ONT Re: Zeroth Order Theories (ZOT's)
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JA = Jon Awbrey
SR = Seth Russell
JA: The programme that I composed on an old 286 in 1989, and that
I've not up-scaled a jot, a line, or a tilde in all that time --
well, it still serves me well to amplify my powers of logical
acuteness, and to extend my range of analytic intuition many
octaves of variables beyond what I can accomplish on my own.
SR: A couple examples of actual input and corresponding output might
help us understand the abilities of this program better. Huh?
Might just do.
Here's a hint of where we're off to, just for starters:
¤~~~~~~~~~¤~~~~~~~~~¤~ELECTATIO~¤~~~~~~~~~¤~~~~~~~~~¤
Extensions Of Logical Graphs
01. http://www.virtual-earth.de/CG/cg-list/msg03351.html
02. http://www.virtual-earth.de/CG/cg-list/msg03352.html
03. http://www.virtual-earth.de/CG/cg-list/msg03353.html
04. http://www.virtual-earth.de/CG/cg-list/msg03354.html
05. http://www.virtual-earth.de/CG/cg-list/msg03376.html
06. http://www.virtual-earth.de/CG/cg-list/msg03379.html
07. http://www.virtual-earth.de/CG/cg-list/msg03381.html
An earlier exposition.
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Differential Analytic Turing Automata (DATA)
http://suo.ieee.org/email/msg03004.html
http://suo.ieee.org/email/msg03026.html
Clone Colonies
http://suo.ieee.org/ontology/msg00596.html
http://suo.ieee.org/ontology/msg00618.html
Brief Automata
By way of providing a simple illustration of Cook's Theorem,
that "Propositional Satisfiability is NP-Complete", here is
an exposition of one way to translate Turing Machine set-ups
into propositional expressions, employing the Ref Log Syntax
for Prop Calc that I described in a couple of earlier notes:
Notation:
Stilt(k) = Space and Time Limited Turing Machine,
with k units of space and k units of time.
Stunt(k) = Space and Time Limited Turing Machine,
for computing the parity of a bit string,
with Number of Tape cells of input equal to k.
I will follow the pattern of the discussion in the book of
Herbert Wilf, 'Algorithms & Complexity' (1986), pages 188-201,
but translate into Ref Log, which is more efficient with respect
to the number of propositional clauses that are required.
Parity Machine
| 1/1/+1
| ------->
| /\ / \ /\
| 0/0/+1 ^ 0 1 ^ 0/0/+1
| \/|\ /|\/
| | <------- |
| #/#/-1 | 1/1/+1 | #/#/-1
| | |
| v v
| # *
o-------o--------o-------------o---------o------------o
| State | Symbol | Next Symbol | Ratchet | Next State |
| Q | S | S' | dR | Q' |
o-------o--------o-------------o---------o------------o
| 0 | 0 | 0 | +1 | 0 |
| 0 | 1 | 1 | +1 | 1 |
| 0 | # | # | -1 | # |
| 1 | 0 | 0 | +1 | 1 |
| 1 | 1 | 1 | +1 | 0 |
| 1 | # | # | -1 | * |
o-------o--------o-------------o---------o------------o
The TM has a "finite automaton" (FA) as its component.
Let us refer to this particular FA by the name of "M".
The "tape-head" (that is, the "read-unit") will be called "H".
The "registers" are also called "tape-cells" or "tape-squares".
In order to consider how the finitely "stilted" rendition of this TM
can be translated into the form of a purely propositional description,
one now fixes k and limits the discussion to talking about a Stilt(k),
which is really not a true TM anymore but a finite automaton in disguise.
In this example, for the sake of a minimal illustration, we choose k = 2,
and discuss Stunt(2). Since the zeroth tape cell and the last tape cell
are occupied with bof and eof marks "#", this amounts to only one digit
of significant computation.
To translate Stunt(2) into propositional form we use
the following collection of propositional variables:
For the "Present State Function" QF : P -> Q,
{p0_q#, p0_q*, p0_q0, p0_q1,
p1_q#, p1_q*, p1_q0, p1_q1,
p2_q#, p2_q*, p2_q0, p2_q1,
p3_q#, p3_q*, p3_q0, p3_q1}
The propositional expression of the form "pi_qj" says:
| At the point-in-time p_i,
| the finite machine M is in the state q_j.
