’t like
Thats what Ive called the Horatio principle. I agree, and would add, especially on the Web. , 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.
I cant help expressing my amusement at the naiveity of this casual remark. Patrick, have you ever been on a standards working group?
[PC] >> If both relations [“in”] are useful, then both
>> need to be included in one's ontology. They are not inconsistent
>> unless one insists on giving relations with two different meanings the
>> same label. [PH] But this answer is too glib. First, the key point of that anecdote was that these people had been using the same English word all their lives, and would both have said that they were in perfect agreement on its meaning; and the ontological difference that was revealed was invisible in any dictionary definition. (The moral being that one cannot trust either dictionaries or naive introspective intuition when comparing ontologies.) So forcing them to make a distinction that neither of them apparently found useful isn't likely to lead to a successful tool. If no one finds the distinction useful then it need not be encoded, and the general “in” would include both possible interpretations. The point of the anecdote as I heard it was that someone did find the distinction useful..
No, it was that trying to formalize their intuitions revealed the difference very quickly, to everyones amazement. as it had previously been invisible. Of course, building ontologies forces us to think more analytically about distinctions we don’t usually concern ourselves with.
Quite. But why should it? After all, we seem to manage bumbling through life without ever having to think about these distinctions. If we are all using a mental ontology to do it, how do we manage?
[PH] . But in any case, it seems obvious that these two notions of 'inside' are very closely related, to the point where most people for most purposes wouldn't want to distinguish them. [1] What, in your vision, records this important semantic fact? If we just coin two names for them, these two are no more logically related than sugar and salt. No, they are both subrelations of a more general relation that is ambiguous with respect to the more precise relations.
That doesn't work for this case. Just try writing the axioms and you will see why not.
[PH] Cyc has already tried this, which is why it needs (and has) something like 12 different senses of 'cover', and its not hard to find examples which will split any of those into sub-cases when more can be said about the things covered and covering. (For example, if a balding man grown his sparse hair extra long and combs it to cover his baldness, in which sense is the bald scalp covered with hair?) The resulting explosion of closely related but logically distinct relations and concepts rapidly becomes overwhelming even for human thinkers, let alone machine reasoners. That is one of the reasons why Doug Lenat ventured a guess (personal communication) that the number of semantic primitives may be up to 15,000, to accommodate such fine distinctions. Maybe. I suggest we discover the truth by building the FO and seeing what is required, if we explicitly search out the primitives.
I believe that the Cyc methodology tried hard to do just that, for purely engineering reasons, and failed to find many. So tell me (us), what methodology would you adopt to identify which concepts of the millions of concepts in Cyc are likely to be 'primitive'?
About the catalog of time theories: [PH] > There is no single model of temporal ordering No, there are inconsistent theories, and to call all of these “times” by the same term would be ontological malpractice.
I (deeply) disagree. Of course they are all times: what else are they? If they are not times, then there are no times at all in any temporal ontology.
At this point we seem to be getting redundant. I believe that these can all be described by a single set of primitives, and apparently PH doesn’t think so. It can’t be resolved here, and needs to be the subject of a proper experiment.
I know they cannot, and the 'experiment' is already done. Those various temporal theories can all be expressed in terms of three concepts: time-point, time-interval and duration. Duration cannot be reduced to the other two (there's a model-thoeretic argument in the paper) and the other two can be reduced to oine in some, but not all, of the theories. That gets you down to two or at most three concepts, known to be irreducible to smaller sets. And still, there are many variations possible in the ontologies.
And there is no reason at all to think that this is exceptional. I did push these ideas into describing space for a while, but gave up as there were just too many alternatives to consider. Do you allow space-filling curves? They exist in Euclidean R3 space. Their existence can be proven from the usual mathematical axioms underlying spatial formalisms. Can anyone think of a three-dimensional continuum that supports such intuitive notions as inside and outside, but in which these intuitive-pathological cases don't occur?
It appears that PH has drawn the wrong lesson from some of the experiences of his distinguished career. Roger Schank’s impoverished set of primitives have no more relation to the ontological representation that I am discussing than do the cross-linguistically inspired set of 60 primitives suggested by Wierzbicka. Both inventories of primitives are too small for this purpose, and the machines they had to work with were too slow to do the kind of reasoning that is practical now.
