G53KRR handout on defaults. Defaults or default rules as opposed to normal or categorical rules are ways of drawing conclu- Summary: G53KRR handout on defaults. Defaults or default rules as opposed to normal or categorical rules are ways of drawing conclu- sions which are justified unless there is some explicit reason to believe otherwise. So normal rule will say `if x is a natural number then it is greater or equal to 0' and this is really true without exceptions for all natural numbers. A default rule would say `if x is a bird then it can fly (unless there are good reasons to believe otherwise)'. In other words, if all we know about x is that it is a bird, then it is reasonable to conclude that it can fly. Later however we may discover that it is a special kind of bird which does not fly. Non-monotonicity In classical reasoning, entailment is monotonic: if KB1 |= and KB1 KB2, then KB2 |= . In other words, if is entailed by KB1 and we add more sentences to KB1, will still be entailed by the resulting knowledge base; the larger the knowledge base, the more consequences it has: if KB1 KB2 then Consequences(KB1) Consequences(KB2). Default reasoning is nonmonotonic. If we have KB1 = { `Birds normally can fly', `Tweety is a bird' } then we can derive by default that Tweety can fly. However, if we learn more about Tweety, for example that it is a penguin, then `Tweety can fly' no longer follows even by default. The question is, how to make this work formally (define what are valid default conse- quences)? In this lecture, consider three approaches: closed-world assumption, circumscription, default logic. Next lecture (related): subjective probability. Closed-world reasoning Closed-world assumption (CWA): if an atomic sentence is not in the knowledge base, it is assumed to be false. (Like negation as failure in production rule systems: Collections: Computer Technologies and Information Sciences