The sentence that uses a preposition to express a logical relationship is, the spider scurried under the kitchen cabinet.
Prepositions are used to express the relationship between two or more places, persons or time or express a relationship in time or space.
For instance,
The Last Time I met him was opposite the cinema. - preposition 'opposite' indicates place.
Reena was walking down the street. - the preposition 'down the street' indicates the place
I love eating ice-creams during the summers. - the preposition 'during' indicates the time.
Therefore, in the given sentence 'the spider scurried under the kitchen cabinet.' , the preposition 'under' indicates the place of the spider and express a relationship between the spider and the kitchen cabinet.