That last question seems simple to me. Incomplete moves are not part of the game. That is why they are not written on the score sheet. The last position of the game is not a dead draw, so the player loses. The rules are complete enough to give a clear answer for that example. There is no doubt that deadness does not apply to states between two moves.
I concur with my honorable colleague on that point!
What I meant is that deadness applies to a position. The position in the diagram is not dead and after that rook move is made you get a dead position (stalemate). You are asking if a certain state is dead, but deadness is not defined for that state. So it may better to say that it is not a position and therefore deadness is not defined.
Precisely my point. Positions are assumed to coincide with full move boundaries and with relevant knowledge of the preceding game, necessary to decide castling rights and such.
You assume that positions coincide with full move boundaries. This is not anywhere stated in the laws.
FIDE use the term "position" in three different senses in the laws. Firstly "position of a piece", secondly "position on the chess board" and thirdly just "position" (in the game).
Nowhere is the term "position" defined in the rules, so the normal English usage must be assumed. In the case of "position of a piece" this clearly means the square it occupies. In the case of "position on the chessboard" this clearly refers to the type and colour of pieces occupying the squares of the chessboard. In the case of "position (in the game)", my view is this means simply situation arising in a game.
It is true that in the chess community "position" has come to mean something different, though there is no general agreement. Sometimes it is synonymous with "position on the chessboard", sometimes that with the addition of which player has the move, sometimes a FEN and sometimes a PGN. These meanings are not defined in the laws and should be ignored in interpreting the laws.
For practical purposes, positions in a game can be regarded as the same in any interval where no event referred to in any rule occurs. But when an event referred to in a rule occurs then you have a different position in the normal English sense. The possible actions by the players are changed. When a player touches a piece, for example, it then becomes possible for him to release it on a square, whereas it previously wasn't. When a player completes a move it then becomes possible for his opponent to move, whereas it previously wasn't. When a player makes a draw offer it then becomes possible for his opponent to accept it, whereas it previously wasn't.
The FIDE laws nowhere state that some of the rules have a different status from others in in interpreting the term "position". In fact it is implied in
7.5.1 An illegal move is completed once the player has pressed his clock. If during a game it
is found that an illegal move has been completed, the position immediately before the
irregularity shall be reinstated. If the position immediately before the irregularity cannot
be determined, the game shall continue from the last identifiable position prior to the
irregularity. Articles 4.3 and 4.7 apply to the move replacing the illegal move. The game
shall then continue from this reinstated position.
that whether or not a player has touched a piece is regarded as part of the position, otherwise arts. 4.3 and 4.7 could not apply in the reinstated position.
This definition is commonly used in composition chess but I am not sure it is well defined in the FIDE handbook.
Definitions used in composition chess should also be ignored in interpreting the laws. It is not defined (well or otherwise) in the FIDE handbook, so the normal English usage should be assumed (in the English version).
It's not only the dead rule that doesn't apply to an inter-position state. Almost nothing applies, including the movement of pieces. Which is a good thing, or you could start a completely new move when in the middle of the previous one!
In my view "position" and "state" are synonymous. Your classification of "inter-position" state is based on an assumption about the meaning of "position" that nowhere is justified in the laws. There is nothing in the laws to contradict the usual assumption that all laws are in effect for the duration of the game (though some laws may specifically override others).
It follows that in my view everything applies in what you call an "inter-position state".
Whether or not a player may start a new move in the middle of a previous one is governed by:
1.2 The player with the light-coloured pieces (White) makes the first move, then the players
move alternately, with the player with the dark-coloured pieces (Black) making the next
move.
(this is the only rule that prevents players making multiple moves on their turn) and
Article 4: The act of moving the pieces
which defines valid ways of moving the pieces in terms of touching a piece, releasing a piece on a square and order of these when multiple pieces are involved.
By the way, all this doesn't mean that FIDE somehow needs to decide about deadness in the "MARattigan state". In a context of formal mathematical systems, the statement MARattigan-state is dead would be considered a language/syntax error (type mismatch). That's the math way. No need to resolve.
A formal mathematical system is perfectly capable of taking into account all of the events described in the FIDE rules (though it would need to make many assumptions about situations that are inadequately defined in those rules).
