middle can be calculated by stir the want of an preposition divided by the want of that preposition
locative_preposition is spatial_preposition. middle is point. spatial_preposition is preposition. middle is not part. atelic_directional_preposition is spatial_preposition. directional_preposition is spatial_preposition. atelic_directional_preposition is not spatial_preposition. preposition_of is preposition. middle is part. middle is not point.