Author: Steven Edwards
Date: 05:04:31 03/18/04
Go up one level in this thread
On March 18, 2004 at 05:56:38, Dan Andersson wrote:
> It reminds me a lot of automated theorem provers. And that makes me muse on the
>possibility of retrofitting chess knowledge and patterns of heuristics on one of
>those.
Yes; there is a strongly suggestive resemblance to automated predicate calculus
theorem proving in the plan formation process.
Example:
Given the theorem: f1(x) and f2(x, y) and f3(y, z) => g(x, y, z)
From instances f1(a), f2(a, b), and f3(b, c), the plan generator can
"prove" the plan g(a, b, c).
The idea is that the planner knows the dependencies among the functions and this
helps guide the plan generation.
Even better, the planner can see where a plan is *almost* proven and take steps
to force a proof by inserting new terms among the antecedents; these terms
correspond to subgoals which in turn correspond to move sequences played on the
board. This is the essence of combinatorial play; I also believe that it will
work for positional (micro-tactics) play.
Symbolic's plan library is really a list of such pseudo-theorems. In addition
to expressing predicate relationships, each library entry also contains
estimation functions for the probability of success and the material/positional
gain(loss). The values of these functions for a particular plan instantiation
are multiplied together and this product is used to rank competing plans for
ordering them in the verification process.
One can see the potential for adding machine learning here by adding history
experience coefficients to library entries. Even better, although much harder,
is the prospect of automating plan library entry synthesis itself.
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