Obviously Roger's original set was too small, but that isn't the basic point. It was that even within their self-imposed limitations, it quickly because clear that an adequate encoding of the simple sentence meanings couldn't be done by composing primitives: one needed at every stage to add more information. And this has been the universal experience of all KR/AI and all applied ontology construction. UNIVERSAL, without exception. So, to turn the question around, from where do you get this idea that at some point, this proliferation of concepts is bound to stop?
PatH
PatC Patrick Cassidy MICRA, Inc. 908-561-3416 cell: 908-565-4053 From: Pat Hayes [mailto:phayes@xxxxxxx]
Sent: Wednesday, January 07, 2009 5:06 PM
To: [ontolog-forum] ; Patrick Cassidy
Cc: edbark@xxxxxxxx
Subject: Re: [ontolog-forum] Next steps in using ontologies as standards On Jan 6, 2009, at 10:58 AM, Patrick Cassidy wrote:
Ed,
The point you miss is that the foundation ontology does not need to take
a stance on **any** theories that are contradictory, it merely needs to
provide the conceptual vocabulary with which to **describe** theories people
build. But that is not an ontology: it is a meta-theory of alternative ontologies. This might indeed be a worthy research effort, but its important not to confuse it with actual ontology-writing.
Alternative theories can be represented in extensions to the
foundation ontology 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.
(or in John Sowa's terms, as a 'lattice of theories').
In that way, the similarities and differences among theories can be
logically specified, and where there are consistent though syntactically
different representations, they can be translated into each other. No
ontology can make people agree on inconsistent models, but having the
logical vocabulary to properly describe the differences will allow people
(and machines) to recognize where the differences are, how the differences
affect practical issues, and whether there is data that can refute any of
the proposed models. Again, you seem here to be talking about a comparative meta-theory of alternative ontologies, a kind of uber-meta-ontology which talks about ontologies rather than about the world that those ontologies describe. This is an interesting-sounding idea, but I have no idea how to begin approaching it.
My confidence comes from 15 years of looking at all of the examples
(there aren't many) of "inconsistent" ontological representations, and
realizing that they fall into one of two different categories:
(1) different models.
Consider Newtonian and Einsteinian space.
For simplicity let us say per Newton "space is flat(Euclidian)"
And per Einstein "space is curved"
But this begs the question. Calling Newtonian space "flat" is only meaningful from Einstein's viewpoint. In Newton's ontology, space isn't either flat or curved. The idea of its having these attributes is (literally) meaningless.
The foundation ontology has the meanings of 'space', 'flat(Euclidian)'
and 'curved',
And the attribute relation 'is' encoded. It can describe the two
theories.
Then its already Einstein's theory.
The two theories themselves are contained in a "physics" extension
to the
Foundation ontology. More detail can be added as needed, using a
single
logically consistent representation of the basic concepts (i.e.
the foundation
ontology)
Maybe you could share with us a sketch of this logically consistent basic physics which has Newton and Einstein as extensions? Good luck. (Seriously: isn't it surely just obvious that this is pure fantasy?)
I believe that this is in essence similar to the way that Andreas Tolk
describes
His approach to alternative models. I view the foundation ontology
as the
set of concept representations that do *not* depend on models for
which
there are disputed alternatives, and I believe that that set of
logically consistent
ontology elements is large enough to serve as the conceptual
vocabulary with
which all of the alternative models can be described.
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.
One point
that Andreas made,
if I interpret him properly, is that it often occurs that what
people view
as different "models" are actually different *views* that are
logically
consistent, but contain representations of different aspects (e.g.
attributes)
of the same entity. This may be true in many cases, but it is most definitely not true in the hard cases that cause the most grief, such as the notion of a 'continuant' which underlies the BOF and DOLCE ontologies. In a 4-d ontology, being a continuant isn't a missing attribute: its impossible. So here is DOLCE which says that people are continuants, and here is EPISTLE which says they are 4-d. So what am I, in this combined ontology? I can't be what DOLCE says I am, in EPISTLE, since in EPISTLE it is fairly easy to show that none of those things can possibly exist. The DOLCE view is that EPISTLE has me mis-classified as an occurrent. The EPISTLE view is that everything in space and time - every physical thing - has the attributes that DOLCE restricts to events. The key point is that ontologies do not only assert attributes that things have. They also make assertions about attributes that things cannot have. If you believe in continuants, then continuants cannot have temporal parts. It is inconsistent (or an error of some kind) to even talk about such things. If you think in the EPISTLE way, then of course anything that lasts a time has temporal parts: that is a necessary truth in EPISTLE. What kind of basic theory can reconcile these differences of opinion?