The semi formal system in Nunquam's link http://home.planet.nl/~narcis45/Chess/Chess%20Math%20Definition.pdf
is based on sequences of moves, but is not intended as an accurate description of the FIDE laws (even in 2011). The authors say:
We did not use game theoretic notions like players and gains and losses. Also claims, clocks, the act of moving, etc
are not dealt with in this article.
A full description would need to take into account all the events described in the rules. In fact the article doesn't describe a game at all because there is no account of the roles of the players.
The dead rule there circumvents the self reference problem I described in #88. It doesn't accurately represent the intention of the rule though, because it allows for games that continue after a dead position is reached.
The FIDE version could be corrected by changing
1.5 If the position is such that neither player can possibly checkmate the opponent’s king,
the game is drawn (see Article 5.2.2).
and
5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the
opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This
immediately ends the game, provided that the move producing the position Was in accordance with
Article 3 and Articles 4.2 — 4.7.
to
1.5 If the position is such that neither player could possibly checkmate the opponent’s king were the game continued ignoring this article, the game is drawn. This immediately ends the game.
In that case the positions in post #88 would definitely be dead.
(Note that 5.2.2 adds nothing other than explicit termination to 1.5 and could profitably be dropped.)
That last question seems simple to me. Incomplete moves are not part of the game. That is why they are not written on the score sheet. The last position of the game is not a dead draw, so the player loses. The rules are complete enough to give a clear answer for that example. There is no doubt that deadness does not apply to states between two moves.
I concur with my honorable colleague on that point!
Incomplete moves are quite clearly part of the game otherwise you couldn't have complete moves. More importantly they are part of the laws (Article 4). They are not written on the score sheet because there is no requirement in the laws to do so.
Compare the following situation: a player removes enemy piece with intent to capture. There is only one legal move to capture that piece, and that move is a ceheckmate. Once the enemy piece is touched, there is no other legal move. But making the move also requires moving the capturing piece to new square (and releasing it). Suppose flag falls with captured piece removed but capturing piece in starting square.
I understand that a move interrupted by flag fall before making it is parsed by retracting it to the position before the move started, and the outcome evaluated from that position. Correct?
There is nothing in the laws to that effect, nor in the UK Chess Arbiters Association guidance. I would say the correct result in that case would be a draw. Similarly if the capture would leave his opponent incapable of mate for any reason, including termination of the game. In fact the same should be true if the player had touched the opponent's piece before his flag fell, without actually removing it from the board.
If multiple captures were possible then a draw should result only if any capture would leave the opponent incapable of mating.
@MARattigan: I am glad that, in spite of what appears to be large gap, we actually have narrowed down the issue to the understanding of the relationship of deadness to the fullness of positions and the fullness of moves - or simply to the diagram + story I gave in #119. I suppose you'd claim that touching the rook there would result in a draw by deadness. Since there are quite a lot of positions where touches or other partial moves would cause deadness by your definition, you'd expect FIDE to arbitrate it at some point. Provided there is any chess player on the planet who agrees with you and protests a full move verdict.
Problemists do not generally (though they do on specific points) change the FIDE laws but they often need more preciseness in their understanding - for instance to define types like MDR. The current issue is closely connected to the understanding of the relationship between diagrams and positions and states which we have hardly touched. Edit: For instance, with the alternate interpretation of the dead rule, I suspect that quite a lot of Andrew Buchanans dead reckoning problems would be cooked. You cannot play a move unless you first touch a piece which might easily result in a form of premature deadness in many cases. It is sort of strange to interpret a rule in such a way that it would destroy a body of compositions precisely made to demonstrate that FIDE rule. Don't you think some FIDE official would have addressed Andrew on his "flawed understanding"? Guess I will have to find some examples for that.
Numquams math article does not attempt to match the FIDE laws but to match the conceptual understanding of the FIDE laws and redesign them in a mathematical format - precisely the process I described as suitable. Note that FIDE itself does similar redesigns for instance when splitting the laws in "basic" and "competitive" articles or when redefining checkmate. Even when the redesigns appear drastic, their purpose is mostly just to clarify the same laws in a more digestible format. Probably the next version will contain a lot of stuff on "positions". It's all about communication.
