Hi Doug,
Comments below,
-Rich
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx]
On Behalf Of doug foxvog
Sent: Thursday, July 07, 2011 6:44 AM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] Why most classifications are fuzzy
On Thu, July 7, 2011 0:58, Rich Cooper said:
> Comments interspersed below,
>
> -Rich
[extract]
> DF:] The issues in the database world are different from those of
the
> ontological world, and implications from one of the fields does
not
> necessarily apply to the other. However, i will respond to
the database
> comments below, from an ontological perspective.
> RC:] Surely you are not implying that databases are not
ontologically
> expressive;
I am not implying that. I meant what i carefully said.
Different fields
have different perspectives and issues. That in no way implies
that
there is no connection between them.
But that is true of logic also. The examples in logic
always use symbols which are intuitively defined, just as database domains are.
> ...
> RC:] Perhaps you prefer to think of the universe as including
classes
> AS WELL AS properties.
Yes, i prefer to do so. Of course, any class is equivalent in
extension
to a unary predicate. The concept of Class in an ontological
sense
carries a lot of meaning and implication -- all of which can be mapped
to information about unary predicates.
This is true, but not very practical in embedded engineering
systems where performance is a critical issue, so the resources required to
evaluate predicates discourage as much computation as possible in most such
systems.
In the vehicle example, pattern recognition is used to
identify the moose, possum, child, rabbit or duck in milliseconds so that the
appropriate collision avoidance strategy can be selected and implemented while
there is still time to avoid the collision.
Instead, the predicate function is based on collected laboratory
databases of samples previously identified and classified through empirical
experimentation. The samples are related to avoidance strategies
manually, and then stored in the embedded database as well.
Then the classifications are stored in lab and embedded database
columns which index the recognition processing procedures. So a database
would contain indexes to recognition procedures, to object classes defined for
the task, and to avoidance procedures keyed to the classification of the
objects.
Classification is done over long time periods in the lab DB where
a response is not time critical, and where many recognition procedures can be
inventoried in a library of such data. Determining the properties which
can effectively separate the samples into classes, and relating the classes to
avoidance procedures, is time consuming, so once those have been established,
the CONCLUSIONS are stored in the database rows which will be used in the
vehicle.
This means the FCA work is done in long slow time where such
predicates can be tolerated, but there are so many ways to do pattern
recognition during the classification discovery process that it is impractical
to do it in real time. That is typical for engineering systems, though
there are some with the luxury of time to spend.
That is what I plan to do with linguistic samples. But
generalization of linguistic samples to cases that can be handled by various
interpretation procedures is needed to organize the data sample database. But
the embedded DB capable of chatting linguistically has to represent how to
handle every eventuality, even previously unknown samples into a default class,
which is case based.
>
> RC:] ... why do you believe that a database of such properties and
> classes is different in ontologies versus in the database world?
A database is already in the database world. 8)#
I did not say that databases can not use ontologies. I meant that
the different fields were based on different ideas.
While databases can certainly be based on ontological principles, they
can also merely use them, or even ignore them. Databases treat
columns
different than cell contents, while in an ontological sense either
could
express properties. An ontology which has higher-arity relations
can
treat a single usage of a ternary predicate as an object, while a from
a
database perspective, it would often be expressed as a set of cells in
a
single row.
Actually, the database world uses the concept of
transactions, which are complete threads through the database, not just to one
table, but to several interlinked tables, with anywhere from zero to large
numbers of rows in some of the tables. Rows are equivalent to terms, such
as f(a,b,c…) where f is a table, a, b and c are columns, and each row of
f is one instance of that term. But a transaction is far more
complex.
This is not a criticism of database technology, merely a recognition
that
different fields can handle the same situations in different ways.
Which gets back to the point of subjectivity in how the
logic of DBs is used to implement systems.
I leave the full discussion below. It seems not to have been
shared with
the ontolog forum.
That is correct. Most of the readers don’t seem
interested in the subjectivity issues, other than perhaps Gary Berg-Cross. So
I doubt if it would stir up other posts anyway. I’m beginning to
think that the topic simply doesn’t work in this group, no matter how
important it is.
