Attempts to get at such formal definitions have been made at formal definitions of eye. Let's link from there or merge these pages.
Secondly, this formal definition includes "adjacent", "string", "stones of a player". I think these should be formalized as well and linked to. Dieter
"eye" and "two-eye-formation" are two different concepts. Therefore merging the pages would be very inappropriate.
An eye can be larger than an empy intersection of a two-eye-formation, an eye can contain dead opposing stones, and then there are also eyes in sekis and anti-sekis.