Ultimately, the reason I believe your model will fail, is because it introduces unnecessary complexity by destroying the distinction between the atomic and the subatomic level. Levels give structure give clarity. It is possible to provide mathematical instructions for your viewpoint but they will be quite a bit longer than in the math link and much less user friendly. Why would anyone aim for that?
@Arisktotle
No I wouldn't claim that touching the rook in your diagram in #119 would result in a draw by deadness. I'd claim that the FIDE laws are not properly constructed to give an verdict on the point. Were they changed to take out the self reference as suggested in my last post then I would say touching the rook would result in a draw by deadness. If they were changed in some other way then what I would say would depend on what they said as changed.
Numquam's math article attempts to match a subset of the FIDE laws. Warmerdam omits, as he makes explicit, the laws regarding actions that are asynchronous with moves, viz. those governing claims and the act of moving, which latter presumably encompasses the whole of article 4. This allows him to define games inductively in a relatively simple manner. The full set of rules could be used in a similar manner, but yes, the induction would naturally be more complicated to encompass all the FIDE laws. It would also need some addition to describe how it relates to the game; it doesn't, as it stands say that the players choose the moves used in the induction process, for example, let alone who chooses which.
Regarding the dead position rule in particular, Warmerdam's article deoesn't accurately reflect FIDE's wording, partly because this would be impossible to put onto a correct mathematical basis.
I think it would be beneficial if FIDE produced such a document as the authoritative rules, but they would probably still need to paraphrase it for people with an aversion to maths.
Notice I don't have a model, because there is no model prescribed in the laws. I read them as I would the rules of any other game. You have the model, but it doesn't come from the laws. I'm not passing an opinion on what the laws should be (apart from consistent and preferably complete) only on what I understand them to say.
@MARattigan: If you simultaneously claim that the laws are the only source of reference and that they are incomplete, then there is no way forward, not even a discussion forward. It is extremely cheap and we all already know that the laws are not perfect. You claim to understand that the rules are semi-formal but you refuse to accept any consequence of that diagnose. It means they need to be interpreted and understood. The least you can therefore do is take a stand and make suggestions for better rules or how they are intended. There are many ways to read intentions, e.g. by recognizing rationality, concepts and practical use. See for instance what I wrote on Andrew Buchanan in my previous post.
Indeed, Warmerdam omits some sections on the rules but that does of course not imply that the parts he does include are incomplete or not self-contained. By including the dead rule he asserts that the rule can be defined in terms of the objects and sections of the laws he does address. The question is not whether or not the "correct wordings" are used but the correct concepts. If the FIDE concept (by your conviction) cannot be put in a mathematical framework then you just produced the strongest argument against that conviction. Not making the dead rule addressable in a mathematical - and therefore computer - environment would be the last thing FIDE would envision in 2019. Hmm, may be the subatomics are not al that relevant in computer games but that is circumstancial because they were made to disallow article 4 items. If a computer would be assigned the task of arbitrating all player actions by cameras and sensors on board and pieces, they would certainly need to interpret subatomics.
I discussed with Andrew that a proper lawbook should contain laws on several levels. The top layer would consist of concepts providing a framework for whatever interpretations might still be needed. Other levels could consist of mathematics, common law texts and examples addressed to the various profile groups.
I am pretty sure I can zoom in on the rules in such great detail that they only say nonsense. For instance, many word definitions in our natural language end up circular. Even if you try to take them at face value you need loads of contextual understanding. The problem I see in your approach is that you focus on some details in order not to see the obvious. Subsequently, you defend yourself by proclaiming the article is not clear. Of course, nothing is ever clear anywhere, except perhaps math. But such is not an excuse not to attempt to understand what was meant. Which you have trouble with because you can't see that only concepts breed laws and their understandings.
Self-reference issues are almost always fake, whether it is on the dead rule or a posteriori logic or the cretan paradox. Every human already knows this because they intuitively reason on a much higher level than is reflected in our use of written and spoken language. How it can be handled formally is the subject of my molecular moves. And after it is formally handled everyone will say "I already knew that" because everyone did. In the same way that almost every chess player already understands the chess rules but may permit himself to be confused by some formulations of the laws.
@Arisktotle
I do claim that the laws are the only authoritative source of reference and that they are incomplete and, in the case of the dead position rule at least, inconsistent. On some points that means there's no discussion forward, for example what happens when the fellow in #119 touches his rook. I can only wish he'd had his wits about him.
