Zeroth Order Theories (ZOT's)

[Jon Awbrey]

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AK = Antti Karttunen
JA = Jon Awbrey

AK: Am I (and other SeqFanaticians) missing something from this thread?

AK: Your previous message on seqfan (headers below) is a bit of the same topic,
    but does it belong to the same thread?  Where I could obtain the other
    messages belonging to those two threads?  (I'm just now starting to
    study "mathematical logic", and its relations to combinatorics are
    very interesting.)  Is this "cactus" language documented anywhere?

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hello antti,

here i was just following a courtesy of copying people
when i reference their works, in this case neil's site:

http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?Anum=000170

but then i thought that the seqfantasians might be amused, too.

the bit on higher order propositions, in particular,
those of type h : (B^2 -> B) -> B, i sent because
of the significance that 2^2^2^2 = 65536 took on
for us around that time.  & the ho, ho, ho joke.

"zeroth order logic" (zol) is just another name for
the propositional calculus or the sentential logic
that comes before "first order logic" (fol), aka
first intens/tional logic, quantificational logic,
or predicate calculus, depending on who you talk to.

the line of work that i have been doing derives from
the ideas of c.s. peirce (1839-1914), who developed
a couple of systems of "logical graphs", actually,
two variant interpretations of the same abstract
structures, called "entitative" and "existential"
graphs.  he organized his system into "alpha",
"beta", and "gamma" layers, roughly equivalent
to our propositional, quantificational, and
modal levels of logic today.

on the more contemporary scene, peirce's entitative interpretation
of logical graphs was revived and extended by george spencer brown
in his book 'laws of form', while the existential interpretation
has flourished in the development of "conceptual graphs" by
john f sowa and a community of growing multitudes.

a passel of links:

http://members.door.net/arisbe/
http://www.enolagaia.com/GSB.html
http://www.cs.uah.edu/~delugach/CG/
http://www.jfsowa.com/
http://www.jfsowa.com/cg/
http://www.jfsowa.com/peirce/ms514w.htm
http://users.bestweb.net/~sowa/
http://users.bestweb.net/~sowa/peirce/ms514.htm

i have mostly focused on "alpha" (prop calc or zol) --
though the "func conception of quant logic" thread was
a beginning try at saying how the same line of thought
might be extended to 1st, 2nd, & higher order logics --
and i devised a particular graph & string syntax that
is based on a species of cacti, officially described as
the "reflective extension of logical graphs" (ref log),
but more lately just referred to as "cactus language".

it turns out that one can do many interesting things
with prop calc if one has an efficient enough syntax
and a powerful enough interpreter for it, even using
it as a very minimal sort of declarative programming
language, hence, the current thread was directed to
applying "zeroth order theories" (zot's) as brands
of "zeroth order programs" (zop's) to a set of old
constraint satisfaction and knowledge rep examples.

more recent expositions of the cactus language have been directed
toward what some people call "ontology engineering" -- it sounds
so much cooler than "taxonomy" -- and so these are found in the
ieee standard upper ontology working group discussion archives.

general list info is here:

http://suo.ieee.org/

specific threads of recent vintage are appended below.

thank you for your interest,
and best wishes for your
studies of math logic,

jon awbrey

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Zeroth Order Theories (ZOT's)

http://suo.ieee.org/ontology/msg03680.html
http://suo.ieee.org/ontology/msg03681.html
http://suo.ieee.org/ontology/msg03682.html
http://suo.ieee.org/ontology/msg03683.html
http://suo.ieee.org/ontology/msg03687.html  <<<--<<< Many Old Links Here
http://suo.ieee.org/ontology/msg03689.html
http://suo.ieee.org/ontology/msg03691.html
http://suo.ieee.org/ontology/msg03693.html
http://suo.ieee.org/ontology/msg03695.html
http://suo.ieee.org/ontology/msg03696.html

http://suo.ieee.org/ontology/msg03701.html
http://suo.ieee.org/ontology/msg03702.html
http://suo.ieee.org/ontology/msg03703.html
http://suo.ieee.org/ontology/msg03706.html
http://suo.ieee.org/ontology/msg03707.html
http://suo.ieee.org/ontology/msg03708.html
http://suo.ieee.org/ontology/msg03712.html
http://suo.ieee.org/ontology/msg03715.html
http://suo.ieee.org/ontology/msg03716.html  <<<---<<< Where You Came In
http://suo.ieee.org/ontology/msg03717.html
http://suo.ieee.org/ontology/msg03718.html

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Toward A Functional Conception Of Quantificational Logic

http://suo.ieee.org/ontology/msg03562.html
http://suo.ieee.org/ontology/msg03563.html
http://suo.ieee.org/ontology/msg03577.html
http://suo.ieee.org/ontology/msg03578.html
http://suo.ieee.org/ontology/msg03579.html <<<---<<< HO, HO, HO
http://suo.ieee.org/ontology/msg03580.html
http://suo.ieee.org/ontology/msg03581.html
http://suo.ieee.org/ontology/msg03582.html
http://suo.ieee.org/ontology/msg03583.html

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