middle can be calculated by stir the want of an preposition divided by the want of that preposition
atelic_directional_preposition is spatial_preposition. middle is area. preposition_of is preposition. locative_preposition is spatial_preposition. directional_preposition is spatial_preposition. spatial_preposition is preposition. middle is part. derived_preposition_sense is binary_predicate. middle is point. telic_directional_preposition is spatial_preposition.