I am posting the following text on behalf of Chen Zuyuan, who is probably the world's foremost expert on go rules. Apart from the fact that he is a scientist by training and vocation, he is thoroughly conversant with the texts of ancient Chinese go and so has a panoply of texts from two millennia to guide him in his thoughts. He also devised the ruleset used for world mind sports events in China.
There is no ulterior motive behind this posting beyond the fact that Chen felt he would like to have his thoughts recorded somewhere on an Englishspeaking site. He decided that L19 was the best forum.
I have obviously had a hand in the English version. I am neither a mathematician nor a scientist and certainly not a rules aficionado. If you care to suggest corrections to the English translation, I will happily take them on board. But if you have comments on the underlying ideas, do note that the Chinese text is the definitive version.
围棋规则理论的终极化研究
Study on the Ultimate Theory of Weiqi Rules
陈祖源 Chen Zuyuan
前言 终极理论一词(Ultimate Theory)出自物理学，即是以特殊的数学形式完备的描述物理规律。从其发端的麦克斯韦方程组就可以看出它与从牛顿到法拉第的以实验为基础的经典物理学在方法论上的差异。当物理学被数学完美的表达时物理学也完美了，终极了，这就是终极理论的意义。我们以往对围棋规则的研究出发点是围棋已经存在，我们是去尽可能准确合理的规范它。而仿照物理学的终极化的研究方法，是用数学和逻辑的方式自动的生成围棋。也就是说我们把围棋当作是在一块棋盘上演绎的一个独特的数学体系。数学的基础是公理，数学体系是在公理化演绎下产生的。围棋规则的终极化研究就是在围棋公理下产生围棋，那么这样表达的围棋规则理论就是完美的、终极的。
PREFACE The term “Ultimate Theory” comes from physics, being a complete description of the laws of physics in a special mathematical form. From Maxwell’s equations at its origin, we can see the methodological differences between it and the classical physics that were based on experiments from Newton to Faraday. When physics is perfectly expressed by mathematics, physics is also perfect and ultimate, which is the meaning of the Ultimate Theory. The starting point of our previous research on weiqi rules has been that weiqi [go] already exists, and we have tried to describe it as accurately and as reasonably as possible. The research approach instead, imitating the ‘ultimate’ in physics, is to generate weiqi automatically in a mathematical and logical way. That is, we treat weiqi as a unique mathematical system interpreted on a board. Mathematics is based on axioms, and mathematical systems arise under axiomatic deduction. The ultimate study of weiqi rules is to the formation of weiqi via the weiqi axioms, so that the theory of weiqi rules expressed in this way will be perfect and ultimate.
一、围棋规则的公理化构架 公理就是不证自明的，依据理性而公认的，最基本的命题。围棋规则由两类3条公理和1条规则推理，1个目标推理组成： 设定性公理2条；围棋公理1条；规则推理1条；目标推理1条。
I. AXIOMATIC FRAMING OF THE RULES OF WEIQI An axiom is a selfevident, rationally based and accepted, most fundamental proposition. The rules of weiqi consist of three axioms, one rule corollary, and one example of goal reasoning, in two categories: two established axioms, one weiqi axiom, the one rule corollary, and the one case of goalreasoning.
(一）设定性公理： 1、基本描述：围棋由棋盘和黑白两色棋子组成，棋盘为纵横各n道（标准棋盘取n＝19）。标准棋盘19×19，有361个交叉点；棋子数量应该充足。
2、程序规则：双方各执一色棋子。轮流着于棋盘上的空点。着于棋盘上的棋子不再移动。围棋的设定是少而基本的，是自然的，也是必然的，因此可以叫公设。
(i) Established axioms: 1. Basic description: Weiqi consists of a weiqi board and black and white stones, the board is n lines vertically and horizontally (the standard board is taken to be n = 19). The standard board is 19 x 19 and has 361 intersections; there must be a sufficient number of stones.
2. Rules of procedure: Each player has one colour of stones. They take turns to place one stone on an empty point on the board. Stones placed on the board do not move again. These established elements of weiqi are few and basic, natural and inevitable, and can therefore be called established axioms.
（二）围棋公理，即围棋的核心规则或特性规则： 3、吃子规则：无气之子从棋盘上提出。这是围棋的核心，是围棋之为围棋的所在。
(ii) Weiqi axiom, i.e. the core rules or characteristic rules of weiqi: 3. Rule of capture: the stones with no liberties must be removed from the board. This is the core of weiqi and is what makes it the surrounding game it is.