For the "Present Register Function" RF : P -> R,
{p0_r0, p0_r1, p0_r2, p0_r3,
p1_r0, p1_r1, p1_r2, p1_r3,
p2_r0, p2_r1, p2_r2, p2_r3,
p3_r0, p3_r1, p3_r2, p3_r3}
The propositional expression of the form "pi_rj" says:
| At the point-in-time p_i,
| the tape-head H is on the tape-cell r_j.
For the "Present Symbol Function" SF : P -> (R -> S),
{p0_r0_s#, p0_r0_s*, p0_r0_s0, p0_r0_s1,
p0_r1_s#, p0_r1_s*, p0_r1_s0, p0_r1_s1,
p0_r2_s#, p0_r2_s*, p0_r2_s0, p0_r2_s1,
p0_r3_s#, p0_r3_s*, p0_r3_s0, p0_r3_s1,
p1_r0_s#, p1_r0_s*, p1_r0_s0, p1_r0_s1,
p1_r1_s#, p1_r1_s*, p1_r1_s0, p1_r1_s1,
p1_r2_s#, p1_r2_s*, p1_r2_s0, p1_r2_s1,
p1_r3_s#, p1_r3_s*, p1_r3_s0, p1_r3_s1,
p2_r0_s#, p2_r0_s*, p2_r0_s0, p2_r0_s1,
p2_r1_s#, p2_r1_s*, p2_r1_s0, p2_r1_s1,
p2_r2_s#, p2_r2_s*, p2_r2_s0, p2_r2_s1,
p2_r3_s#, p2_r3_s*, p2_r3_s0, p2_r3_s1,
p3_r0_s#, p3_r0_s*, p3_r0_s0, p3_r0_s1,
p3_r1_s#, p3_r1_s*, p3_r1_s0, p3_r1_s1,
p3_r2_s#, p3_r2_s*, p3_r2_s0, p3_r2_s1,
p3_r3_s#, p3_r3_s*, p3_r3_s0, p3_r3_s1}
The propositional expression of the form "pi_rj_sk" says:
| At the point-in-time p_i,
| the tape-cell r_j bears the mark s_k.
¤~~~~~~~~~¤~~~~~~~~~¤~~INPUTS~~¤~~~~~~~~~¤~~~~~~~~~¤
So with all due further ado,
here are the Initial Conditions
for the two possible inputs to the
Ref Log redaction of this Parity TM:
¤~~~~~~~~~¤~~~~~~~~~¤~INPUT~0~¤~~~~~~~~~¤~~~~~~~~~¤
Initial Conditions:
p0_q0
p0_r1
p0_r0_s#
p0_r1_s0
p0_r2_s#
The Initial Conditions are given by a logical conjunction
that is composed of 5 basic expressions, altogether stating:
| At the point-in-time p_0, M is in the state q_0, and
| At the point-in-time p_0, H is on the cell r_1, and
| At the point-in-time p_0, cell r_0 bears the mark "#", and
| At the point-in-time p_0, cell r_1 bears the mark "0", and
| At the point-in-time p_0, cell r_2 bears the mark "#".
¤~~~~~~~~~¤~~~~~~~~~¤~INPUT~1~¤~~~~~~~~~¤~~~~~~~~~¤
Initial Conditions:
p0_q0
p0_r1
p0_r0_s#
p0_r1_s1
p0_r2_s#
The Initial Conditions are given by a logical conjunction
that is composed of 5 basic expressions, altogether stating:
| At the point-in-time p_0, M is in the state q_0, and
| At the point-in-time p_0, H is on the cell r_1, and
| At the point-in-time p_0, cell r_0 bears the mark "#", and
| At the point-in-time p_0, cell r_1 bears the mark "1", and
| At the point-in-time p_0, cell r_2 bears the mark "#".
