[Rich &Knight, ch 7 &8]
In the last section we saw how rules could be extended to allow uncertain conclusions to be made. In general dealing with uncertainty and change is a big topic in AI, and the main approaches will be introduced in this section.
Dealing with uncertainty and change in important in AI because:
Dealing with such things isn't too hard to do in an ad hoc way. We can have rules that delete things from working memory when they change, and/or which have rules and facts with numerical certainty factors on them. What is hard is dealing with uncertainty in a principled way. First order predicate logic is inadequate as it is designed to work with information that is complete, consistent and monotonic (this basically means that facts only get added, not deleted from the set of things that are known to be true). There is no straightforward way of using it to deal with incomplete, variably certain, inconsistent and nonmonotonic inferences. (We also cannot easily use it to explicitly represent beliefs about the world, for reasons that should become clear later.) We would like to have a formal, principled, and preferably simple basis for dealing with beliefe, uncertainty and change.
There are two main approaches to dealing with all this. The first is to use a fancier logic. It is important to remember that first order predicate logic is but one logic among many. New logics pop up every day, and most come with a clear, well defined semantics and proof theory. Some of these fancy logics appear to be just what we need to deal with belief, uncertainty and change (though in practice we tend to find that no logic solves all our problems, so people end up picking a suitable logic off the shelf depending on their application).
The second approach is to base things not on a logic, but on probability theory. This too is a well understood theory, with clear results concerning uncertainty. Unfortunately basic probability theory tends to make too many assumptions concerning the availability and reliability of evidence, so we have to be careful how we use it. However, it still provides a good starting point and a way of assessing more ad hoc approaches to uncertainty - are they consistent with classical probability theory, given certain assumptions?
These two approaches will be briefly discussed below, and in much greater depth in the 4th yr AI course.