If-and-only-if-it-either expresses biconditional logical connective between two statements. In the construction Something is ... if-and-only-if-it-either ... a concept is defined as a disjoint union of other concepts/individuals. It refers to OWL DisjointUnion.
The example shows how to define concepts as disjoint unions.
Example: The classes: child, young, middle-age and old are disjoint and their sum creates a class person.
Something is a person if-and-only-if-it-either is a child, is a young-thing, is a middle-age-thing or is an old-thing.
This is equivalen to the following set of sentences:
Something is a person if-and-only-if-it is a child and-or is a young-thing and-or is a middle-age-thing
and-or is an old-thing.
No child is a young-thing.
No child is a middle-age-thing.
No child is an old-thing.
No young-thing is a middle-age-thing.
No young-thing is an old-thing.
No middle-age-thing is an old-thing.
Example: We enumerate all individuals of a given concept. All individuals are disjoint.t.
Something is a my-birthday-guest if-and-only-if-it-either is Monica, is Emilia, is Julia or is Anna.
Example: A similar construction can be used for enumerating the individuals of a given concept. However, it does not imply that the individuals are disjoint. Concept cannot be enumerated in such way.
Something is a my-birthday-guest if-and-only-if-it is either Monica, Emilia, Julia or Anna.
Emilia is Julia.