Lecture � MAS962, Regier & Carlson, Gardenfors and Hofstadter

Greg Detre

Tuesday, October 29, 2002

 

cheap apartments problem � came out of OpenMind � employs modus ponens and other syllogistic machinery

interesting, because there�s lots of things going on, including not being clear about it

 

Gardenfors � presented by Peter Gorniak

Dennett�s formulation of the Frame problem

in terms of a robot that has to get a wagon out of the room without taking the bomb with it

you have to not only know what�s relevant, but not compute on what�s irrelevant

for symbolic systems, there�s no way of figuring out what�s relevant just from the structure of the statements

�frame problem� is a phrase from psychology (rather than Minsky/McCarthy), meaning a frame of reference within which all of the issues are contained

Dennett doesn�t see this as a purely symbolic problem

probabilistic (e.g. Bayesian) systems still have problems with this

�???

innateness + symbol grounding (vs creation) problem

induction � how can you do that without some sort of semantics attached to the symbol

Deb: is there any meat to the symbol-grounding problem?

what is symbol grounding??? grounded to what???

senses???

Harnad, symbol grounding problem: �How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis of their (arbitrary) shapes, be grounded in anything but other meaningless symbols?�

connectionism:

Peter: usually the NNs that work well are the ones that aren�t opaque, where you�ve done a lot of engineering to pin down a structure that does what you want to do, and that you can understand to some degree � Gardenfors� description is a highly idealised description

conceptual level:

there�s some meaning to each vector

notion of similarity

object/instance as point in low-dimensional quality space, properties as regions

can you differentiate individual objects/instances in this low-dimensional space??? can you interpret the properties??? is there enough information??? is the conceptual level really above the symbolic???

two cups with the same features couldn�t be told apart at the conceptual level

Hugo: unhappy with the idea of similarity as Cartesian distance

his examples are very clean + deceptive

non-geometric space???

Tom: this sort of geometric representation doesn�t work so well for more conceptual stimuli, e.g. animal taxonomies, or diseases

for more structured stimuli, you�re going to need a higher-dimensional space � you can do animal taxonomies, if you look at all of their distinguishing features

the main thing you need to deal with space is a notion of betweenness

is the conceptual level simply the symbolic???

Hugo: he says so at the end

Barbara: why can�t you build it in a connectionist way

but we might not understand what�s going on internally in the connectionist model

Deb: having nameable dimensions doesn�t necessarily mean that it�s symbolic

Deb: connection to metaphor? does having a lower dimensional space make analogy-making easier?

Tom: a lot of symbolic reasoning lacks analogue structures, which they need

surely though real numbers are analogue???

allows you to use geometrical isomorphisms

see them as caricatures of NNs

principle component analysis on the hidden layers

more information at the symbolic level???

when you put a label on a dimension, you impute meaning, you turn it into a symbol

???

pairwise relations between points as a means of 2D representation???

Hugo: even �above� would be much more complicated than the examples Gardenfors gives

Deb: no problem with having hundreds of dimensions

but then �conceptual� becomes a misnomer???

what�s the appeal then???

need temporal (and distance) information too

Hugo: ok, what about emotions then?

Peter: the taste example is perhaps misleading because you�re not necsessarily supposed to find a physical correlate for the quality space

are you supposed to be able to put a name to the quality dimensions???

summarise complaints:

there are many high-dimensional examples that wouldn�t fit in low dimensions

mainly constrained to perceptual spaces

maybe there should be many things in between the connectionist and symbolic (cf Minsky)

one big thing that we can take away from Gardenfors� ideas is that you can leverage the intrinsic structure of your representation

this does help with the grounding

so how does Gardenfors deal with the symbol creation problem???

difference between you can�t yet and won�t ever be able to tell us how that happens

they all seem to think that the conceptual is closer to a sophisticated view of connectionism than to the symbolic

I should have looked at Harnad�s 8 rules of the symbolic � the symbolic is discrete

 

Regier & Carlson � presented by Peter Gorniak

you could put the centre of your attentional exponential fall-off maybe in the centre of mass � but then it wouldn�t reduce to both the PC and COM models

would you have �above�, �left� etc. as quality-dimensions???

or would you have the �absolute� spatial dimensions as the quality-dimensions???

Regier assumes that there�s always an absolute �up�

Regier�s model of above is not symbolic because it has non-discrete components

the original Regier work is all connectionist

Deb: are non-point targets an easy extension?

Peter: no, because of the way he finds attention points

Deb: you can just use the proximal for each, just as you do for the landmark alone

what about multiple objects?

changes your notion of COM, depending on whether you count the balls or their total mass

problem with the human experiments???

artefact introduced by making our concepts explicit??? could we not make things a bit more natural, and divert their attention from an examination of �aboveness�

what if people got into some algorithmic habit?

0-10 vs �1-10

part of the problem is that it�s 2D

sometimes, you test aboveness by dropping the pen, and seeing if it lands on the table � depends on notion of down/gravity

of course, then helium balloons would never be above anything

 

Discussion of Deb�s talk tomorrow

Deb�s talk tomorrow

you need a really good reason to define a level

�leap of faith� processes � there�s Inference to go from one system to another

he doesn�t see that in Gardenfors� connectionist to conceptual

grounded/sensorimotor is the first leap of faith

objective view � seeing the world as objects (track, co-index, same object as before) seems to be the second leap of faith

third leap of faith � Dennett�s intentional stance (object moving with speed vs determination)

fourth level (Jackendoff) � legal systems in ethics, a person level

�levels� implies that they sit on top of each other � whereas these are more like big domains

realms??? stances???

on what basis should we even declare a level?

is it that they self-discretise???

different purposes: unit of analysis � demarcate certain behaviours, perhaps because of the problems it has to solve

levels of intentionality???

Dennett�s stances:

physical

design � knowing what it�s designed to do let�s you abstract away the gears and springs (alarm clock)

intentional � let�s you talk in terms of goals, beliefs and rational planning processes

Deb: is he justified in separating design from both intentionality (function) from physical? there�s no discontinuity

design as a derived goal (i.e. a subset of intentionality)???

the stances are about (convenient/shortcut) ways of interacting with things

Dennett: Martian that can predict all the atoms of the universe � it would be amazed that we have the predictive power that we do

is Deb discussing what�s useful about, or saying (philosophically) that these are the levels?

 

Cheap apartments syllogism

Hugo will post onto the common sense bulletin board

 

Admin

Deb talk tomorrow at 4pm in Media Lab 054

 

Questions

conceptual vs Smolensky�s sub-symbolic???