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In Figure 10, each K-node K (K = K1 or K2), contains 2 Tic-Tac-To board con-
figurations,
K
K
.
K
F
denotes the Tic-Tac-To board configuration
before
the move during the formation of K-node K and
K
F
F
and
F
denotes the Tic-Tac-To
board configuration
after
the move during the formation of K-node K. Note, for two
K-nodes K1 and K2 to be connected such that K1 is the predecessor of K2, it must be
that
K
1
K
2
F
=
F
. That is, the resulting TTT board in the predecessor K-node K1
must be the starting board configuration in the successor K-node K2. This is the crite-
rion that qualifies events
A
B
K
e
to be associated by causality. Based on the
above discussion, we now describe a methodology according to which an AKL is
formed and the computer learns, in the context of the game of Tic-Tac-To.
K
1
2
e
and
Methodology.
Without loss of generality, we assume that the computer makes the
first move upon starting the game. At this point, without having any strategic knowl-
edge, the computer places a 'C' mark on the TTT board and the 1
st
K-node K11 of the
1
st
K-line L1, is formed. The event of K11 is
K
11
K
11
K
11
e
:
F
→
F
B
A
K
11
K
11
F
is the TTT board containing
the 'C' mark placed by the computer-player. Then, the human player plays and the
system forms a new K-node, K12. The event of K12 is
F
=∅
where
, the empty TTT board, and
K
12
K
12
K
12
e
:
F
→
F
B
A
K
12
K
11
K
12
F
is the TTT board configuration resulting from
the move of the human player. For the remaining of the 1
st
K-line, the game continues
in this fashion (i.e., the computer makes a legal move without any kind of strategic
knowledge, and the human responds with another move) until one of the two players
wins (most likely, the human in this case) or the game comes to a tie. At this point, we
record also the number of moves for this game
. Then, the 2
nd
game begins and a new
K-line, L2, starts forming. Again, the computer plays first and the 1
st
K-node K21 is
formed, with event
F
=
F
where
and
B
A
K
21
K
21
e
:
∅→
F
.
A
Next, the human moves and K-node K22 is formed, with event
K
22
K
22
K
22
e
:
F
→
F
.
B
A
K
21
K
22
F
=
F
Recall,
. Next, it is the computer's turn to move. Note, since there is
now previous knowledge available (from K-line L1), the computer investigates if that
knowledge can be utilized to help it in making its next move. In doing so the computer
looks if there is already a K-node K, such
A
B
K
K
22
FF
=
and such that the K-line L
containing that K-node K leads to (i) a win for the computer, or (in the absence of a
computer-winning K-line) (ii) to a tie, or (in the absence of (i) and (ii)) (iii) L is the
B
B
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