Eyespace/Jasiek's formal definition

In 2003/4, Robert Jasiek defined "eyespace" formally under a ruleset like, e.g., the Japanese 2003 Rules or definition set that has already defined "alive" and "dead":

Definition: A black-eye-string is an intersection that is empty and, recursively, any adjacent intersection that is empty or occupied by a stone of a dead white-string.

Definition: A white-eye-string is an intersection that is empty and, recursively, any adjacent intersection that is empty or occupied by a stone of a dead black-string.

Definition: An intersection of a black-eye-string is a black-eye-point if the black-eye-string is adjacent and only adjacent to intersections with stones of one or more than one alive black-strings.

Definition: An intersection of a white-eye-string is a white-eye-point if the white-eye-string is adjacent and only adjacent to intersections with stones of one or more than one alive white-strings.

Definition: An eye-point is either a black-eye-point or a white-eye-point.

Definition: A black-region is an intersection with a stone of an alive black-string and, recursively, any adjacent intersection that has a stone of an alive black-string or is a black-eye-point.

Definition: A white-region is an intersection with a stone of an alive white-string and, recursively, any adjacent intersection that has a stone of an alive white-string or is a white-eye-point.

Definition: A region is either a black-region or a white-region.

Definition: A black-group is the union of all black-strings of a black-region.

Definition: A white-group is the union of all white-strings of a white-region.

Definition: A group is either a black-group or a white-group.

Definition: A black-eye is a black-eye-point and, recursively, any adjacent black-eye-point.

Definition: A white-eye is a white-eye-point and, recursively, any adjacent white-eye-point.

Definition: An eye is either a black-eye or a white-eye.

Definition: A black-eye-space of a black-group is the union of all black-eyes of the black-group's region.

Definition: A white-eye-space of a white-group is the union of all white-eyes of the white-group's region.

Definition: An eye-space is either a black-eye-space or a white-eye-space.

In practice, this definition is the most useful for scoring of the final position at the game end. Earlier during the game, most empty spaces are not completely surrounded yet. Then one can only try to predict likely eyespaces later.