There are four missionaries and four cannibals. The problem is now unsolvable. In ordinary logic, adding sentences that there are four of each produces a contradiction. Belief revision systems ought to make the correct change. Actually what is regarded as an object is the sense of the original statement, since people ordinarily don't remember the words used.
Proofs of impossibility take the following form.
Choose a predicate formula on situations. Show and . Thus you can't get out of the situations satisfying , and the goal isn't included. The simplest is a disjunction of specific locations of the missionaries and cannibals in the reachable situations, but this disjunction is long, and it is very likely possible to do better. We can regard the argument that four can't cross as a kind of elaboration.