...categorization
Mostly, categorization with respect to ``natural categories'', as in an ontology of what is ``out there''.
...extension
I am using the term extension here in the traditional model-theoretic sense of the set of objects in the model's domain that corresponds to a constant symbol. Although part of the argument developed in this dissertation goes against traditional model theory, I will continue to use the term in this way, for convenience.
...categorization.
In particular, the physiology of perception, but perhaps also the physiology of motor control and even the physiology of emotion; cf. [Lakoff 1987].
...itself.
This is essentially the point that Searle tried to prove in his famous Chinese Room argument [Searle 1980]
...perception.
This is true for directly grounded symbols corresponding to categories of perception only. The hypothesis is that other symbols are indirectly grounded by being constructed out of directly grounded ones. Harnad is not very specific on this point.
...not.
The intersection of the set of people using the term``symbol grounding'' with the set of people using the term ``embodiment'' seems to be empty, but I will not let that disturb me.
...semantics
According to Webster's online dictionary, ``a branch of semiotics dealing with the relations between signs and what they refer to and including theories of denotation, extension, naming, and truth''.
...terms''.
In English, there are eleven basic color terms: white, black, red, green, yellow, blue, brown, purple, pink, orange, grey.
...neurophysiological
Relating to the processes and phenomena of the nervous system.
...psychophysical
Relating the magnitude of a psychological response variable such as amount of red or green percept to some physical quality of the stimulus such as spectral composition of a light source, cf. [S. Edelman 1992].
....
I am using this tripartite structure as an organizational tool only; no theoretical claims about the boundaries between these domains are intended.
....
is typically used to represent wavelength in nanometer (nm). then represents the energy of the stimulus as a function of wavelength.
...form.
This simplification does not take into account additional factors like incident and reflection angles, transmission absorption and refraction, etc.
...respectively.
Spectral colors are the pure monochromatic components that white light can be split into by use of a prism (``rainbow colors''), corresponding physically to pure single-wavelength radiation. One can also think of spectral colors as impulse functions in the frequency domain.
...CIE
Commission Internationale de l'Eclairage, or International Committee on Lighting, a Paris-based standards organization.
...interpretation
That is, the external interpretation of the mathematical model, not to be confused with a grounded semantic model used by a cognitive agent.
...altogether.
Non-spectral colors are colors that do not appear in the spectrum of white light, i.e. they are not single wavelength signals but complex signals. In the frequency domain, they are represented as non-impulse functions.
...(CLR),
Thanks to Bill Rapaport for suggesting this acronym, perhaps the most important part of an AI system.
...of
The mapping from a color space to a set of color names, see Section .
...model.
Chances are that the match will be less than perfect, however, without detailed knowledge of the internal model.
...Semantics
I am indebted to many people for the ideas presented in this section, too many to name them all. Discussions on this subject have taken place over a number of years, in settings ranging from CS department courses to the bar of a hotel in Italy. A few of the important conversation partners in this respect have been (in alphabetical order): Stevan Harnad, Henry Hexmoor, William J. Rapaport, Kenneth Regan, Stuart C. Shapiro, and Tim Smithers. The responsibility for what I've turned their ideas into is entirely mine, however.
...language
Or at least a representation language of some kind. The degree of formalism in KRR systems varies considerably, along the lines of what has been called the neat--scruffy debate [Rapaport 1992]. Any (symbolic) knowledge representation language uses terms of some kind, however, with an associated semantics not unlike what I describe here. My characterization of KRR is not meant to be exhaustive, however, and my remarks are addressed only to KRR systems of the kind alluded to.
...kind,
The proof of the stronger claim that all KRR formalisms can be translated into first-order logic is rather simple, if one considers only languages and inference mechanisms which are implemented or implementable on a Turing Machine (TM), and one further considers the TM-equivalence of first-order logic [Boolos \& Jeffrey 1974]. I am not aware of any KRR formalisms which are not implementable on a TM, and I will disregard this possibility in the light of the Church-Turing thesis [Davis \& Weyuker 1983].
