≺, ≻, ≼, ≽

Suppose X and Y are positions with the main pgn file. If the position Y is reached from X by making a nonempty sequence of moves in the pgn file, we say that position X is an ancestor of Y and write this as:

    X≺Y

In ASCII, we would write X[<]Y.

A position is not an ancestor of itself:

  X≺X

is always false.

If either X is an ancestor of Y or X is equal to Y, we write

  X≼Y

(ASCII: X[<=]Y.)

If X is an ancestor of Y then we say that Y is a descendant of X.

The expression

  Y≻X

means that Y is a descendant of X. (ASCII: Y[>]X).

Naturally,

  Y≽X

means that either Y is a descendant of X or Y is equal to X. (ASCII: Y[>=]X).

comparison to <

Recall that if X and Y are positions, then

  X<Y

is true if the positionid of X is smaller than the position id of Y.

On the other hand,

  X≺Y

is true if X is an ancestor of Y .

The positionid of a position is chosen so that any position has a smaller position id than its descendants. Thus, if X≺Y is true, then so is X<Y.

The converse is not necessarily true however. If variations is set in the CQL header, then it might be the case that X<Y is true but X<Y is false. However, if variations is not set in the CQL header, so that only mainline positions are considered, then < and ≺ are identical.

The value of ≺

The value of the positional relational symbols ≺, ≻, ≼, ≽ follows the precedence and conventions of the other relational symbols.

Thus, if X≺Y is true, then its value is equal to X.

Similarly,

  X≺Y≺Z

has value equal to X when the expression is true.