¤~~~~~~~~~¤~~~~~~~~~¤~PROGRAM~¤~~~~~~~~~¤~~~~~~~~~¤
And here, yet again, just to store it nearby,
is the logical rendition of the TM's program:
Mediate Conditions:
( p0_q# ( p1_q# ))
( p0_q* ( p1_q* ))
( p1_q# ( p2_q# ))
( p1_q* ( p2_q* ))
Terminal Conditions:
(( p2_q# )( p2_q* ))
State Partition:
(( p0_q0 ),( p0_q1 ),( p0_q# ),( p0_q* ))
(( p1_q0 ),( p1_q1 ),( p1_q# ),( p1_q* ))
(( p2_q0 ),( p2_q1 ),( p2_q# ),( p2_q* ))
Register Partition:
(( p0_r0 ),( p0_r1 ),( p0_r2 ))
(( p1_r0 ),( p1_r1 ),( p1_r2 ))
(( p2_r0 ),( p2_r1 ),( p2_r2 ))
Symbol Partition:
(( p0_r0_s0 ),( p0_r0_s1 ),( p0_r0_s# ))
(( p0_r1_s0 ),( p0_r1_s1 ),( p0_r1_s# ))
(( p0_r2_s0 ),( p0_r2_s1 ),( p0_r2_s# ))
(( p1_r0_s0 ),( p1_r0_s1 ),( p1_r0_s# ))
(( p1_r1_s0 ),( p1_r1_s1 ),( p1_r1_s# ))
(( p1_r2_s0 ),( p1_r2_s1 ),( p1_r2_s# ))
(( p2_r0_s0 ),( p2_r0_s1 ),( p2_r0_s# ))
(( p2_r1_s0 ),( p2_r1_s1 ),( p2_r1_s# ))
(( p2_r2_s0 ),( p2_r2_s1 ),( p2_r2_s# ))
Interaction Conditions:
(( p0_r0 ) p0_r0_s0 ( p1_r0_s0 ))
(( p0_r0 ) p0_r0_s1 ( p1_r0_s1 ))
(( p0_r0 ) p0_r0_s# ( p1_r0_s# ))
(( p0_r1 ) p0_r1_s0 ( p1_r1_s0 ))
(( p0_r1 ) p0_r1_s1 ( p1_r1_s1 ))
(( p0_r1 ) p0_r1_s# ( p1_r1_s# ))
(( p0_r2 ) p0_r2_s0 ( p1_r2_s0 ))
(( p0_r2 ) p0_r2_s1 ( p1_r2_s1 ))
(( p0_r2 ) p0_r2_s# ( p1_r2_s# ))
(( p1_r0 ) p1_r0_s0 ( p2_r0_s0 ))
(( p1_r0 ) p1_r0_s1 ( p2_r0_s1 ))
(( p1_r0 ) p1_r0_s# ( p2_r0_s# ))
(( p1_r1 ) p1_r1_s0 ( p2_r1_s0 ))
(( p1_r1 ) p1_r1_s1 ( p2_r1_s1 ))
(( p1_r1 ) p1_r1_s# ( p2_r1_s# ))
(( p1_r2 ) p1_r2_s0 ( p2_r2_s0 ))
(( p1_r2 ) p1_r2_s1 ( p2_r2_s1 ))
(( p1_r2 ) p1_r2_s# ( p2_r2_s# ))
Transition Relations:
( p0_q0 p0_r1 p0_r1_s0 ( p1_q0 p1_r2 p1_r1_s0 ))
( p0_q0 p0_r1 p0_r1_s1 ( p1_q1 p1_r2 p1_r1_s1 ))
( p0_q0 p0_r1 p0_r1_s# ( p1_q# p1_r0 p1_r1_s# ))
( p0_q0 p0_r2 p0_r2_s# ( p1_q# p1_r1 p1_r2_s# ))
( p0_q1 p0_r1 p0_r1_s0 ( p1_q1 p1_r2 p1_r1_s0 ))
( p0_q1 p0_r1 p0_r1_s1 ( p1_q0 p1_r2 p1_r1_s1 ))
( p0_q1 p0_r1 p0_r1_s# ( p1_q* p1_r0 p1_r1_s# ))
( p0_q1 p0_r2 p0_r2_s# ( p1_q* p1_r1 p1_r2_s# ))
( p1_q0 p1_r1 p1_r1_s0 ( p2_q0 p2_r2 p2_r1_s0 ))
( p1_q0 p1_r1 p1_r1_s1 ( p2_q1 p2_r2 p2_r1_s1 ))
( p1_q0 p1_r1 p1_r1_s# ( p2_q# p2_r0 p2_r1_s# ))
( p1_q0 p1_r2 p1_r2_s# ( p2_q# p2_r1 p2_r2_s# ))
( p1_q1 p1_r1 p1_r1_s0 ( p2_q1 p2_r2 p2_r1_s0 ))
( p1_q1 p1_r1 p1_r1_s1 ( p2_q0 p2_r2 p2_r1_s1 ))
( p1_q1 p1_r1 p1_r1_s# ( p2_q* p2_r0 p2_r1_s# ))
( p1_q1 p1_r2 p1_r2_s# ( p2_q* p2_r1 p2_r2_s# ))
¤~~~~~~~~~¤~~~~~~~~~¤~INTERPRETATION~¤~~~~~~~~~¤~~~~~~~~~¤
Interpretation of the Propositional Program:
Mediate Conditions:
( p0_q# ( p1_q# ))
( p0_q* ( p1_q* ))
( p1_q# ( p2_q# ))
( p1_q* ( p2_q* ))
In Ref Log, an expression of the form "( X ( Y ))"
expresses an implication or an if-then proposition:
"Not X without Y", "If X then Y", "X => Y", etc.