...semantics.
The preferred interpretation is one that relates the symbols used in the equations to such things as mass and velocity of objects, although one can doubt whether these are things ``in the world'' or just more abstractions derived from our perceptual experience (cf. [Heisenberg 1988], [Schrodinger 1988]).
...mind,
Or ``cognitively impenetrable'', as [Pylyshyn 1981] calls it.
...capability.
One rather sobering observation about artificial neural networks concerns the size of the models, typically no more than a few hundred artificial neurons, compared to the estimated 10 billion neurons in the human brain, each of which may compute functions that are quite a bit more complex than the typical artificial neuron does. Even taking the difference in speed of the underlying technology into account, the complexity gap is huge.
...completeness).
These definitions are rather informal; some more formal ones are discussed below.
...``mind''.
Or as Cris Kobryn put it in a comp.ai electronic news article: ``How does one verbally explain what the color blue is to someone who was born blind? The problem here is to explain a sensory experience (e.g. seeing `blue') to someone lacking the corresponding sensory facility (e.g., vision)'' (article <200@kvasir.esosun.UUCP>). Note that this formulation presupposes a person with a developed language capability, however, which makes the problem considerably less hard than in the case of an artificial agent.
...environment.
I do not consider producing or accepting natural language surface forms to constitute interaction; indeed, I would claim the blind agent I described cannot understand the meaning of the color words it might produce or accept.
...language.
Alternatively, one could say the rules are sound iff every derivable wff is true, and the rules are complete iff .
...theorems.
Strictly speaking, this applies to monotonic inference only. Since it has no bearing on the gist of the argument, I will disregard non-monotonic inference for now.
...vector),
Details of the construction of such a space are left as an exercise for the reader.
...strange.
In an informal inquiry I did not find any natural language that uses such a term on a regular basis, and I speculate (with many other researchers) that there is no such language, for a reason which will become apparent later.
....
This is not meant to denigrate the efforts of the Cyc team. I believe that they are doing an excellent job within the parameters of their project. I merely mean to point out some fundamental problems with the approach itself, which does not reflect on the integrity of the Cyc team members or the value of their work.
...terms.
I will relax the point assumption in Chapter . This example also ignores possible differences in the relative saturation and brightness of colors, but without loss of generality.
...terms.
Using some metric on the color space, Euclidean or other; cf. [Shepard 1987].
...color,
The limitations of language become very apparent here.
...sense.
The term achromatic color sounds somewhat contradictory to most ears, but is used as a technical term in the color vision literature.
...space.
There are many other phenomena related to the graded nature of color categories that could be expressed with similar meaning postulates, but it would lead us too far to discuss those now.
...it.
Artificial neural networks have also embraced the notion of continuous-valued quantities rather than discrete symbols, and I believe this is partly responsible for their success in modeling some aspects of human perception and cognition. My own work is hybrid in nature, using both discrete symbols and continuous numerical quantities. Recent neural network research has also attempted to re-introduce symbolic representations [Zeidenberg 1990].
...night.
Along the same lines, one might doubt whether there is any sky to begin with, but I will not make that case.
...thought.
The latter proposal is entirely circular, in my opinion.
...innate,
Even this is a simplification. As [Maturana \& Varela 1987], [G. Edelman 1992] and [Zeki 1993] point out, for instance, there is considerable plasticity in even the adult brain. But for the purpose of our discussion that is not immediately relevant.
...LGN
Lateral Geniculate Nucleus, a body of cells roughly halfway between the retina and the primary visual cortex V1.
...publication.
For instance, the 1931 functions were measured for a 5 degree field of view, and in 1964 the CIE published similar functions for a 10 degree field of view. Other revisions have been proposed by Judd, Vos, & Walraven, and others [Wyszecki \& Stiles 1982].
...NTSC
National Television Standards Committee, alternatively known as the ``Never The Same Color'' standard.
...coordinates
Another type of color space coordinates endorsed by the CIE.