On the other hand the rules do pretty well almost all the time, because the're rarely looked at. People playing White don't generally move the Black pieces etc. because there's a shared convention about how chess is played independent of the written rules. It's unfortunate that there are no authoritative answers on some points, but really that's up to FIDE to correct and I wouldn't expect them to take any notice of what I say whatsoever.
I have nevertheless suggested a couple of possible improvements. One is the rewording of the dead position rule as in #126 (but from your red edit above I wouldn't expect you to regard that as an improvement), the other is that FIDE should first of all produce the rules in mathematical form similar to Warmerdam's article - if they did that sufficiently rigorously it would at least force them to tie up a lot of loose ends.
I would say Warmerdam's coverage is incomplete on the question of game termination. This occurs automatically for checkmate and stalemate because his induction process necessarily terminates at those points, but termination is not built into the model for the other conditions which it needs to be, at least for the dead position rule. (There are no claim events built in so obviously the threefold repetition and 50 move rules also have no termination condition, but the draw conditions for these are in any case incorrect). His dead rule actually models the first sentence of my suggested replacement in #126, it wouldn't model the rule itself if a termination mechanism were included in the model (and of course it doesn't model the rule itself because there is no termination mechanism).
I don't think the FIDE wording of the dead position rule can be placed on a sound mathematical basis because it's implicitly self referent and leads to exactly the aforementioned fellow's problem with his rook. I have to assume FIDE's concept correspond with the words. I don't see how that conviction argues against itself, it just means I think FIDE cocked up.
I answered to some of your points in the new red sections of my last post.
And I definitely agree Warmerdam is incomplete as well. He very much concentrates on what he considers "basic chess" which is not the same as in the handbook. Everything competitive is horrifying to him.
I noticed he didn't give an algorithm for determing death but only defined it by a set-result. It's a valid way to define the condition but insufficient to execute it. Intuitionists would reject it on that basis. But I understand it for the reason in one of the very first posts I wrote. There is no algorithm for a draw, unless you can make the game finite. That is why I am happy with e.g. the 5REP rule. It makes the game finite. Now you can detect a dead position by exploring all moves until a 5REP.
I am pretty happy with your improvement of the dead rule in #126 which could also be used e.g. for checkmates "it is checkmate if the king will be captured on the next move, while ignoring restrictions on selfcheck and capturing kings" (don't say it, I know, there is stalemate to consider). Notice the similarity with the dead rule you suggest. I have yet an even safer model for handling molecular issues which is of course equivalent in the end. And, the only way you could suggest the improvement is by understanding what the rule intended rather than what it said - so we may be closer on this than I thought.
The main point of contention on the dead rule are however the full move boundaries and they are not addressed by this change.
@Arisktotle
I do claim that the laws are the only authoritative source of reference and that they are incomplete and, in the case of the dead position rule at least, inconsistent. On some points that means there's no discussion forward, for example what happens when the fellow in #119 touches his rook. I can only wish he'd had his wits about him.
On the other hand the rules do pretty well almost all the time, because the're rarely looked at. People playing White don't generally move the Black pieces etc. because there's a shared convention about how chess is played independent of the written rules. It's unfortunate that there are no authoritative answers on some points, but really that's up to FIDE to correct and I wouldn't expect them to take any notice of what I say whatsoever.
I have nevertheless suggested a couple of possible improvements. One is the rewording of the dead position rule as in #126 (but from your red edit above I wouldn't expect you to regard that as an improvement), the other is that FIDE should first of all produce the rules in mathematical form similar to Warmerdam's article - if they did that sufficiently rigorously it would at least force them to tie up a lot of loose ends.
I would say Warmerdam's coverage is incomplete on the question of game termination. This occurs automatically for checkmate and stalemate because his induction process necessarily terminates at those points, but termination is not built into the model for the other conditions which it needs to be, at least for the dead position rule. (There are no claim events built in so obviously the threefold repetition and 50 move rules also have no termination condition, but the draw conditions for these are in any case incorrect). His dead rule actually models the first sentence of my suggested replacement in #126, it wouldn't model the rule itself if a termination mechanism were included in the model (and of course it doesn't model the rule itself because there is no termination mechanism).
