Mathematical definition of “unconditionally alive group”

[tiger314]

I don't get the need for a definition of "absolutely unconditionally alive". E.g.: a solid two-eyed group is unconditionally alive, but that's not a rule. That's a consequence of the rules.

If there were no such groups, there would be no go.

You do not need such a definition to play the game, but people with a theoretical or mathematical bent like to come up with them.

Pretty much the only moment when definitions of this sort start becoming relevant to the game is when there is a dispute about group status under Japanese rules. Since a playout cannot be used to settle the dispute, it is nessesary to distinguish live groups through a rule of some sort.

[Bill Spight]

I don't get the need for a definition of "absolutely unconditionally alive". E.g.: a solid two-eyed group is unconditionally alive, but that's not a rule. That's a consequence of the rules.

If there were no such groups, there would be no go.

You do not need such a definition to play the game, but people with a theoretical or mathematical bent like to come up with them.

Pretty much the only moment when definitions of this sort start becoming relevant to the game is when there is a dispute about group status under Japanese rules. Since a playout cannot be used to settle the dispute, it is nessesary to distinguish live groups through a rule of some sort.

The Japanese 1989 rules settle life and death disputes, of which I am unaware of any in pro play in modern times, by play. It is just hypothetical play with special rules. (Not that I like the J89 rules, but they do not rely upon definitions of unconditionally live groups or any such.)

[tiger314]

Looking through the J89 rules (Davies' translation), it seems that there is no playout, but an investigation of all possible sequences according to special (ko) rules. Could you point me to the playout paragraph of the rules? I found this in the commentary, but I am not sure how to interpret it:

A player does not have to remove opposing dead stones from his territory
by occupying all their liberties as in Article 5. He can remove them as is,
without making further moves.

[RobertJasiek]

Japanese 1989 Rules interpretation:

http://home.snafu.de/jasiek/j1989c.html
http://home.snafu.de/jasiek/j2003.html
http://home.snafu.de/jasiek/j2003com.html

[Bill Spight]

Looking through the J89 rules (Davies' translation), it seems that there is no playout, but an investigation of all possible sequences according to special (ko) rules. Could you point me to the playout paragraph of the rules? I found this in the commentary, but I am not sure how to interpret it:

A player does not have to remove opposing dead stones from his territory
by occupying all their liberties as in Article 5. He can remove them as is,
without making further moves.

The J89 rules make use of hypothetical play, but the principle that life and death are decided by play is the basis of it.

Some territory rules, such as Ikeda's, Lasker-Maas rules, and Spight rules, have an explicit encore with actual playout. However, such rules do not necessarily produce the same results as those desired by the Japanese rules makers.