-Rich
-- doug
> Sincerely,
> Rich Cooper
> EnglishLogicKernel.com
> Rich AT EnglishLogicKernel DOT com
> 9 4 9 \ 5 2 5 - 5 7 1 2
> -----Original Message-----
> From: doug foxvog [mailto:doug@xxxxxxxxxx]
> Sent: Wednesday, July 06, 2011 7:46 PM
> To: Rich Cooper
> Cc: doug@xxxxxxxxxx; 'John F. Sowa';
> ontolog-forum-bounces@xxxxxxxxxxxxxxxx;
> Christopher Menzel; AzamatAbdoullaev
> Subject: RE: [ontolog-forum] Why most classifications are fuzzy
>
>
>
> On Wed, July 6, 2011 17:29, Rich Cooper said:
>> Doug, Azamat, John,
>> Let me propose an alternative that uses some of Azamat's ideas
and some
>> of Doug's responses.
>> Suppose there is a universe of "PRIMITIVE"
properties, i.e. those that
>> are terminal, not decomposable into other properties.
> DF:> There is not necessarily a unique set of such
properties. Consider
> just a universe of three property dimensions. Any three
orthogonal
> property
> vectors can be chosen -- even spatially one has the option of
three
> straight
> non-colinear vectors, polar coordinates with an arbitrary axis, or
one of
> an
> infinite number of cylindrical coordinate systems -- with no
purely
> logical
> reason to prefer one set of "primitive" properties over
another.
>
>
>
> RC:] Yes, I agree that is correct, and the choice of which properties
to
> make terminal for the universe is indeed arbitrary, i.e.,
subjectively
> chosen. Many people choose properties in their
classification universe
> based on the chooser's view of what is important. For a
current example,
> the individual Democrats and Republicans are now viewing the US debt
> crisis
> in completely different ways, and classifying revenue improvement
tactics
> by
> their choices of what is important to each individual in each
party.
> Their
> choices lead to very different classes, and very different
assignments of
> individuals to classes.
>
>
>
>
>
> DF:] Someone may select A, B, & C as three primitive
properties to span a
> space, but another person might select A&B, B&C, and
C&~A as primitive
> properties. Each "primitive" property in one set
can be decomposed into
> an
> _expression_ of the "primitive" properties of the other
set. Any situation
> that can be defined as a combination of the properties of one set
can be
> defined as a combination of the properties of the other set.
>
>
>
> RC:] While that statement is absolutely correct, it is relatively
easy in
> most engineering situations to choose a coordinate system so that
a
> proposed
> system can be analyzed in detail and the analyses communicated to
other
> members of the teams. In software engineering specifically,
the
> requirements sentences are worked through in meetings designed to
> establish
> either consensus among the requirements specifiers as to the
coordinate
> system, or multiple coordinate systems for comparing various
design
> concepts
> to be explored based on the requirement coordinate choices.
>
>
>
> One good example of what you described is from smart vehicle
design.
> Consider a radar sensor in the front bumper of a car and a video
camera on
> the roof. Some of the objects found by the radar have to be
translated
> into
> a coordinate system that can also fuse the objects detected by the
camera.
> This way, the designers can organize a database of object tracks
which can
> be fused to establish which detected objects in one sensor are in
fact the
> same objects recognized in the other sensor. This fusion
need is usually
> handled in systems in exactly this way, and illustrates how the
detection
> and tracking of objects depends on multiple perceptions of the
same
> objects,
> using different independent sensors.
>
>
>
>> That is, there are terminal and nonterminal properties,
>
>> as there are terminal and nonterminal symbols in an ontology,
>
>> or a language, or a group of logical expressions,
>
>> as Chris alluded to.
>
>
>
> DF:] There can certainly be a set of terminal and non-terminal
properties
> in
> an ontology. But that does not mean that the universe
described by that
> ontology necessarily decrees which properties must be terminal and
which
> should not be. The selection can be up to the ontologist.
>
>
>
> RC:] That is absolutely correct; the perceiver is biased, or the
> requirements agreed to by a team of engineering perceivers is
biased, and
> there is no way around it for most practical situations.
>
>
>
>> This should be easy to agree on for most, but is still
>
>> the context of whatever metrics have been chosen to separate
the
>> entities
>
>> into classes.
>
>>
>
>> I'll call them the P[i] properties.