公理即人为的规定到此为止，规则的其余均应从此三条公理推出，不应再有别的人为的规定。 The axioms, that is, the artificial stipulations, end here, and all the rest of the rules must be inferred from the three axioms, so that no other artificial stipulation need be made.
（三）推理 4、规则推理：打劫规则 本条是2、和3、的推论。此条后面再解释。
(iii) Corollary 4. Rule corollary: the ko rule This item is an inference from 2. and 3. This item will be discussed later.
5、目标推理：围棋的目标 游戏的目标是规则的产物。围棋规则以公理体系构建，则目标就必须出自公理之中，即是公理的推理。因此公理化的目标只能是公理中的两种实物：公理1中的棋盘或棋子。
5. Goal corollary: the goal of weiqi The goal of the game is a product of the rules. Since the rules of weiqi are constructed in a system of axioms, the goal must come out of the axioms, i.e. be an axiomatic corollary. Thus the goal of an axiomatisation can only be one of two physical objects in the axioms: the board or the stones in Axiom 1.
（1）以公理1中的棋子为目标，则公理1中的棋盘就是实现目标的工具:在棋盘上依照第2、3、4条公理，生存更多的棋子。这就是古代围棋规则，一般称之为数子规则。 当然也可以是吃对方更多的棋子。死子多就是活子少，活子规则和死子规则其实是一回事。
(1) With the stones in Axiom 1 as the goal, the board in Axiom 1 is the vehicle for achieving the goal: more stones survive on the board in accordance with Axioms 2, 3 and 4. This is the ancient rule of weiqi, generally known as ‘stone scoring.’ Of course, it can also mean capturing more of the opponent's stones. More dead stones means fewer live stones, and the scoring with live stones or dead stones is actually the same thing.
（2）以公理1中的棋盘为目标，则公理1中的棋子就是实现目标的工具。用棋子依照第2、3、4条公理，去占取棋盘上的点（19×19＝361），以占取更大的部分为目标。
(2) Taking the board in Axiom 1 as the goal, the stones in Axiom 1 are the tools to achieve the goal. That means using the stones to occupy the points on the board (19 x 19 = 361) in accordance with Axioms 2, 3 and 4, with the goal of taking the larger share.
但什么是占取？最公理化的占取就是用棋子直接的占领，那结果就等同（1）。但（1）中的眼位是不能算的，因为那里不能生存棋子。但如果目标是棋盘上的点，眼位这个点是占取的棋子的组成部分。因此包含眼位的占取可以认为也是公理化的，虽然程度可能稍弱一些。这就是现在的中国规则，一般称之为计地规则。
But what is ‘occupation’? The most axiomatic occupation is to occupy with stones directly, and the result is equivalent to (1). But the eyepositions in (1) do not count, because no stones can live there. But if the goal is points on the board, the points of the eyepositions are part of the occupying stones’ group. Therefore, containing the eyepositions can be considered axiomatic as well, although perhaps to a slightly weaker extent. This is now the Chinese rules, generally known as ‘area scoring.’
解释：那么能不能还有其他目标呢？公理1围棋组成只有棋盘和棋子，再没有三，因此公理化推论下的必然目标就只有这两个。再设其他目标就是在公理体系以外的人为的加入了。一个公理性的围棋规则体系，如果目标设定在公理体系之外，就很可能会导致体系的不和谐。日本的计空规则，包括死子回填，是一个与公理性无关的人为的设计。不是从公理推导出来的人为设计的规定，很可能会与其他公理冲突，导致自我逻辑悖理。
Discussion: Can there be other goals then? Axiom 1 is that weiqi consists of only the board and the stones, and there is no third element, so that the only two natural goals under axiomatic inference are these. To set other goals would be an artificial addition outside the axiomatic system. An axiomatic system of weiqi rules with goals set outside the axiomatic system is likely to lead to discord in the system. Japanese territory scoring, including backfill of dead stones, is an artificial design that has nothing to do with axiomatics. Artificially designed rules that are not deduced from axioms are likely to conflict with other axioms and lead to selflogical paradoxes.
空的价值意义只有在作为（1）或（2）目标体系中的推理时才成立。使用空这个推理是因为它可以简化（1）或（2）的目标的计算。本质的的公理化的目标只能是（1）或（2）。日本规则的失误就在于被表面所模糊，失落了本质。
The value meaning of the territory only holds when it is used as an inference in the system of goals of (1) or (2). The inference of territory is used because it simplifies calculation of the goal of (1) or (2). The intrinsic axiomatisation of a goal can only be (1) or (2). The failure of Japanese rules is that they are obscured by appearances and so lose their essence.
