Search is the process of looking for one or more entities of interest in one or more spaces of interest. The entities carrying out the search are the searchers. Search pre-supposes that the entities of interest are contained in space and identifiable. Consequently, the fundamental focus of the searchers is to determine this containership and verify the identity of the entities of interest. A search is wholly successful if and only if the intent of the search is realized.
Consider Y a primitive man. Y is hungry and must hunt for his meal. So, he sets out to hunt for a game and thus begins his search for an entity of interest. His search pre-supposes that the game is contained in space (perhaps based on experience or intuition) and that he can identify it when he sees it (say an antelope). Y's search is successful only if he is able to capture the antelope for food because his intent at the beginning of the search was to hunt a game for food. Now if his intent when he left his cave was to sight an antelope then just sighting an antelope constitute a successful search.
All searches are not tangible. Intangible searches look for intangible states of being. An example of intangible search is the search for purpose and meaning.
In the final analysis, the Pj Problem of Interest with respect to any search is of type Identity that is buttressed by containership and realized by the expressions of the other Pj problems.