>
>>
>
>> Classification is the process of choosing (with whatever
method you
>> wish)
>
>> unique properties that are to be used in dividing a given
sample group
>
>> into classes by the classification scheme.
>
>> I will only use terminal properties
>
>> in the classification scheme, whatever their origin.
>
>
>
>> Then there is some list of such P[i] which serve to make a
distinction
>
>> among the samples. That distinction is, by my
definition,
>
>> whatever primitive properties separate according the values of
each
>> entity
>
>
>> with each property in the chosen list.
>
>
>
> DF:] Are you here defining the primitive properties as those which
make a
> distinction among the individuals? Earlier it seemed that
you wished
>
> to define as primitive those which distinguished among classes.
>
>
>
> RC:] In my vehicle example, the properties are chosen by the
designers who
> specify how the radar and camera algorithms establish separate
objects,
> and
> how they assign those objects into classes. For example, an
object which
> is
> "approximately" stationary in the database could be
another vehicle
> traveling in front or back of the object. Another example;
an object
> which
> is stationary with respect to the road is stopped. It might
be a lamppost
> (which the vehicle should avoid colliding with at all costs) or a
moose
> (which it would be highly preferable not to collide with, but
there is
> relatively less danger to the vehicle or its occupants.
Therefore objects
> which fit a stationary profile should preferably be avoided, even
when
> they
> can be partitioned into specific classes of object kinds (Azamat's
word)
> or
> types (my preferred choice). Of course there are
intermediate types -
> dogs,
> people, bridges - choose your favorite perceived object type
abstraction.
>
>
>
> In my definition, I used "primitive" or
"terminal" in the sense of the
> intended application - vehicle trajectory kinematics
management. But as
> you
> pointed out, the choice again is subjective. It depends on
the
> experience,
> knowledge and perceptions of the requirements and design teams.
>
>
>
>> For example, in a relational database, there are columns which
serve
>> this
>
>> purpose, and for which select statements can be written that
refer to
>
>> exactly those properties.
>
>
>
> DF:] The clearest such property in a relational database would be
the
> ID_Number property. That uniquely defines each entity, but
is not very
> useful for ontological purposes.
>
>
>
> RC:] Every detected object should indeed have some unique
identifier
> assigned and stored in the database at detection, whether the
identifier
> is
> stored as one or as a concatenated plurality of such columns. But
the
> identifier assigned by the radar perceiver is clearly different
from that
> of
> the camera perceiver, which acquires different kinds of
information from
> the
> radar profile.
>
>
>
> Further classification of objects detected by radar can
iteratively be
> done
> by partitioning the detected objects according to yet other rules,
each
> rule
> represented as a cluster of columns and value sets. Thus the
database can
> have abstract rules stored in rows of certain relations, and
interpreted
> by
> the classification algorithm (for easy discussion, I choose the
FCA
> algorithm as an example).
>
>
>
> So a single column might be adequate for identifying the set of
all unique
> radar object instances currently detected in the database.
However, that
> single column is inadequate for further classification
(subclasses) of the
> objects which map into radar recognition. The camera might
even see
> things
> the radar cannot see, so there must be yet other assigners (the
camera
> interpreter) of object instances and still other assigners of
subclass
> properties and values for other types of optically detected
objects.
>
>
>
> DF:] The issues in the database world are different from those of
the
> ontological world, and implications from one of the fields does
not
> necessarily apply to the other. However, i will respond to
the database
> comments below, from an ontological perspective.
> RC:] Surely you are not implying that databases are not
ontologically
> expressive; John posted a number of descriptions on this list to
show
> clearly that SQL practices every FOL form that can be expressed.
> For example, the classification schemes themselves are developed
in
> testbeds
> which collect large numbers of samples. Engineers then use
the samples to
> distinguish among the test example objects, and to postulate and
test the
> known classes based on (arbitrarily) selected properties drawn from
that
> universe of properties. In the vehicle example, it is
reasonable that the
> properties detectable by the radar perceiver overlap in some ways,
but not
> in others, from properties in the universe which are perceivable
by the
> cameras.
>> The group-by clause specifies the precise logical
>> combination of property values to be used in sorting the
various
>> entities returned by the select statement.
> DF:] And many such queries would return multiple entities.
At some level,
> each query defines a class, but one would not normally consider
such
> classes as primitive.
