The Frame Problem and the Three Missionaries

McCarthy (in Dennett 1984, p161) describes this aspect of the frame problem with the famous puzzle of the missionaries and the cannibals:

"Three missionaries and three cannibals come to a river, A rowboat that seats two is available. If the cannibals ever outnumber the missionaries on either bank of the river, the missionaries will be eaten. How shall they cross the river? Obviously the puzzler is expected to devise a strategy of rowing the boat back and forth that gets them all across and avoids disaster ...

Imagine giving someone the problem, and after he puzzles for a while, he suggests going upstream half a mile and crossing on a bridge. 'What bridge?' you say. 'No bridge is mentioned in the statement of the problem.' And this dunce replies, 'Well, they don't say there isn't a bridge.' You look at the English and even at the translation of the English into first order logic, and you must admit that 'they don't say' there is no bridge. So you modify the problem to exclude bridges and pose it again, and the dunce proposes a helicopter, and after you exclude that, he proposes a winged horse or that the others hang onto the outside of the boat while two row.

You now see that while a dunce, he is an inventive dunce. Despairing of getting him to accept the problem in the proper puzzler's spirit, you tell him the solution. To your further annoyance, he attacks your solution on the grounds that the boat might have a leak or lack oars. After you rectify that omission from the statement of the problem, he suggests that a sea monster may swim up the river and may swallow the boat. Again you are frustrated, and you look for a mode of reasoning that will settle his hash once and for all."

McCarthy's idea illustrates that when we think about a puzzle or a real-life problem we (almost instinctively) know the frame of the problem; but we can achieve a solution (and even prove that it is a solution to that problem), and then discover our solution invalidated by the addition of a new element to the posing of the problem; e.g. 'I forgot to tell you - there are no oars'. An artificial system with a well-stocked compendium of frames appropriately linked to each other and to the impingements of the world via its perceptual organs, would face the world with an elaborate system of what might be called habits of attention and benign tendencies to leap to particular sorts of conclusions in particular sorts of circumstances.

The frame problem may not be a problem that humans have to solve as often as at first it appears if most of what we do is actually unconscious and is controlled by specific routines that are learned almost by rote. Thus McCrone suggests that over a lifetime of conscious learning the brain accumulates thick strata of local routines - habits of perception and reaction that allow most things to be processed swiftly and automatically (McCrone 1999). Only when one of these routines struck a snag would we switch to a more global and exploratory form of reaction; nevertheless we would then be faced with the frame problem.

The frame problem is a serious hurdle facing the designers of intelligent systems. There, are arguably, however, even more serious problems facing strong AI; one of these - the Chinese Room problem posed by Searle - is related to the real nature of computation.