I don't think the FIDE wording of the dead position rule can be placed on a sound mathematical basis because it's implicitly self referent and leads to exactly the aforementioned fellow's problem with his rook. I have to assume FIDE's concept correspond with the words. I don't see how that conviction argues against itself, it just means I think FIDE cocked up.
You can give a mathematical definition of dead draw if you use my interpretation of the dead draw and that is exactly what Warmerdam did. Just because it doesn't follow your interpretation of the dead draw rule, doesn't mean it is wrong. Warmerdam read the rule the same way I did and this mathematical definition of a dead draw can also be used for tournament games, because the dead draw rule as you know doesn't refer to tournament rules. There is no need to build in a termination mechanism other than checkmate, because checkmate is the only termination mentioned in the dead draw rule. Of course the series of legal moves automatically terminates when there is no legal move too, in other words stalemate.
Also all chessplayers know what is meant with the term 'position'. The article I linked gave a mathematical definition. There is no reason whatsoever to believe that FIDE intends anything else. Rule 3.10.3 indicates that they use the term the same way as everybody else in the chess world. If 99.99% of all people interprets word x as y, then there is no need to precisely define what is meant with word x. Just because you are the 0.01% who uses a different meaning of the word 'position', does not mean the usage is not clear.
The only issue with the dead draw rule is that there is no algorithm known yet to determine if a position is dead. Arisktotle said: "There is no algorithm for a draw, unless you can make the game finite. That is why I am happy with e.g. the 5REP rule. It makes the game finite." I don't think that is correct. The 5REP rule does not need to be included to determine dead draws. You can simply check if you get the same position twice in a series of moves. If that is the case, then you did not make any progress towards checkmate. So either there exists a series containing unique positions which leads to checkmate or the position is dead. Edit: I guess you could use some brute force algorithm. I meant there is no fast algorithm known yet.
I agree that it is better to define the rules in mathematical format where possible. If FIDE were to do that, I'd expect something very similar to that article. I don't think they'd follow your interpretation of dead draw. That would have prevented this whole discussion. 
You can simply check if you get the same position twice in a series of moves. If that is the case, then you did not make any progress towards checkmate. .
Yes, that is the interesting point which can be made (and which I always was aware of).
The same is true for the Gödel sentence. Viewed algorithmically it contains a repetition which could be detected as making no progress and therefore not leading to proof. However, the complete semantic status for the G-sentence is not decided in the system but moved to the model accompanying it which is no longer purely axiomatic.
The "problem" is that a formal system cannot reflect on itself and therefore not detect what a repetition is without knowing how semantic values for positions are derived. The system might for instance contain an axiom that a pawn must be added on every multiple of 100 moves following move 500. That may require a position to "repeat" many times before a winning position can be achieved. Without reflection, how would the system know that such an awkward rule does not exist?
I am almost sure that you think this is a ridiculous argument but that is only because as a human being, your logic is vastly superior to that of an axiomatic system. It simply is about the stupidest thing in the whole universe.
By including a repetion rule based on the properties of positions as defined in the game rules, we make an axiomatic assertion that from this point no progress can be made. What we already know by understanding the rules, needs to be told to the system formally. I agree that, in terms of the dead rule just one unavoidable repetition is sufficient to create a finite game but the 5REP performs the same function and why add an extra rule? Except if you want deadness to ignore 5REP which might force you to add another repetition rule which is dead rule sensitive. The latter is not as ridiculous as it sound but requires yet another page of text.
To give a somewhat realistic example of why "repetition" depends on "semantic context", imagine a chess composition with the stipulation to checkmate in no less than 40000 moves. This probably requires more repetitions than allowed which makes the problem unsolvable. But that is only because we chose the competitive game scoring semantic (win, loss, draw) as the basis for our repetition rules. Problemists might need another one for certain problem types. I'm not stating that the game rules should take the problem requirements into account, only that a system which cannot reflect on its own semantic context, is incapable of making the distinction. And therefore we need to tell it.
You can simply check if you get the same position twice in a series of moves. If that is the case, then you did not make any progress towards checkmate. .
Yes, that is the interesting point which can be made (and which I always was aware of).