In such cases, both *views* could be
represented in
a consistent ontology, because they can be translated into each
other, using the
basic concept representations. They cannot be translated into one another at all, with or without any basic representations. They disagree about the fundamental structure of reality. They are in metaphysical opposition.
(2) terminology disputes
The function of a foundation ontology is not to force anyone to accept
another
Person's use of a particular term, but to create logical
specifications of terms
So that similarities and differences in term usage can be accurately
represented.
In one example of this problem, a very competent ontologist described
a session in which
there was a discussion of the meaning of being "inside" a structure;
is the paint on
the wall inside or is it part of the structure? When one views the
foundation ontology
as a defining vocabulary, the answer is quite obvious - to say the
paint
is "inside" is one meaning of "inside" (insideIncludingPaint), and if
one
wants to say the paint is part of the structure, and no part of the
structure is "inside",
then one creates a different relation (e.g. insideNotIncludingPaint or
insideNotPartOfStructure)). If both relations are useful, then both
need to be included in one's ontology. They are not inconsistent
unless one insists on giving relations with two different meanings the
same label.
But this answer is too glib. First, the key point of that anecdote was that these people had been using the same English word all their lives, and would both have said that they were in perfect agreement on its meaning; and the ontological difference that was revealed was invisible in any dictionary definition. (The moral being that one cannot trust either dictionaries or naive introspective intuition when comparing ontologies.) So forcing them to make a distinction that neither of them apparently found useful isn't likely to lead to a successful tool. But in any case, it seems obvious that these two notions of 'inside' are very closely related, to the point where most people for most purposes wouldn't want to distinguish them. [1] What, in your vision, records this important semantic fact? If we just coin two names for them, these two are no more logically related than sugar and salt. Third, this simple strategy is bound to explode in your face immediately. Cyc has already tried this, which is why it needs (and has) something like 12 different senses of 'cover', and its not hard to find examples which will split any of those into sub-cases when more can be said about the things covered and covering. (For example, if a balding man grown his sparse hair extra long and combs it to cover his baldness, in which sense is the bald scalp covered with hair?) The resulting explosion of closely related but logically distinct relations and concepts rapidly becomes overwhelming even for human thinkers, let alone machine reasoners. [note 1] In fact, my analysis of that story was that they were using the same notion of 'in', but different notions of 'room' or 'office'. But again, this analysis could be disputed, so maybe we would finish up with splitting the 'in' relation and also the 'habitable space' concept, giving 2.2=4 alternative readings of the English sentence. These multiplications expand more rapidly than one can keep track of, with no sign that they will eventually stop; and indeed, no logical or engineering technique available for preventing them expanding beyond any known limit.
. . .or combinations of both.
When looking over Pat Hayes' catalog of time theories, there were
indeed different
"theories" that depended in different models of time, but they could
all be
described using the same basic conceptual vocabulary.
No, they couldn't. The notions of 'point' and 'interval' were all dependent on the particular ontology. Thats why I called it a catalog of theories rather than a theory.
In the
foundation ontology
one can have open intervals, closed intervals, and semi-open
intervals. They
are all different things, and confusion arises only if one tries to
give two
different concepts the same label. You completely miss the point. You are assuming that the intervals being described are the usual intervals on the real line, but that completely begs the question. Some of those temporal theories don't even have the real line as a possible model. In most of the ontologies, there was no distinction between open and closed intervals. In some of them, an interval could be both open and closed. In others, these notions could be defined but did not have their usual mathematical meaning because the underlying order structure was different. There is no single model of temporal ordering. Some ontologies allow time branching, others don't. Some allow alternative futures to converge, others don't. Some allow closed intervals to meet, others don't. The Allen interval algebra works in many of them but not all of them. The only ontology common to all of them is the weakest one possible, which amounts to saying that points are (at least) partially ordered and intervals have points at their ends; and this alone isn't hardly enough to do any useful temporal reasoning at all, certainly not enough for temporal planning.
Likewise, one may have two
different
functions called generically "concatenation"; to concatenate two
"glass intervals" and have the resulting interval continuous is a
*different*
Function from concatenating those two intervals and having the
resulting
Interval missing a point in the middle. No problem occurs as long as
One doesn't try to give the same label to two different functions. Its not that simple. In many of the ontologies, there isn't any glass continuum; in fact, in the conventional real line theory one can prove that there are no glass intervals.
