Re: computer-go: Evaluating positions

[Don Dailey <drd@xxxxxxxxxxxxxxxxxxxxx>]

Yes,  this is more like it!   

How do you express "hot on the attack" in this language?  :-)

Don



   Date: Thu, 21 Jun 2001 09:50:56 -0400 (EDT)
   From: Tim Klinger <klinger@xxxxxxxxxxxxxxxxx>

   Actually, some of the things you are talking about I address in my
   thesis.  If you are interested in theorizing about human play at some
   formal level then you need an appropriate language to express those
   theories.  Game logic (my variant -- there are others) allows you to do
   this.  It has three modal operators: 

   1. est(i, P) --- Player i has a legal strategy to make P true (establish
   P), but the opponent may have a refutation that establishes not P after.

   2. irr(i, P) --- P is true now and player i has a strategy to maintain its
   truth till the end of the game.

   3. ach(i, P) <-> est(i, irr(i, P)) --- Player i has a strategy to
   establish P irrefutably.

   If you have a given position, call it s, then you can say s \models est(i,
   P), for example, to mean that player i can establish P from position s.

   Using these operators you can formalize strategic theories, including
   theories of life and death, and anything else you can work up.

   For example, to say that a given point p is Black's from a position s,
   i.e. he has a strategy to keep it his no matter how White plays, you can
   write:

   s \models irr(Black, Occ(p, Black))

   Where Occ(p, c) means that point p is occupied by color c.

   It is also possible to say that a given goal P is irrefutable even if
   Black doesn't play directly to defend it, by using notions of
   independence of goals.  There's more in the thesis if anybody's
   interested.

   Tim