Interesting quote from AI book

[RE01 Rice Brian T. EM2]

> lets' assume that it takes N graphs of arrows to describe all of the
> aspects of an equation embodied by a written statement.  these N graphs
> wouldn't apply to just that equation, though.
> 
> example:
> 		n=m+1
> 
> there would be an arrow between the atoms for 'n' and 'm+1' that would be
> part of the graph linked to '=' (think of '=' as a relation, and as a set
> of arrows).
> there would be an atom for 'm+1' would be an arrow in the '+' graph
> linking the atoms for 'm' and '1'.
> 'n', 'm', and '1' would be arrows (selectors) from sets of atoms: 'n' and
> 'm' would be part of a particular user context vocabulary (called an
> ontology), and '1' would be an arrow from the set of natural or integer or
> whatever kinds of numbers (again, in a graph).
> 
(parenthetic:  i'm really happy that my ideas are coming across well, now,
and i intend to continue my efforts in that direction.  this discussion i'm
intending to use to provide examples for the paper, along with diagrams;
this process is already underway, but difficult.)

to continue,
there's more to this example than '=' and '+', as is obvious: this is where
the concept of an ontology (and the resulting relativism) comes into play.
we'd like to specify the set of vocabulary that is defined within a given
context, and use this to shift contexts computably and preserve the meaning
of the vocabulary.

basically, i'm looking at mappings (think of arrows from domain to range
collected into a graph) from those original arrows to collections of nodes.
these collections of nodes would constitute 'wiring diagrams' for building
contexts, and could be manipulated for that purpose.  these collections are
the ontologies, and they determine what 'n', 'm', and the purpose of the
equation and addition arrows themselves in the given context.  i'd like to
use an iteration scheme as a proof of computability for my N-graph problem
for a given situation.

more concepts are due in the paper, and it will be re-structured again
(while preserving the core ideas and arguments) within a week, guaranteed.
also diagrams will replace text for the conference-ready versions that
address the sorts of aspects in which each is interested.

oh, yes!  in two weeks, i will be in Seattle again, for six weeks.  that
means full throttle research rates, and much more development.