...#colorperception>):
The assumption of linearity is widely held in color science, e.g., [Wyszecki \& Stiles 1982]. There may, however, be some non-linear phenomena involved in color perception, as I will discuss below.
...superimposed:
Unless specified otherwise, I will always refer to mixtures of colored light, rather than dyes or pigments. The former are known as additive mixtures, the latter as subtractive.
...space.
The reddish-green and yellowish-blue reported to be perceived in some experiments [Crane \& Piantanida 1983], and which apparently contradicts opponent process theories of color vision, seems to be a function of lateral interactions in the cortex, and occurs only under very special circumstances, mostly in the absence of a corresponding retinal stimulus. As such it is not a major objection to opponent process theories, since they deal with ordinary stimuli in the main visual pathway.
...process.
Of course it is easy to see this with the 20/20 vision of hindsight. At the time Cairo wrote his dissertation, these models were just as ``hip'' as graded cognitive models are today. Although his assumptions are now relatively widely regarded as wrong, his work nevertheless provides some valuable insights.
....
The term theory is used here in the sense of David Marr's distinction of the computational theory, algorithm, and implementation levels [Marr 1982].
...colors
Apparent colors that are perceived in proximity to certain other colors.
...bands
Narrow bands of lighter or darker shades of a color perceived around the boundary separating two bands of different colors.
...screen),
Thanks to Chris Brown for pointing this out to me at the outset of my work. I wasn't convinced until he told me to look for a brown light.
...colors,
Apparent colors that are perceived when looking at a temporally alternating series of colors.
...space
Neuro-Psycho-Physical color space; thanks to K.N. Leibovic for the suggestion.
...functions
Response is a function of both the wavelength and the radiance of the stimulus.
...range.
This is also true for perceived loudness (the decibel (dB)) or perceived pitch (semitones, octaves), for instance.
...experiments
The stimulus radiance levels are given as attenuation relative to the maximum available, in log units.
...state
The article states that ``the animal was maintained under a low level of light adaptation'', and the pauses between 1-second stimuli were 30 to 60 seconds, which should be long enough to re-establish the previous adaptation state if it were at all affected by the preceding stimulus.
...spikes/sec,
K.N. Leibovic, personal communication.
...data.
Modeling the negative (inhibitory) responses with a sigmoid function may be questionable, but in view of the small inhibitory responses relative to the excitatory ones, it does not make much difference anyway. The unified approach to modeling both inhibitory and excitatory responses is to be prefered, in my opinion.
....
Although I could have used the Interpolation function directly on the data set in two dimensions, that would not have resulted in the typical sigmoid behavior in the radiance domain, which I consider important.
...pairs
The terminology of ``mirror images'' should be interpreted loosely, with respect to the overall shape of the response profiles. The functions are by no means exact mirror images of each other.
...nm.
The zero crossings actually vary slightly with radiance, which may be related to the Bezold-Br;ucke effect [Wyszecki \& Stiles 1982], but we can ignore that for the purpose of the present discussion.
...response.
Of course, their model is merely that, and it is not without problems of its own. The existence of unique yellow and green wavelengths is well established, however. As with all psychophysical measurements, there is some interpersonal variability in the exact numbers, but not in the general trend.
...1.
The technical reason for choosing is that the ratio of the integral of the positive to the integral of the negative phase of the functions is greatest at that radiance, which results in a more ``regular'' shape of the normalized color space.
...#solfigbr>.
One could apply equation to the 6 component functions before they are combined into opponent functions. I have tried this, but the resulting fits to the non-linear functions are no better than when applying the equation to the opponent functions directly.
...size.
The relevant measure is the area ``under'' the curve with respect to the Y axis, or the integral of the functions with respect to wavelength.
...only.
For the function is used, or the integral over the negative values only, since that function is an inhibitor with an all-negative response.
...excitation.
The equation given is for functions with inhibitive responses in the lower wavelength range, and excitative responses in the higher wavelength range. For the functions with the reverse profile, the inequalities have to be exchanged. For non-opponent functions, can be thought of as for inhibitors and for excitators.