The same is true for the Gödel sentence. Viewed algorithmically it contains a repetition which could be detected as making no progress and therefore not leading to proof. However, the complete semantic status for the G-sentence is not decided in the system but moved to the model accompanying it which is no longer purely axiomatic.
The "problem" is that a formal system cannot reflect on itself and therefore not detect what a repetition is without knowing how semantic values for positions are derived. The system might for instance contain an axiom that a pawn must be added on every multiple of 100 moves following move 500. That may require a position to "repeat" many times before a winning position can be achieved. Without reflection, how would the system know that such an awkward rule does not exist?
I am almost sure that you think this is a ridiculous argument but that is only because as a human being, your logic is vastly superior to that of an axiomatic system. It simply is about the stupidest thing in the whole universe.
By including a repetion rule based on the properties of positions as defined in the game rules, we make an axiomatic assertion that from this point no progress can be made. What we already know by understanding the rules, needs to be told to the system formally. I agree that, in terms of the dead rule just one unavoidable repetition is sufficient to create a finite game but the 5REP performs the same function and why add an extra rule? Except if you want deadness to ignore 5REP which might force you to add another repetition rule which is dead rule sensitive. The latter is not as ridiculous as it sound but requires yet another page of text.
To give a somewhat realistic example of why "repetition" depends on "semantic context", imagine a chess composition with the stipulation to checkmate in no less than 40000 moves. This probably requires more repetitions than allowed which makes the problem unsolvable. But that is only because we chose the competitive game scoring semantic (win, loss, draw) as the basis for our repetition rules. Problemists might need another one for certain problem types. I'm not stating that the game rules should take the problem requirements into account, only that a system which cannot reflect on its own semantic context, is incapable of making the distinction. And therefore we need to tell it.
I can kind of get what you mean, but isn't there a simpler way to solve that? Let's say we have some dead position and we make the assumption that the series of legal moves has to be finite. Then we can prove for every length N that there is no series of legal moves with that length which leads to checkmate. I don't think this assumption is unreasonable, because a game of chess does not go on forever.
Edit: We can even deduce from the rule itself that the series has to be finite, because an infinite series of moves can't end in checkmate, because checkmate terminates the series.
I can kind of get what you mean, but isn't there a simpler way to solve that? Let's say we have some dead position and we make the assumption that the series of legal moves has to be finite. Then we can prove for every length N that there is no series of legal moves with that length which leads to checkmate. I don't think this assumption is unreasonable, because a game of chess does not go on forever.
I agree my text may appear complex, but how is my solution not simple? I suggest to do absolutely nothing, as the existing rules are sufficient to make the game finite. Only if you want deadness not to apply to 5REP and 75M there is still sort of a problem. This is not my view but if you insist I think it can be turned into a simple solution as well - even when its justification may take some text.
There is no absolute necessity to address the rules in terms of a formal axiomatic system but it does have the advantage that its formulas can be proven by chess moves complemented by FOL (first order logic) which most people understand very well - having studied it or not. Every player uses minimax (maximin) logic to determine the best move in a position, which is more complex than anything needed to embrace deadness.
Propositions of the nature you suggest can be made and they all introduce information not available in an axiomatic system like the understanding that positions will not continue to change forever because you know they are finite within your preferred semantical context - caused by the fact that you know that the influence of a position history is very limited. That is also how the Gödel sentence is "proofed" in the model. By introducing an understanding of what the concept "proof" means you can eliminate falsity as the outcome. But the ultimate question is: do you want moves or do you want (mathematical) proofs for chess rules?
Edit: We can even deduce from the rule itself that the series has to be finite, because an infinite series of moves can't end in checkmate, because checkmate terminates the series.
Prelim note: I don't think that is a valid argument because between the finite and the infinite is the undecidable - not being able to determine whether or not the answer is finite or infinite by proper algorithm. There is no number of moves N such that you can be sure that - when no checkmate is found - you will not find a checkmate at a move number >N. So you must go on looking forever. Unless of course you introduce one of a million meta-observations to reflect your (non-axiomatic) understanding of the game.
Since it is relevant, I chose to interpret your question freely as raising the issue of the finity of the chess game.
