Logic can be a very complex topic, but here we are interested mainly in three relationships which you probably did not even think of as "logic." They are 1.) "Identity" 2.) "Extension" (in time and space) and 3.) Cause / Effect. As words group together to form sentences, the connections often reflect these logical relationships.
Many adjectives, adverbs, and prepositional phrases answer the questions "Which?" "What?" "What kind of?" In the sentence "They saw the little boy enter the house on the corner." we can say that "little" indicates which boy and thus helps the reader identify the boy. Similarly "on the corner" tells which house, so it identifies the house.
2. Extension in Time and Space
Some adjectives, adverbs and prepositional phrases answer questions such as "When?" "Where?" "How long?" "How far?" Thus they reflect relationships in time and space. Note that in the example for identity, "on the corner" identifies the house by locating it in space. Often, however, the modifiers simply reflect time and space. In "They played baseball in the park for three hours." "in the park" indicates where the playing occurred. "For three hours" explains how long the playing extended in time.
Some adjectives, adverbs, and especially prepositional phrases answer the question "Why?" They therefore indicate a cause/effect relationship between the words (or phrases) and the word being modified. In "They went to the store for milk." "for milk" tells why they went to the store.