A text string expression of the form "( X ( Y ))"
parses to a graphical data-structure of the form:
X Y
o---o
|
@
All together, these Mediate Conditions state:
| If at p_0 M is in state q_#, then at p_1 M is in state q_#, and
| If at p_0 M is in state q_*, then at p_1 M is in state q_*, and
| If at p_1 M is in state q_#, then at p_2 M is in state q_#, and
| If at p_1 M is in state q_*, then at p_2 M is in state q_*.
Terminal Conditions:
(( p2_q# )( p2_q* ))
In Ref Log, an expression of the form "(( X )( Y ))"
expresses a disjunction "X or Y" and it parses into:
X Y
o o
\ /
o
|
@
In effect, the Terminal Conditions state:
| At p_2, M is in state q_#, or
| At p_2, M is in state q_*.
State Partition:
(( p0_q0 ),( p0_q1 ),( p0_q# ),( p0_q* ))
(( p1_q0 ),( p1_q1 ),( p1_q# ),( p1_q* ))
(( p2_q0 ),( p2_q1 ),( p2_q# ),( p2_q* ))
In Ref Log, an expression of the form "(( e_1 ),( e_2 ),( ... ),( e_k ))"
expresses the fact that "exactly one of the e_j is true, for j = 1 to k".
Expressions of this form are called "universal partition" expressions, and
they parse into a type of graph called a "painted and rooted cactus" (PARC):
e_1 e_2 ... e_k
o o o
| | |
o-----o--- ... ---o
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
@
The State Partition expresses the conditions that:
| At each of the points-in-time p_i, for i = 0 to 2,
| M can be in exactly one state q_j, for j in the set {0, 1, #, *}.
Register Partition:
(( p0_r0 ),( p0_r1 ),( p0_r2 ))
(( p1_r0 ),( p1_r1 ),( p1_r2 ))
(( p2_r0 ),( p2_r1 ),( p2_r2 ))
The Register Partition expresses the conditions that:
| At each of the points-in-time p_i, for i = 0 to 2,
| H can be on exactly one cell r_j, for j = 0 to 2.
Symbol Partition:
(( p0_r0_s0 ),( p0_r0_s1 ),( p0_r0_s# ))
(( p0_r1_s0 ),( p0_r1_s1 ),( p0_r1_s# ))
(( p0_r2_s0 ),( p0_r2_s1 ),( p0_r2_s# ))
(( p1_r0_s0 ),( p1_r0_s1 ),( p1_r0_s# ))
(( p1_r1_s0 ),( p1_r1_s1 ),( p1_r1_s# ))
(( p1_r2_s0 ),( p1_r2_s1 ),( p1_r2_s# ))
(( p2_r0_s0 ),( p2_r0_s1 ),( p2_r0_s# ))
(( p2_r1_s0 ),( p2_r1_s1 ),( p2_r1_s# ))
(( p2_r2_s0 ),( p2_r2_s1 ),( p2_r2_s# ))
The Symbol Partition expresses the conditions that:
| At each of the points-in-time p_i, for i in {0, 1, 2},
| in each of the tape-registers r_j, for j in {0, 1, 2},
| there can be exactly one sign s_k, for k in {0, 1, #}.
Interaction Conditions:
(( p0_r0 ) p0_r0_s0 ( p1_r0_s0 ))
(( p0_r0 ) p0_r0_s1 ( p1_r0_s1 ))
(( p0_r0 ) p0_r0_s# ( p1_r0_s# ))
(( p0_r1 ) p0_r1_s0 ( p1_r1_s0 ))
(( p0_r1 ) p0_r1_s1 ( p1_r1_s1 ))
(( p0_r1 ) p0_r1_s# ( p1_r1_s# ))
(( p0_r2 ) p0_r2_s0 ( p1_r2_s0 ))
(( p0_r2 ) p0_r2_s1 ( p1_r2_s1 ))
(( p0_r2 ) p0_r2_s# ( p1_r2_s# ))
(( p1_r0 ) p1_r0_s0 ( p2_r0_s0 ))
(( p1_r0 ) p1_r0_s1 ( p2_r0_s1 ))
(( p1_r0 ) p1_r0_s# ( p2_r0_s# ))
(( p1_r1 ) p1_r1_s0 ( p2_r1_s0 ))
(( p1_r1 ) p1_r1_s1 ( p2_r1_s1 ))
(( p1_r1 ) p1_r1_s# ( p2_r1_s# ))
(( p1_r2 ) p1_r2_s0 ( p2_r2_s0 ))
(( p1_r2 ) p1_r2_s1 ( p2_r2_s1 ))
(( p1_r2 ) p1_r2_s# ( p2_r2_s# ))
In briefest terms, the Interaction Conditions merely express
the circumstance that the sign in a tape-cell cannot change
between two points-in-time unless the tape-head is over the
cell in question at the initial one of those points-in-time.
