Layered Chess Concepts

A thread to contain discussions related to the layering of chess concepts.

Here the meaning of layering is the one from computer science.

From searchsoftwarequality.techtarget.com/definition/layer
"In computer programming, layering is the organization of programming into separate functional components that interact in some sequential and hierarchical way, with each layer usually having an interface only to the layer above it and the layer below it. "

In mathematics most mathematicians take the lowest layer to be mathematical logic - some first order logic with equality is the usual thing done. Then what are called "non logical axioms" are added. That is a term-of-art that looks strange to the uninitiated. The phrase is used because the "logical axioms" are the axioms of the first order logic with equality. Any additional axioms are hence called "non logical axioms". The axioms of ZFC are non logical axioms - they are the axioms of the most used set theory.

Mathematicians then build layers of lemmas, theorems, and corollaries onto these other layers. It is a hierarchical system of statements that are provable. Each layer has access to all the layers below it.

In chess, the lowest layer is the rules of chess. Here, when I say chess, I mean SCC as defined in
lichess.org/forum/team-jomegas-tabia/theoretical-chess#3

Many people who play chess do not learn it from the lowest level up. Instead they are introduced to the "rules" as seen from a higher level, and sometimes even from concepts that are not compatible with the rules. An example of this is the way many people think about checkmate. Their understanding of it is based on an idea that the King could be captured. The rules of SCC do not allow the King to be captured and do not define checkmate by talking about the King being captured.

Axiomitizing chess is essential what has to be done to have a computer program play by the rules. You can get an idea of what would have to be done from looking at lichess.org/forum/team-jomegas-tabia/theoretical-chess?page=2#15

However, on that page, the function "moves" was assumed given. For a computer program or person the moves available in a position have to be defined. Also the representation of the position(s) has to be defined.

I'm going to assume that the lowest level of chess is understood. I do want to point out two things.

1. There is a fundamental idea that is so internalized immediately that it is not thought about again - namely that you have to keep track of all the pieces on the board, that they occupy exactly one square, and no two pieces occupy the same square at the same time. "Occupation of a square" is a very low level concept in chess.

2. The concept that a chess unit (man, colloquial piece) can "directly attack a square" is at the lowest layer of chess. It is this concept that is used to define the legal movements of a King, the castling rights, and the concepts of checkmate and stalemate.

In my Beginner Course I talk about the basic roles that pieces play. That starts in the study


Those roles, attack/defend/block/restrict, are at the next layer above the rules of chess.

I'll now give definitions and examples in no particular order.

BLOCK
The definition of block is based on the lowest layer definition of how pieces move. All line pieces, pieces that move in a straight line, (i.e. the Rook, Bishop, King, Queen, Pawn), may not move over any intervening pieces. They also cannot move onto the same square as some piece on that line unless it is an opponent's piece and they are capturing it.
The piece(s) that are such intervening pieces (or occupy directly connected squares in the trivial case) are said to "block" the piece that would try to move to some square. Hence, they also block the direct attack of that piece on those squares.

Pieces can block the pieces of the same color as well as the opposite color. So you can block yourself and your opponent.

Knights are allowed to move over pieces; hence they cannot be blocked.

A piece that moves to block another pieces is said to have interposed between the piece they are blocking and the square(s) they now block, and any pieces on those squares.

Examples:
1. In the initial position of SCC the White pawns are blocking the Rooks, Bishops, Queen and King from moving.
2. After 1.e4 e5, the e4 and e5-pawns are blocking each other from advancing.
3. After 1.f4 e6. 2.Nc3 Qh4+, the move 3.g3 causes the g3-pawn to block the Black Queen's attack (check) on the White King. The g-pawn has interposed between the Black Queen and White King.
4. It is not possible to interpose between a Knight that is checking a King. A Knight check cannot be blocked.

RESTRICT
The strictest definition of restrict is the situation of a direct attack of pieces on squares that keeps a King from being able to move/capture on those squares. The King is said to be "restricted" from moving to those squares and the pieces are said to "restrict" the King.
People naturally extend the definition to other cases where some piece cannot move (or doesn't want to move) to some squares. For example, a Knight absolutely pinned by a Bishop is said to be restricted from moving. A further abuse of the term would be to say that in the initial position of chess that the White King Bishop is restricted from moving by the e-pawn. I'll try not to abuse the terms.

ATTACK
Above the lowest level definition of "directly attacking a square" are a number of extensions of the word "attack".
An opponent's piece on a directly attacked square is said to be "attacked" by the pieces causing the direct attack.
A piece that is blocked from a direct attack of square(s) is said to be "indirectly attacking" the square(s), and any opponent piece(s) on those square(s).
Indeed, the adjectives "directly" and "indirectly" are usually omitted.

DEFEND
A piece that is directly attacking a square is said to "directly defend" that square. Similarly, if there is a friendly piece on that square the first piece is said to be "directly defending" that friendly piece.
"Indirectly defend" is similarly defined based on indirectly attack.

Examples:
Consider the following position:



The d1-Rook is directly attacking the d2-square, directly defending the d2-square and d2-Rook, indirectly attacking every other square on the d-file, and indirectly attacking both the Black Rooks.

In the position in #7 a strong enough player instantly sees that Black is about to lose material. He sees it so fast that we know it cannot be that he is doing a calculation. So what is going on in his mind to see it that fast?

There are two reasonable explanations, both of which might be the case depending on the position.
a) Pattern recognition. Analogous position to one seen before.
b) There is some "structure" in the mind allowing an instantaneous static tactical evaluation.

From reading the chess literature, listening to strong players talk about positions, and knowing how I do it, I've come to the conclusion that strong chess players build a structure in their mind that is at a high layer. I call that structure the attack/defense network. The stronger the player the more complex the structure is.

I also posted about the A/D network here:
lichess.org/forum/team-jomegas-tabia/the-schools-of-chess?page=2#12

In the Beginner Course I introduce the A/D Network here:



Subsequent chapters in that same study lead up to the introduction to the Exchange Rules-ofThumb (EROT).

In the position above let's consider what might be part of the structure in the mind, the A/D network, of the stronger player; who I will refer to as the master.
After 3.d4 it is Black to play. The master has, as part of the A/D network, that White is defending the d4-pawn directly with the c3-Knight and Queen. Black has the d4-pawn attacked directly twice; with the c5-pawn and c6-Knight. But the A/D network includes a ordering and value components. The force value of the pieces involved and the order of any capturing involved must be taken into account to avoid material loss.

Let's consider how a beginner learns EROT and to build the A/D network.
Consider the standard opening for the Ruy Lopez.



White has direct attacks indicated by the red arrows. Black has defenses indicated by the green arrows.
The beginner starts with the simple point count system for Force:
Pawn = 1, Bishop/Knight = 3, Rook = 5, and Queen = 9.
Though the actual geometry of the chess board is 2-dimensional with line-attacks by pieces other than the Knight, and then the Knight's special move, let's consider a simplification for the moment by inventing a notation that is linear.

White's pieces will be on the left of the (), and will be the normal capital letters used in FEN. Black's pieces will be on the right of the () and in lower case. The () indicates a square and any man may be on that square.

w:[N (p) n]: The network on e5.
w:[B (n) p p]: The network on c6.

The initial w indicates that it is White's move.