I started a reply and it grew and it grew and it will end up quoting system theory A-Z. So I aborted and decided on a short synopsis: This is the decidability question which depends on the finiteness of positions, not of move series. They are indeed finite - by our understanding of the game semantics - but not necessarily for different chess rules or different stipulations as in the examples of my forelast post. If you succeed in entering our understanding of the finiteness of positions in the definition of the axioms (plus language, alphabet ...), then you can indeed theoretically determine the scoring status of every position. If you can not or do not, you can enter it in the form of a repetition axiom - which has already been done in standard chess. Algorithmically, the use of a repeat axiom is highly preferred, since it is funny to base the diagnosis that a position will end in a draw, on the complementary elimination of all positions which might end in checkmate.
Edit: We can even deduce from the rule itself that the series has to be finite, because an infinite series of moves can't end in checkmate, because checkmate terminates the series.
Prelim note: I don't think that is a valid argument because between the finite and the infinite is the undecidable - not being able to determine whether or not the answer is finite or infinite by proper algorithm. There is no number of moves N such that you can be sure that - when no checkmate is found - you will not find a checkmate at a move number >N. So you must go on looking forever. Unless of course you introduce one of a million meta-observations to reflect your (non-axiomatic) understanding of the game.
I don't see how that would make the argument invalid. If a series of moves ends in checkmate, then it is always a finite series of moves. So you don't have to know if a series is finite or infinite. Only the series which turn out to be finite can potentially end in checkmate.
That is the complexity of infinities. Suppose you start with a dead position - which of course you won't know beforehand - at which point do you decide that no checkmate will be found and the position is therefore dead?
Whatever approach you chose you must guarantee that what you look for will be found or disproved in a finite number of steps. It is insufficient to state that you will find it in a finite number of steps only if it is there. If you were sure a checkmate was there in the first place, you didn't need to run an algorithm at all. Apparently you had the answer you are looking for all along.
edit: I think the issue you are addressing is different from mine. You are evaluating all the branches of the move tree - some of which are infinite - in order to find the one which leads to checkmate. I ignore that exercise and concentrate on the possibility that none get there, making your parallel algorithm disappear in infinity.
That is the complexity of infinities. Suppose you start with a dead position - which of course you won't know beforehand - at which point do you decide that no checkmate will be found and the position is therefore dead?
Whatever approach you chose you must guarantee that what you look for will be found or disproved in a finite number of steps. It is insufficient to state that you will find it in a finite number of steps only if it is there. If you were sure a checkmate was there in the first place, you didn't need to run an algorithm at all. Apparently you had the answer you are looking for all along.
edit: I think the issue you are addressing is different from mine. You are evaluating all the branches of the move tree - some of which are infinite - in order to find the one which leads to checkmate. I ignore that exercise and concentrate on the possibility that none get there, making your parallel algorithm disappear in infinity.
Do you disagree with the following statement: 'If a series ends in checkmate, then the series is finite.'
It follows directly from that statement that series has to be finite. You know before you use some algorithm to find if it a dead draw that the series has be finite. So you don't even look at infinite series.
I think you lost me. Of course I agree with your first statement and it is part of my argument. I do not suggest trying to look for infinite series. Infinity is something you always run into unintentionally. The problem of an algorithm going to infinity is that it cannot interrupt itself and say "what I'm doing is silly, I stop" like a human would. And while it's going to infinity it is shouting at every move: "where is the checkmate, where is the checkmate" hoping to find it. Only we know it never will but the algorithm knows not. It can however continue playing "next moves" forever without a repeat rule to stop it.
Compare the following situation: a player removes enemy piece with intent to capture. There is only one legal move to capture that piece, and that move is a ceheckmate. Once the enemy piece is touched, there is no other legal move. But making the move also requires moving the capturing piece to new square (and releasing it). Suppose flag falls with captured piece removed but capturing piece in starting square.
I understand that a move interrupted by flag fall before making it is parsed by retracting it to the position before the move started, and the outcome evaluated from that position. Correct?
Not quite! There is a dead rule for anticipated draws but no victory rule for anticipated checkmates. The dead rule by itself is so silly, that I couldn't believe this was true at the time it was introduced. What they should have made right from the start was the one result rule. Quit the game when the outcome is sure whatever that outcome is.
The situation you describe is similar to the one we are discussing in this thread. We do not all agree on the outcome. My position is indeed like you describe.