Nonmonotonic Reasoning

Lemmings may present new problems for nonmonotonic reasoning.

1. It is a general feature of nonmonotonic reasoning to implicitly infer that the facts being taken into account are all that are relevant to the phenomenon being reasoned about. However, this has not been put into the formalism explicitly. Making it explicit may be important for reasoning about Lemmings. A Lemmings player learns to win a particular game by repeated trying. He uses the fact that the same action in the same situation always has the same result. Formally this is assumption is incorporated in the use of a function result to get a new situation s' = result(e,s), i.e. the new situation is determined by the old situation and the event (action) that occurs in the old situation.

   However, a player uses more than the functionality of the result of an event, because he wants to learn not merely from exact repetitions of the situation but from repetitions of those aspects of the situation that are relevant to the phenomenon he is learning about.

   Therefore, we need to be able to express as a circumscription jumping to the conclusion that we have repeated the relevant aspects of a previously examined situation. In Lemmings, this is related to locality, i.e. it doesn't matter what the lemmings elsewhere in the scene are doing.

2. Something like the philosophers' paradox of the heap comes up in Lemmings, and a solution suggests itself that may have more general application. Suppose a lemming is removed from a bunch of lemmings. We draw the nonmonotonic conclusion that we still have a bunch. If you repeatedly draw this conclusion enough times, one of the conclusions will be false, because you will have eliminated the whole bunch. So what? The reasoning was nonmonotonic and admittedly risky.

   There is a related fact about nonmonotonic reasoning. Suppose for a variable x you infer nonmonotically p(x). Your nonmonotonic logic should be such that this does not allow you to infer , i.e. universal generalization is not allowed.