二、关于打劫规则 打劫规则是围棋中一个特殊的规则，一直来都以“在反复回提一个子之前需在棋盘其他地方下一着棋”的方式规定。这个规定显然不够自然。因此人们提出了禁止全局同形，这是一个很好的理论，但这也是新设了一条公理，而严格地说它的公理性偏弱。事实上我们无须特别规定打劫规则，它已经逻辑性的隐含在规则2和3之中。
II. About the ko rule The ko rule is a special rule in weiqi and has always been laid down in the form of "Before a stone can be repeatedly removed, a move must be made elsewhere on the board." This rule is obviously not natural enough. Thus, the idea of prohibiting repetition of the game position has been proposed, which is a good theory, but this is also a new axiom，and strictly speaking its axiology is weak. The fact is that we do not need to specify the ko rule, which is already logically implicit in Rules 2 and 3.
劫子立即回提这个动作：把对方刚下的棋拿走，把对方刚吃的棋子重新放回去，因此它在本质上是否定了对方上一着棋，即否定了公理2赋予的对方的一次着子权利。虽然它有公理3的依据，但有了着子规则才有吃子规则，公理3是在公理2以后产生的，因此公理2优先。因此打劫规则可以认为是公理2和3的推理。
Immediate removal of a kostone by this action: Taking away a stone the opponent has just played and putting back a stone the opponent has just captured, essentially negates the opponent's previous move, i.e. negates the right of the opponent to place a stone under Axiom 2. Although it has a basis in Axiom 3, there is a rule of placing before there is a rule of capturing, and Axiom 3 arises after Axiom 2, so Axiom 2 takes precedence. Thus the korule can be considered as a corollary of Axioms 2 and 3.
如果把禁止否定从上一着引申到之前任一着： 禁止否定对方的棋着，即不得使对方面临其曾面临过的局面。这也就是禁止全局同形。虽然引申会导致逻辑必然性降低，但面对循环劫尤其是假生，采用这个引申还是需要的。
Where the prohibition on negation is extended from the previous move to any of the previous moves: It is forbidden to negate the opponent's moves, that is, to make the opponent face a game situation he has already faced. This means prohibiting repeated game positions. Although extension leads to a reduction in logical necessities, it is nevertheless still necessary to adopt this extension for multiple kos, and in particular for cases like moonshine life.
三、其他 1、虚着 由于围棋以活子或占地为目标，着一子就是活子也是占地，因此如果不着子就是表示不再下棋了，如果对方也不着子，双方都不下棋了，对局结束。因此不着子视为提议终局和同意终局，可以理解为是规则5的推理。如果对方继续下棋，棋局当然继续，这时刚才那未着子的行为称为虚着或弃着。
III. MISCELLANEOUS 1. Void move (pass) Since weiqi aims at living or occupying space, a move is a move to live or to occupy space, so if no move is made it implies that the game is no longer to be played, and if the opponent does not make a move either, both players are no longer playing and so the game is over. Therefore, making no moves is regarded as proposing the end of the game and then agreeing to the end of the game, which can be understood as a corollary to Rule 5. If the opponent continues to play, the game of course continues, and the unplayed move is then called a void move or a pass.
2、禁着点 在公理化体系中自杀当然是不禁的。
2. Forbidden moves Suicide is of course not forbidden in the axiomatic system.
3、终局与协议终局 这是协议性程序规则，是在规则1、2、3、4的前提下保证规则5的结果的实现。
3. End of the game and agreement as to end of the game These are agreed procedural rules that guarantee the achievement of the outcome of Rule 5 subject to Rules 1, 2, 3 and 4.
4、贴先 这属于约定，不是围棋的基本规则。所有现行的围棋规则文本中都没有贴先的规定，而是在比赛规则中设定。因为原则上说贴先只是平衡先行之利的方法之一，是不是用这种方法，贴多少，怎么贴，都是可以有选择性的。
4. Compensation for first move [komi] This is a convention, not a basic rule of weiqi. There is no provision for compensation in any of the current weiqi rules texts, but rather it is set out in the competition rules. Because, in principle, komi compensation is only one of the ways to balance the advantage of playing first, the available options are whether to use this method, how much to compensate, and how to compensate.
Last edited by John Fairbairn on Sun May 14, 2023 1:27 am, edited 2 times in total.
