When playing WaterWorld, what particular propositions are involved? To consider this, we think of a generic board, and wonder what the underlying statements are. They are statements like "location A contains a pirate" ("A − unsafe"), "location G has 2 adjacent pirates" ("G − has − 2") and so on. Each of these statements may be true or false, depending on the particular board in question.
Here are all the WaterWorld propositions (Section 6.5) that we'll use.
Remember that B − unsafe doesn't mean "I'm not sure whether or not B is safe"; rather it means "B is unsafe" it contains a pirate. You may not be sure whether (the truth of) this proposition follows what you see, but in any given board the variable has one of two values, true or false.
Every WaterWorld board has the same set of propositions to describe it: A − unsafe, B − has − 2, etc. However, different boards will have different underlying values of those propositions.