So far, when we have assumed that if the preconditions of a rule hold, then the conclusion will certainly hold. In fact, most of our rules have looked pretty much like logical implications, and the ideas of forward and backward reasoning also apply to logic-based approaches to knowledge representation and inference.
Of course, in practice you rarely conclude things with absolute certainty. Usually we want to say things like ``If Alison is tired then there's quite a good chance that she'll be in a bad mood''. To allow for this sort of reasoning in rule-based systems we often add certainty values to a rule, and attach certainties to any new conclusions. We might conclude that Alison is probably in a bad mood (maybe with certainty 0.6). The approaches used are generally loosely based on probability theory, but are much less rigorous, aiming just for a good guess rather than precise probabilities. We'll talk about this more in a later lecture.