What is A Posteriori (AP)?

Question

A number of problem-related questions recently mention AP by which they mean “A Posteriori”.

What are they talking about?

It seems as if the guys talking about it don’t have a common understanding. Is there in fact a unique well-grounded meaning?

Answer 1

It seems to me that if I just explain in detail the solution of one difficult AP problem (Double Petrovic type), Laska's colleague will take it as an answer.

[Title "h#2 AP - Nikita M. Plaksin Valery Liskovets Die Schwalbe 99 06/1986"]
[FEN "r3kN2/p4pp1/3B1pp1/2PP4/2PpP2B/1P1B1N2/1p2P3/n3K2R w - - 0 1"]

    1. dxc3ep 0-0 2. 0-0-0 Ba6#

To solve the problem, we need to prove that black is eligible for dxc3ep. To do this, we need to prove that White's last move was c2-c4. Why white's right to castling is needed here is obvious. Otherwise, any last move of the white king is possible and 1. ... Nc2-a1. But why we also need black's right to castling is, as they say, a "good question." Here you will have to start from afar. Ask the question: "And from which pawn did we get the second white bishop walking on the black fields?"

And then it turns out that there are only two options (immediately exclude the obvious captures of black exf6 and hxg6. There will be one capture for black and 6 for white).

1. He got out of the pawn g2 (f2).

Capture scheme: White (6): gxfxe; fxexd(pawn); axbxc (d2-d5!) Black (1): c5xd4

And here, in any case, the white pawn passes through d7 and sends a big hello to the castling of black.

And to unlock black, white's last move takes place: axb3.

2. The bishop turned out to be the a2 pawn.

Capture pattern: White (6): axb(pawn); gxfxe; fxexd; dxc (b2-b3!) Black (1): c3xb2

And here black's castling has been preserved, and to unlock black, only the return of the c2-c4 move is suitable.

Total: the right to castling of white is necessary so that the black knight a1 cannot walk; Black's right to castling is necessary so that White's last move a2xb3 is not possible.

And we, having "promised" as many as two castlings, must do both in the solution. It's good that the cooperative!

Retro (for example): 1. c2-c4 cxb2 2. Nh2-f3 c4-c3 3. fxe4! (2. e3-e4 c4-c3 3. fxe3!)

Answer 2

There is a clear definition:

If a player needs the right to castling in order to solve a problem, then in the process of solving the castling must be performed directly, regardless of whether it is necessary for the solution or not.

The wording is completely exhaustive and has never caused any controversy.

The fact is that if you need the right to castling to solve a problem (not the castling itself, but only the right to it) in the decision-making process, you will still have to castling to confirm the "promised" right.

It is useful to familiarize yourself with this: https://www.janko.at/Retros/Glossary/Castling-and-En-passant.htm

However, only AP (type Petrovic) is described here. The author of the article, Werner Keym, for some reason, does not describe the second type (Keym type) here, calling it controversial. :) Although what is there to argue about? Blacks have the same rights as whites. Is anyone against it?

There is an interesting step-by-step logic scheme here. Having allowed AP (type Petrovic) once, we have no reason to ban AP (type Keym for white), because the technique is the same, just the goal is different. And having allowed AP (type of Keym for white) once, we no longer have any reason to prohibit AP (type of Keym for black). Because the reception is the same, but conducted by the other side.

==

Explanation in simple words

If a player has the right to castling, it may lead to a change in the playing conditions in the starting position, for example:

1. it becomes possible to do e.p.;
2. the right to move passes to the other side.

In a simple way, the procedure can be described as follows:

1. the player makes a statement that he has the right to castling;
2. there are consequences caused by this statement (we use the right to e.p.; the turn of the move goes to the other side);
3. Before the end of the game, the player who made the statement must perform castling.

That is, de facto changes come immediately, but de jure take effect only after the castling is done. And if castling is not performed before the end of the game, then all changes caused by the statement of the right to castling do not take effect and the entire game that followed the player's statement is recognized as illegal.

The principle is a posteriori: we get the benefit from the statement immediately, we give proof of the truth of the statement later.