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Linguistic Geometry: Adversarial Reasoning for Real Life
Problems
Boris Stilman University of Colorado Denver, USA STILMAN Advanced Strategies, USA
An Abstract Board Game is the following eight-tuple
< X, P, Rp, {ON} , v, Si, St, TR>
X = {xi} is a finite set of points; P = {pi} is a finite set of elements; P=P1 ∪ P2, P1 ∩ P2={ }; Rp(x, y) is a family of binary relations of reachability in X (x ∈ X, y ∈ Y, p ∈ P); y is reachable from x for p; ON(p) = x is a partial function of placement of elements P into X; v> 0 is a real function, v(pi) are the values of elements; Si is a set of initial states of the system, a certain set of formulas {ON(pi)=xi}; St is a set target states of the system (as Si); TR is a set of operators TRANSITION(p, x, y) for transition of the system from one state to another described as follows precondition: (ON(p) = x) ^ Rp(x, y) delete: ON(p) = x add: ON(p) = y
1981
First Hierarchy
of Languages, a predecessor of LG
1981- 1985
a(f6)a(e5)a(e4)a(f3)a(g2)a(h1)
1
2
3
4
5
6
7
8
a b c d e f g h
1981
Language of Trajectories
Z = t(po, a(1)a(2)a(3)a(4)a(5), 5)t(q3, a(6)a(7)a(4), 4)
Experiments with State Space Chart: NO-Search Approach
WB-Intercept and BB-Protect
W-Zone
B-Zone
WB-Protect and BB-Intercept
W-Zone
B-Zone
WB-Protect and BB-Protect
W-Zone
B-Zone
WB-Intercept and BB-Intercept
W-Zone
B-Zone
Start State
DRAW
BlackWins
WhiteWins
DRAW
1996
First Proof of Strategies Optimality
Planning of Maintenance Planning of Power Units (0,0,p)
1(1,0,p)
1(2,0,p)
1(g,0,p)
1
p1
Q11
Q21
(1,1,r) (1,0,r) (2,1,r) (2,0,r) (3,1,r) (3,0,r)
(1,0,q) (2,0,q) 1 1
2 2 2(1,0,q) (2,0,q) (3,0,q)
(0,0,p) (1,0,p) (2,0,p) (g,0,p) 2 2 2 2
(0,1,p) (1,1,p) (2,1,p) 2 2 2
Q12 22
p2
Q Q23
Pres1
P2
resP
3
res
q 2
q1
loss loss
loss loss loss
1997
First Artificial Enemy in LG
1 2 3 4 5 6 7 8
1 2 3 4 1 2 3 4 5
x y
z
n-1 n
n-2
n n-1 n-2
.
.
Computational complexity of the
specific classes of abstract board games is polynomial with respect to the length of the input.
1999
First Proof of Polynomial Run Time
• Linguistic Geometry (LG) is a new type of game theory; • LG replaces search by construction, making the games computationally tractable.
Manuscript finished in 1999
Published in 2000
1999
9/9/99 Denver, CO
www.stilman-strategies.com
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DARPA JFACC Experiments 1999 – 2001
Validation of SEAD Strategies: Expert Opinions
2004-08 DARPA RAID Experiments
Validation of MOUT Strategies: Competition with People
• Chess Masters’ Problem Solving • Search Reduction Techniques • Subclass of Gaming Problems of Polynomial Complexity • No-Search Paradigm for Decision Making: “From Search to Construction” • OR maybe, it is something else . . .
What is Linguistic Geometry? John von Neumann
Mikhail Botvinnik
It appears that LG is a model of human thinking about conflict resolution, a warfighting model at the level of superintelligence . . .