> RC:] You are using the word "primitive" to adjectify
that CLASS in your
> above statement, and that adjectification is different from the
way the
> word
> "primitive" was used to distinguish among the universe
of PROPERTIES.
> Perhaps you prefer to think of the universe as including classes
AS WELL
> AS properties.
>
>
>
> Other than that, why do you believe that a database of such
properties and
> classes is different in ontologies versus in the database world?
> Databases
> practice FOL in any way you want to construct and interrelate
their
> component tables, columns, domains and queries. I don't see
why there is
> NECESSARILY a difference. In many simple business accounting
> applications,
> your statement matches practice fairly well. But in
engineering
> applications, it doesn't match so well. Perhaps you can
explain further
> WHY
> and HOW databases do not encode ontologies.
>
>
>
>> Any further specification of how those properties are combined
or
>> grouped
>
>> is part of an arbitrary (read subjective) classification
theory.
>
>
>
> Couldn't the selection of the properties to begin with be
similarly
>
> arbitrary?
>
>
>
> -- doug f
>
>
>
> Yes; there always more than one way to skin a cat - any cat, even
a lion
> or
> a tomcat. The lion might require different preparations in
the software
> than the tomcat does, and hence different property choices.
One is
> dangerous; the other probably isn't, for example.
>
>
>
> Thanks for continuing an intriguing discussion - we may actually
yet be
> getting somewhere with relating subjective perception to
ontologies.
> Please
> continue, si vous plait.
>
>
>
> -Rich
>
>
>
>> JMHO,
>
>> -Rich
>
>>
>
>> Sincerely,
>
>> Rich Cooper
>
>> EnglishLogicKernel.com
>
>> Rich AT EnglishLogicKernel DOT com
>
>> 9 4 9 \ 5 2 5 - 5 7 1 2
>
>>
>
>> -----Original Message-----
>
>> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
>
>> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
doug foxvog
>
>> Sent: Wednesday, July 06, 2011 1:20 PM
>
>> To: [ontolog-forum]
>
>> Subject: Re: [ontolog-forum] Why most classifications are
fuzzy
>
>>
>
>> On Wed, July 6, 2011 14:38, AzamatAbdoullaev said:
>
>>> John wrote
>
>>>> "And a warning: Unless you can find an
immutable law of nature
>
>>>> that creates a classification, don't expect it to be a
solid
>
>>>> foundation for a "standard ontology".
>
>>
>
>>> Agree. Here are five methodogical rules from the standard
ontology:
>
>>> 1. Class is determined by a single property;
>
>>
>
>> This definition would block many subclasses, unless the
property
>
>> is defined as membership in the class.
>
>>
>
>>> 2. Kind is determined by a set of properties;
>
>>
>
>> Is this a useful distinction?
>
>>
>
>>> 3. Natural Kind is determined by a set of lawfully related
properties
>
>>> (laws);
>
>>> 4. Natural Genus is the set of things sharing a basic law;
>
>>
>
>> I haven't heard this term except in the context of Linneaen
taxonomy.
>
>>
>
>>> 5. Natural Species is the set of things sharing a
particular law.
>
>>
>
>> The term has a useful meaning in biology; but what is its use
otherwise?
>
>>
>
>>> Many classifications are mostly at the level one, like the
five
>
>>> classifications for natural resources, such as land,
water, soils,
>
>>> plants,
>
>>> animals, solar power, etc, divided by a single property:
origin;
>
>>> renewability, availability, development stage or
distribution scope.
>
>>
>
>> There are many gradations of wetlands reaching from soggy
ground to
>
>> standing shallow water. A rigid division between land
and water is
>> quite
>
>> arbitrary. Fungi used to be classified as plants, but
now they are a
>
>> different kingdom.
>
>>
>
>>> A more
>
>>> scientific understanding of resources is asking for
reaching higher
>
>>> levels.
>
>>
>
>> Even at this level there are difficulties.
>
>>
>
>> -- doug foxvog
>
>>
>
>>
>
>>> Azamat Abdoullaev
>
>>>
>
>>> ----- Original Message -----
>
>>> From: "John F. Sowa" <sowa@xxxxxxxxxxx>
>
>>> To: "[ontolog-forum]"
<ontolog-forum@xxxxxxxxxxxxxxxx>
>
>>> Sent: Wednesday, July 06, 2011 7:45 PM
>
>>> Subject: [ontolog-forum] Why most classifications are
fuzzy
>
>>>
>
>>>
>
>>>> This forum has been quiet for a while, and I'd like to
stir the pot
>
>>>> with a controversial issue.