Both of these common cases are consistent with, and can benefit from,
using a logically consistent set of ontological representations of the
primitive concepts that can accurately describe the alternatives. Plain flat wrong. Provably wrong, in fact, in this case. There is no such set of primitive concepts for these ontologies. (Think about it for a second: the only concepts in most of them were those of timepoint and time-interval, and in all but the simplest, these are in fact interdefinable, so one can make do with one. What more "primitive" concepts can one reduce this set to?)
Perhaps you can suggest a very specific case where there is a logical
inconsistency
that *cannot* be described using a single logically consistent set of
concepts?
The time catalog will do as a first example. It documents many of the inconsistencies in the text.
If you accept this description of the structure and function of a common
foundation ontology, there still remain two questions:
(1) how many basic concepts are there that can be agreed on, once one
agrees
That all **logically consistent** views (translatable into each
other) can be
Represented in the foundation ontology itself, or in some internally
consistent
Extension module?
(2) Will the inventory of logically consistent basic concepts in fact be
large
Enough to ontologically describe any data structure in any
application?
If not, how frequently will the foundation ontology need
supplementation?
I don't know the answer to these questions, and they can only be answered
by a serious attempt to build such a foundation ontology, and test it
systematically for its adequacy as a conceptual defining vocabulary.
I
believe that it is important to answer those questions, because if we can
identify a necessary and sufficient inventory of primitive concepts that
will give us a powerful tool to enable accurate semantic interoperability by
using the foundation ontology to translate information from one viewpoint to
another. Very doubtful. First, this would be true only if everyone agreed to use the same foundation ontology, and there is not the slightest shred of evidence to suggest that people or organizations will be willing to do this. The army currently has thirteen incompatible knowledge models in use, all of them with a large user community and a huge associated investment in training and software development, everyone agreeing this a a huge problem, but no forseeable prospect of anyone agreeing to adopt any of the others. And this is in a controlled military environment where the grunts at the bottom have to obey orders. Second, its simply not clear that the existence of a single common ontology does in fact make interoperation easier, although this is often asserted as though it was self-evidently true. Until a convincing demonstration is forthcoming, I think the jury should remain out on this. There are many reasons why being forced to use a highly developed ontology might make knowledge interoperation harder to achieve. Do you have no curiosity at all about whether such an inventory of
primitive concepts exist?
I did, briefly, when I was a graduate student. I quickly convinced myself that it does not, partly by watching Roger Schank try to do it. Every attempt I have seen to create one has been a dismal failure. The idea is now firmly placed in the realm of recurrently occurring mad ideas, like perpetual motion and cold fusion.
Do you think that answering this question is
actually valueless? I think that for all practical purposes the question is already answered, in the negative. In 30 years I have never seen a good argument in favor of it. You havn't offered any, only your repeated insistence that it must be possible and the observation that if it were, things would be a lot better. But of course the same is true of perpetual motion and cold fusion (not to mention a Lofstrom loop.)
-----Original Message----- Sent: Tuesday, January 06, 2009 1:00 PM
To: Patrick Cassidy
Cc: '[ontolog-forum] '
Subject: Re: [ontolog-forum] Next steps in using ontologies as
standards
Patrick Cassidy wrote:
Your gut skepticism is not surprising, but I tried hard to find
some
objective criticism of the proposal in your response, and couldn't.
Interesting. I need to write more clearly. Have you looked at the
collection of biological ontologies in Mark Musen's Bioportal? How
many
different models of human anatomy did you see? Why is there not one
consistent model? And what is the secret formula for removing that
obstacle?
Ask Steve Hobbs about the effort to develop OWLTime, which is a very
"small" fundamental ontology in your vast undertaking. They had to
choose among three competing models of time, after giving up on
usefully
reconciling them. Pat Hayes' paper documents the fundamentally
different axiomatic approaches. According to you, a well-funded
community of great minds will find one model they can all agree on.
What makes you think so?
My gut skepticism is based on published experience. My apologies for
failing to mention more than the biological work and the conflicting
standard upper ontologies. With a bit of effort, I can find a few
others. But my mathematical training tells me one counterexample
disproves a theorem.
What evidence is your unbridled optimism based on?
-Ed
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