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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:

  

Source: Alechina, Natasha - School of Computer Science, University of Nottingham

 

Collections: Computer Technologies and Information Sciences