analogy, generalisation & interpolation (LONG!)

[Ross Gayler]

One week ago I made a posting that attempted to place analogical inference
into the debate on interpolation and generalisation.  I have received a
number of replies (some direct and some via the mailing list) with sufficient
overlap to justify a mass reply via the mailing list - so here it is.
 
- References to my own work in this area
 
Sadly, there are none.  Designing a connectionist architecture to support
dynamic analogical inference and retrieval is my night job, so I lack the
time and resources to produce papers.  Most of my work has been in scribbled
notes and thought-experiments.  My day job is mundane stuff in the
computer industry, but I am searching for a new job right now and would
love to convert my night job to a day one - so all offers will be considered.
 
- References to other connectionist work on analogical inference
 
The classic is:
 
	Holyoak, K.J., & Thagard, P. (1989). Analogical mapping by constraint
		satisfaction. Cognitive Science, 13(3), 295-355.
 
They produced a program (ACME) that performs analogical inference by a
connectionist constraint satisfaction network.  The program takes two
*symbolic* structures (base and target) and attempts to find a consistent
mapping from base to target to fill some gaps in the target structure.
For example, the base structure might describe a planetary system and the
target structure describe a Rutherford atom.  The program tries to map
objects and predicates from the base into the target.  The fun starts when
the structures are not isomorphic, so there is ambiguity as to what is the
'best' mapping.
 
ACME uses a symbolic program to parse the symbolic inputs and create a
connectionist net to solve the constraint satisfaction problem.  The
net uses a localist representation (each unit corresponds to a partial 
mapping) and the weight between the units encode constraints on
combining the partial mappings.  After the net has been constructed it
is set in action and the 'best' mapping read from the settled state.
 
The Holyoak and Thagard paper is connectionist only in the sense that it
uses a connectionist technique to solve the constraint satisafction problem.
The theoretical problem they attacked was how to incorporate pragmatic
constraints into the mapping.  There was no intent for the specific 
mechanism to be plausible or useful.
 
My aim is to produce a practically useful analogical retrieval mechanism.