...functions
Or transmittance functions, which makes no difference for our purpose.
...function,
Again ignoring other factors such as atmospheric absorption and scattering, viewing angle, etc., as I did in equation (p. ).
...color
For those having a color print available, or viewing this document on a color monitor. It is interesting to view this and related figures with a PostScript previewer like ghostview, where one can see the surface being built up in 3D. This gives a better appreciation of the shape, probably as good as possible short of an animated plot.
...surface.
Were it not that there is no such thing as a real color, of course.
...stimulus.
Sometimes a non-flat spectrum is used as the white reference, e.g. the CIE standard light sources A to D, but the differences are not important for our purpose.
...by
For integrating the linear response functions any relative radiance will do, as long as it is the same for all functions, since the result is scaled before sigmoidification. I have chosen a relative radiance of 1 for convenience.
...surfaces.
A note of caution: the color rendering of Figure and the like is only approximate, as explained before, so we should not give too much weight to the visual appearance of the OCS surface in these figures. Nevertheless, the color rendering is a reasonable approximation, the algorithm used is exactly the same for all spaces shown, and a picture is certainly worth a thousand words for our purpose.
...space
Whenever I say ``the shape of the color space'' I really mean the shape of the OCS surface as represented in the color space, of course. The color space as such has no shape. The OCS surface is very well suited for this purpose, since it represents the limit of physically realizable colors. The Munsell color system is also based on the appearance of surface colors. The combination of the OCS surface and the color space can be thought of as the representation of physical or ``outside world'' constraints in the internal perceptual mechanism.
...space
For this purpose, the XYZ space has been rotated appropriately to make the gray axis vertical and to position the four primary colors in positions similar to the ones they occupy in the NPP space.
...undefined.
I have used a threshold of , which corresponds to the smallest representable value with an 8-bit resolution.
...below.
Whether one sees the artificial neural network technique described below as learning or as optimization depends largely on one's background and one's theoretical likes and dislikes. I will freely use ``learning'' in the remainder of this section because that term is traditionally used in the neural networks literature, but the reader should feel free to substitute ``optimization'' if (s)he finds the other term offensive. Please contact the author for an Emacs lisp function to enforce the usage of choice.
...error
As determined by some experimental attempts to do so.
...N-layer
There is some confusion as to whether N should refer to the number of layers of nodes or connections. If the layer of input nodes is not counted, these measures are identical. I will refer to the number of layers of nodes by N, however.
...#nnspectra>.
This subset is itself infinite since the parameters are real-valued, but its cardinality is obviously less than that of the set of all possible spectra. By discretizing the domains of each of the parameters we can bring the cardinality down to a finite integer number.
...differences.
In addition, I have used the most common 5 degree 1931 CIE functions, and there are several modified versions as well as 10 degree versions available. I have not investigated the effects of using any of these sets of functions on the accurateness of the transform.
...#ngaussian>.
By an N-dimensional normalized Gaussian function I mean a function of N variables.
...#bctenglish>).
The choice of CIE A as a light source is somewhat unfortunate, since its spectral power distribution is considerably skewed, which results in lower resolution measurements for some parts of the spectrum, as well as problems with color constancy, since most color work is done relative to either a C or a flat spectrum light source. We are thus forced to use perceptual color constancy in a somewhat perverse way, assuming that it takes care of any distortions introduced by the light source, but ignoring it for all other purposes.
....
These measurements have been made relative to magnesium oxide as white reference, and with a CIE C light source -- hence the assumption we have to make about color constancy.
...signals.
But of course I won't speculate.
...time.
See below for some remarks on learning versus optimization, and for a sketch of such an algorithm.
...vector
The term ``vertex'' may be somewhat misleading here, as we are concerned with every stimulus along the boundary of the category, regardless of whether it happens to lie on a straight segment of the boundary or not.
...trial-and-error
I am somewhat bothered by the frequent need for ``magic numbers'' like this, and the associated arbitrariness. But then to some extent the choice of any mathematical model is a somewhat arbitrary event, of course.