All that we have to do is to see how they manage to say this.
In Ref Log, an expression of the following form:
"(( p<i>_r<j> ) p<i>_r<j>_s<k> ( p<i+1>_r<j>_s<k> ))",
and which parses as the graph:
p<i>_r<j> o o p<i+1>_r<j>_s<k>
\ /
p<i>_r<j>_s<k> o
|
@
can be read in the form of the following implication:
| If
| at the point-in-time p<i>, the tape-cell r<j> bears the mark s<k>,
| but it is not the case that
| at the point-in-time p<i>, the tape-head is on the tape-cell r<j>.
| then
| at the point-in-time p<i+1>, the tape-cell r<j> bears the mark s<k>.
Folks among us of a certain age and a peculiar manner of acculturation will
recognize these as the "Frame Conditions" for the change of state of the TM.
Transition Relations:
( p0_q0 p0_r1 p0_r1_s0 ( p1_q0 p1_r2 p1_r1_s0 ))
( p0_q0 p0_r1 p0_r1_s1 ( p1_q1 p1_r2 p1_r1_s1 ))
( p0_q0 p0_r1 p0_r1_s# ( p1_q# p1_r0 p1_r1_s# ))
( p0_q0 p0_r2 p0_r2_s# ( p1_q# p1_r1 p1_r2_s# ))
( p0_q1 p0_r1 p0_r1_s0 ( p1_q1 p1_r2 p1_r1_s0 ))
( p0_q1 p0_r1 p0_r1_s1 ( p1_q0 p1_r2 p1_r1_s1 ))
( p0_q1 p0_r1 p0_r1_s# ( p1_q* p1_r0 p1_r1_s# ))
( p0_q1 p0_r2 p0_r2_s# ( p1_q* p1_r1 p1_r2_s# ))
( p1_q0 p1_r1 p1_r1_s0 ( p2_q0 p2_r2 p2_r1_s0 ))
( p1_q0 p1_r1 p1_r1_s1 ( p2_q1 p2_r2 p2_r1_s1 ))
( p1_q0 p1_r1 p1_r1_s# ( p2_q# p2_r0 p2_r1_s# ))
( p1_q0 p1_r2 p1_r2_s# ( p2_q# p2_r1 p2_r2_s# ))
( p1_q1 p1_r1 p1_r1_s0 ( p2_q1 p2_r2 p2_r1_s0 ))
( p1_q1 p1_r1 p1_r1_s1 ( p2_q0 p2_r2 p2_r1_s1 ))
( p1_q1 p1_r1 p1_r1_s# ( p2_q* p2_r0 p2_r1_s# ))
( p1_q1 p1_r2 p1_r2_s# ( p2_q* p2_r1 p2_r2_s# ))
The Transition Conditions merely serve to express,
by means of 16 complex implication expressions,
the data of the TM table that was given above.
