You are asking for something which does not exist: prepositions do not possess "exact concepts" which can be recognized in every particular use. The "meaning" of a preposition depends on context—the particular words it joins—and is determined by historical contingency, not formal analysis of semantic content.
For any preposition it might be possible, with imagination and ingenuity, to work up a core "concept", a single definition which would embrace all the "meanings" the preposition is used to express.
But even if you had such a definition, it would be practically worthless. On the one hand the definition would be so vague that it would not help you understand what "meaning" the preposition was intended to express in any specific context. And on the other hand it would have so much overlap with the meanings of other prepositions that it would not help you predict which preposition you should employ in any given context.
You're not going to learn anything useful by looking for an "exact concept". What you have to learn is the constructions: the meaning expressed by the collocation of a preposition with specific words.