...representative
No pun intended.
...#normalizedgaussian>).
In neurophysiological terms one might think of the ``receptive field'' of a neural (sub)network ``implementing'' a particular category, and it is not unreasonable to assume that those receptive fields might be somewhat differently shaped from one category to the next, and not necessarily spheroid in terms of the underlying color space coordinates -- but all this is highly speculative.
...fitted.
In Chapter we will evaluate the model on other data sets as well.
...to.
I am purposely avoiding terms like ``training'' and ``learning'' here.
...exceptions.
We should keep in mind that the Berlin and Kay data represents averaged judgments over a number of subjects, which may introduce phenomena that are not necessarily present in any individual subject's data.
....
It would be easier to reproduce a piece of Mathematica code here than to try to write this down in standard mathematical notation, as I have done. Mathematical notation is just not meant to deal with complex data structures and other objects that occur frequently in programs.
...mechanism.
These concepts derive in part from Edelman's Nobel Prize winning work in immunology.
...#bct>).
There is some evidence that there may be more than 11 such universal categories, but I will ignore that for now.
...discussion.
The location of the foci may have more to do with the environment in which the color perception mechanism evolved than with any intrinsic features of the mechanism itself, but at this point I can only speculate on this matter.
...categories.
If we think of a category model as a fuzzy characteristic function for the corresponding fuzzy set , we could write , but I am avoiding this notation because of the potential confusion with the category parameter .
...values:
The description of the various steps is mainly for explanatory purposes, and need not reflect an actual implementation strategy. The first two steps can easily be combined into one, for instance.
...stimulus.
In practice I apply a ``fudge factor'' to , so that the condition becomes , with . The reason for this is that the minimization procedure as described in the previous chapter often results in values slightly below for the boundary stimuli, because of the RMS error metric used.
...coordinates:
Again, the description is for explanatory purposes, and not meant to suggest an implementation strategy.
...non-foozles,
This is of course hard to imagine, but let's assume it is the case for the sake of the argument.
...too).
Flemish has a term ``ros'' which means ``red'', but is only applicable to hair, to my knowledge.
...related.
In some cases, one can completely internalize the indirect referent of one's symbols, e.g. by eating it.
...applications.
For instance, despite repeated attempts and written assurances that the information would not be spread any further, I could not convince the manufacturer of the color scanner I used to acquire some of the test images to provide me with the spectral sensitivity functions of the scanner's color sensors. These sensitivities can be measured given the right equipment, which I did not have access to, however. Sad to say, I have had no more success getting similar information from some academic sources that shall remain equally anonymous.
...irregular.
An extreme case would be a single-frequency light source, in which case the effects can never be undone, and no color perception is possible at all.
...images.
And of course, people's adaptive mechanism can fail too, under certain specific circumstances. The important thing is that it works under most ordinary circumstances.
...NTSC
Never The Same Color.
...colors.
These objects are relics of a robotics project that was supposed to include manipulation of the objects with a robot arm as well as color perception (Appendix ). Unfortunately the project met with a premature demise, mainly due to lack of working equipment and funding.
...GLAIR
Grounded Layered Architecture with Integrated Reasoning
...interact.
Our discussion of architecture in this paper extends beyond any particular physical or software implementation.
...environment.
A machine like a vending machine or an industrial robot has responses, but it is unconscious. See [Culbertson 1963] for a discussion of independence of consciousness from having a response. Also, intelligent behavior is independent of consciousness in our opinion.
...embedded
``Embedded agents are computer systems that sense and act on their environment, monitoring complex dynamic conditions and affecting the environment in goal-oriented ways.'' ([Kaelbling \& Rosenschein 1990] page 1).
...processing.
We consider body-related processes to be unconscious, but that is not meant to imply anything about their complexity or importance to the architecture as a whole. Indeed, we believe that the unconscious levels of our architecture (the Perceptuo-Motor level and the Sensori-Actuator level) are at least as important to the architecture as the conscious one (the Knowledge level). We reserve the term sub-conscious for implicit cognitive processes such as category subsumption in KRR systems. See [Shapiro 1990] for a discussion of sub-conscious reasoning.