>
>>>>
>
>>>> Two widely known rigid classifications established a
paradigm,
>
>>>> which some people mistakenly consider the norm:
the periodic
>
>>>> table in chemistry and the Linneaen taxonomy of living
things.
>
>>>> But the rigid boundaries of those categories are the
result of
>
>>>> underlying laws of nature that explain why
intermediate cases are
>
>>>> impossible (periodic table) and rare (taxonomy of
species).
>
>>>>
>
>>>> For physics and chemistry, quantum mechanics implies
discrete steps,
>
>>>> which create discrete classifications of elementary
particles.
>
>>>> At the next level up, it also implies discrete
combinations of
>
>>>> such particles -- combinations of quarks to form
baryons (protons
>
>>>> and neutrons) and combinations of atoms to form molecules.
>
>>>>
>
>>>> For biology, discrete molecular operations support the
stable
>
>>>> molecules needed for life and the mechanisms for
replicating the
>
>>>> huge molecules needed for DNA. But those
mechanisms are only
>
>>>> weakly stable -- that leads to random mutations.
>
>>>>
>
>>>> For the next level up, natural selection creates fuzzy
boundaries
>
>>>> among interbreeding populations, but crisp boundaries
between
>
>>>> isolated populations. For example, look at the
sharp distinction
>
>>>> between foxes and wolves, but fuzzy boundaries among
dogs. When
>
>>>> humans allow dogs to "do their own thing",
the breeds quickly
>
>>>> revert to a generic ur-dog -- which is usually
healthier and
>
>>>> more robust than many breeds.
>
>>>>
>
>>>> Some biological classifications are not based on
DNA. Examples
>
>>>> are trees and berries. For example, the family
Rosaceae includes
>
>>>> rose bushes, apple trees, and raspberries.
Biologically, all
>
>>>> berries are fruit, but apples are more likely to be
grouped with
>
>>>> oranges as "typical" fruit than with
raspberries.
>
>>>>
>
>>>> By height and woodiness, an apple tree is more likely
to be
>
>>>> classified with a remotely related spruce tree than
with
>
>>>> a rose bush. And many evergreens become bushes
or trees
>
>>>> at the whim of some human with a pair of shears.
>
>>>>
>
>>>> There is even a debate in India whether bamboo should be
>
>>>> classified as grass or tree: "Recently
there was a controversy
>
>>>> when the union ministry of environment and forests
asked states
>
>>>> across India
to recognise bamboo as a minor forest produce."
>
>>>>
>
>>>> See http://www.bbc.co.uk/nature/life/Bamboo
>
>>>>
>
>>>> In general, what makes any classification rigid is
some *law*,
>
>>>> which could be a law of nature or some human
rule. Since it's
>
>>>> a lot easier to change human laws, such
classifications are
>
>>>> likely to change with culture, technology, or fads.
>
>>>>
>
>>>> Summary: Fuzzy boundaries are the norm in most
classifications.
>
>>>> Whenever a boundary seems to be sharp, look for some
axiom, law,
>
>>>> principle, or convention that creates the
distinction. Those
>
>>>> laws are more fundamental than any grouping by
"similarity".
>
>>>>
>
>>>> And a warning: Unless you can find an immutable
law of nature
>
>>>> that creates a classification, don't expect it to be a
solid
>
>>>> foundation for a "standard ontology".
>
>>>>
>
>>>> John Sowa
>
>
>
>
>
> =============================================================
>
> doug foxvog doug@xxxxxxxxxx
http://ProgressiveAustin.org
>
>
>
> "I speak as an American to the leaders of my own nation. The
great
>
> initiative in this war is ours. The initiative to stop it must be
ours."
>
> - Dr. Martin Luther King Jr.
>
> =============================================================
>
>
>
>
=============================================================
doug foxvog doug@xxxxxxxxxx
http://ProgressiveAustin.org
"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be
ours."
- Dr. Martin Luther King Jr.
=============================================================
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