¤~~~~~~~~~¤~~~~~~~~~¤~~OUTPUTS~~¤~~~~~~~~~¤~~~~~~~~~¤
And here are the outputs of the computation,
as emulated by its propositional rendition,
and as actually generated within that form
of transmogrification by the program that
I wrote for finding all of the satisfying
interpretations (truth-value assignments)
of propositional expressions in Ref Log:
¤~~~~~~~~~¤~~~~~~~~~¤~OUTPUT~0~¤~~~~~~~~~¤~~~~~~~~~¤
Output Conditions:
p0_q0
p0_r1
p0_r0_s#
p0_r1_s0
p0_r2_s#
p1_q0
p1_r2
p1_r2_s#
p1_r0_s#
p1_r1_s0
p2_q#
p2_r1
p2_r0_s#
p2_r1_s0
p2_r2_s#
The Output Conditions amount to the sole satisfying interpretation,
that is, a "sequence of truth-value assignments" (SOTVA) that make
the entire proposition come out true, and they state the following:
| At the point-in-time p_0, M is in the state q_0, and
| At the point-in-time p_0, H is on the cell r_1, and
| At the point-in-time p_0, cell r_0 bears the mark "#", and
| At the point-in-time p_0, cell r_1 bears the mark "0", and
| At the point-in-time p_0, cell r_2 bears the mark "#", and
|
| At the point-in-time p_1, M is in the state q_0, and
| At the point-in-time p_1, H is on the cell r_2, and
| At the point-in-time p_1, cell r_0 bears the mark "#", and
| At the point-in-time p_1, cell r_1 bears the mark "0", and
| At the point-in-time p_1, cell r_2 bears the mark "#", and
|
| At the point-in-time p_2, M is in the state q_#, and
| At the point-in-time p_2, H is on the cell r_1, and
| At the point-in-time p_2, cell r_0 bears the mark "#", and
| At the point-in-time p_2, cell r_1 bears the mark "0", and
| At the point-in-time p_2, cell r_2 bears the mark "#".
In brief, the output for our sake being the symbol that rests
under the tape-head H when the machine M gets to a rest state,
we are now amazed by the remarkable result that Parity(0) = 0.
¤~~~~~~~~~¤~~~~~~~~~¤~OUTPUT~1~¤~~~~~~~~~¤~~~~~~~~~¤
Output Conditions:
p0_q0
p0_r1
p0_r0_s#
p0_r1_s1
p0_r2_s#
p1_q1
p1_r2
p1_r2_s#
p1_r0_s#
p1_r1_s1
p2_q*
p2_r1
p2_r0_s#
p2_r1_s1
p2_r2_s#
The Output Conditions amount to the sole satisfying interpretation,
that is, a "sequence of truth-value assignments" (SOTVA) that make
the entire proposition come out true, and they state the following:
| At the point-in-time p_0, M is in the state q_0, and
| At the point-in-time p_0, H is on the cell r_1, and
| At the point-in-time p_0, cell r_0 bears the mark "#", and
| At the point-in-time p_0, cell r_1 bears the mark "1", and
| At the point-in-time p_0, cell r_2 bears the mark "#", and
|
| At the point-in-time p_1, M is in the state q_1, and
| At the point-in-time p_1, H is on the cell r_2, and
| At the point-in-time p_1, cell r_0 bears the mark "#", and
| At the point-in-time p_1, cell r_1 bears the mark "1", and
| At the point-in-time p_1, cell r_2 bears the mark "#", and
|
| At the point-in-time p_2, M is in the state q_*, and
| At the point-in-time p_2, H is on the cell r_1, and
| At the point-in-time p_2, cell r_0 bears the mark "#", and
| At the point-in-time p_2, cell r_1 bears the mark "1", and
| At the point-in-time p_2, cell r_2 bears the mark "#".
In brief, the output for our sake being the symbol that rests
under the tape-head H when the machine M gets to a rest state,
we are now amazed by the remarkable result that Parity(1) = 1.
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Sequential Interactions Generating Hypotheses (SIGH's)
01. http://suo.ieee.org/email/msg02607.html
02. http://suo.ieee.org/email/msg02608.html
03. http://suo.ieee.org/email/msg03183.html
A piece of a real live honest-to-funded-research
dataset represented as a constrained disjunction
in Cactus Language.
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What Language To Use?
Sowa's Top Level Categories
Sowa's TLC In And Out Of KIF
Sowa's TLC In Cactus Language
01. http://suo.ieee.org/email/msg01949.html
02. http://suo.ieee.org/email/msg01956.html
03. http://suo.ieee.org/email/msg01966.html
04. http://suo.ieee.org/email/msg02463.html
05. http://suo.ieee.org/email/msg02466.html
06. http://suo.ieee.org/ontology/msg00048.html
07. http://suo.ieee.org/ontology/msg00051.html
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Zeroth Order Logic (ZOL)
01. http://suo.ieee.org/email/msg01246.html
02. http://suo.ieee.org/email/msg01406.html
03. http://suo.ieee.org/email/msg01546.html
04. http://suo.ieee.org/email/msg01561.html
05. http://suo.ieee.org/email/msg01670.html
06. http://suo.ieee.org/email/msg01739.html
07. http://suo.ieee.org/email/msg01966.html
08. http://suo.ieee.org/email/msg01985.html
09. http://suo.ieee.org/email/msg01988.html
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Nuf Fer Now ...
Jon Awbrey
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