...parallel.
This autonomy is similar to Brooks's subsumption architecture [Brooks 1985], but at a more macroscopic level. Brooks does not distinguish between the three levels we describe, as his work is solely concerned with behaviors whose controlling mechanism we would situate at the Perceptuo-Motor level.
...the-cup-that-I-am-holding
This kind of designation is merely a mnemonic representation intended to suggest the entity and aspect under consideration, for the purpose of our exposition. It is not the actual representation that would be used by an agent.
...input.
For instance, in the context of autonomous vehicles, if obstacle avoidance or returning to the base is a lower-level behavior than planning exploration strategies, then a failure of the hardware implementing the latter does not necessarily prevent the former.
...Friday''.
The plan is to get in the car to go to the travel agency to get a ticket to fly to LA on Friday. Today is Thursday and it is near the end of the business day. Also, the agency won't accept telephone reservations. This example is suggested in [Pollock 1992].
...object.
See [Shapiro \& Rapaport 1987] for our use of ``intensional representation''.
...it,
Of course this also depends on how far the object is removed from the body, or how far the arm is stretched out, but that can be taken into account (also in body-specific terms). People's Perceptuo-Motor level idea of how heavy something is is most likely not in terms of grams, either (in fact, a conscious estimate in grams can be far off), but in terms of how much effort to apply to something to lift it. That estimate can be off, too, which results in either throwing the object up in the air or not being able to lift it at the first attempt, something we have all experienced. On the other hand, having a wrong conscious estimate of the weight of an object in grams does not necessarily influence one's manipulation of the object.
...fire).
An appropriate reflex for a robot (arm) might be to withdraw or stop when it meets too much mechanical resistance to its movement, as evidenced for instance by a sharp rise in motor current draw. Such a reflex could supplant the more primitive fuse protection of motors, and make an appropriate response by the system possible. Needless to say, a robot that can detect and correct problems is much more useful than one that merely blows a fuse and stops working altogether.
...fire).
The fact that the withdrawal reflex may not be as strong, or not present at all, when doing this intentionally may point to the need for top-down inhibition as well.
...large.
It is never a problem as long as agents need not communicate with the outside world (other agents), of course, cf. [Winston 1975].
...same.
This is of course the ``duck test'', made famous by a former US president.
...things.
Retrieving ``canned'' parameterized routines is still a low-level programming style that we want to avoid.
...people.
The term ``knowledge'' should be taken in a very broad sense here.
...resources.
Many reasoning problems are NP-complete, meaning there are no polynomial-time deterministic algorithms known for solving them, or in plain English: they are very hard to solve in a reasonable amount of time (see e.g. [Levesque 1988]). Elephants don't stand a chance.
...behavior
E.g., visual reflexes in [Regan \& Beverly 1978]: Here responses are generated to certain visual stimuli that do not require detailed spatial analysis.
...model.
Albus defines a world model as the agent's best estimate of objective reality [Albus 1991].
...world,
Situated cognition and reactive planning are proponents of avoiding world modeling, e.g., [Suchman 1988][Brooks 1990].
...agent.
Even the prominent advocators of doing away with world models actually use a variety of models, some of which qualify as kinematic/perceptual models. For instance, see Chapman's work on Sonja [Chapman 1990] where Sonja has to build a convex hull of obstacles and compute angles in order to decide the best way to avoid them.
...away.
Inhibiting this reflex might turn the agent from a chicken with a long life expectancy into an eagle with short life expectancy.
...subsets
Let's define a subset of a PMA to be a disjoint PMA, i.e., B is a subset of A iff all components of B are subsets of components of A and no transitions exist between actions in B and those in A-B.
...man's
He-man or She-man.
...WWW
Really the greatest thing since sliced bread!

lammens@cs.buffalo.edu