Another way to search is called backwards or regression search, in which we start at the goal. So we take the description of the goal state, C1 is at JFK and C2 is at SFO. So that’s the goal state. And notice that that’s the complete goal state. It’s not that I left out all the other facts about the state. Is that, that’s all that’s known about this state is that these two propositions are true and all the others can be anything you want. And now we can start searching backwards. We can say, what actions would lead to that state? Now, remember in problem solving we did have that option of searching backwards. If there was a single goal state, we could say, what other arcs are coming into that goal state? But here, this goal state doesn’t represent a single state, it represents a whole family of states. So with different values for all the other variables. And so, we can’t just look at that. But what we can do, is to look at the definition of possible actions that will result in this goal. So let’s look at it one at a time. Let’s first look at what actions could result at C1, JFK. Well, we look at our action schema, and there’s only one action schema that adds an at, and that would be the unload schema. So unload of CPA adds CA, and so what we will know is if we want to achieve this, then we would have to do an unload where the C variable would have to be C1. The P variable is still unknown, it could be any plane. And the A variable has to be JFK. So, notice what we done here, we have this representation in terms of logical formula that allows us to specify a goal as a set of many world states. And we can also use that same representation to represent an arrow here, not as a single action, but as a set of possible actions. So this is representing all possible actions for any plane P of unloading cargo at the destination. And then we can regress this state over this operator, and now we have another representation of this state here. But just as this state was uncertain, not all the variables were known, this state, too, will be uncertain. For example, we won’t know anything about what plane P is involved. And now, we continue searching backwards until we get to a state where enough of the variables are filled in, and where we match against the initial state. And then, we have our solution, we found it going backwards, but we can apply the solution going forwards.