Re: AND/OR Search Spaces in Graphical Models

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

Rich, CG List,

There are inherent conceptual and structural inefficiencies in the use
of AND/OR graphs and the associated search spaces, like those implicit
in Peirce's alpha structures.  Those inefficiencies can be alleviated
to a considerable degree by moving on to the generalization of trees
that graph theorists call "cacti".

When I began my efforts to implement Peirce's logical graphs on
the computer back in the mid 70's -- does anyone remember SNOBOL? --
I quickly ran into the computational side of these inefficiencies.
By the mid 80's I had learned enough about cacti to have programmed
a few prototype logical utilities that implemented generalizations
of Peirce's basic ideas.

Once you take the step into the cactus patch, many collateral
advantages of using cactoid structures quickly become apparent.

Some of this work is documented -- or in the process of being documented --
on assorted pages of a wiki-based directory, for instance, these pages:

http://www.mywikibiz.com/Directory:Jon_Awbrey/Projects/Cactus_Language
http://www.mywikibiz.com/Directory:Jon_Awbrey/Papers/Futures_Of_Logical_Graphs
http://www.mywikibiz.com/Directory:Jon_Awbrey/Projects/Theme_One_Program

Incidentally, this site is open to anyone and implements a very nice variation
on the usual wiki protocol, one that allows both collaborative work (in the main
space on the discussion pages) while preserving the proprieties of "owned" work
by individual authors (in the labelled directory pages).  So the talk pages at
that site are available for extended discussion if anyone is interested.

Well-Seasoned Cheers and Happy New Years,

Jon Awbrey

CC: Arisbe List, Inquiry List

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
inquiry e-lab: http://stderr.org/pipermail/inquiry/
mwb: http://www.mywikibiz.com/Directory:Jon_Awbrey
mathweb: http://www.mathweb.org/wiki/User:Jon_Awbrey
getwiki: http://www.getwiki.net/-UserTalk:Jon_Awbrey
zhongwen wp: http://zh.wikipedia.org/wiki/User:Jon_Awbrey
ontolog: http://ontolog.cim3.net/cgi-bin/wiki.pl?JonAwbrey
http://www.altheim.com/ceryle/wiki/Wiki.jsp?page=JonAwbrey
wp review: http://wikipediareview.com/index.php?showuser=398
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o