What's Wrong with Non-Monotonic Logic?

In this paper ' I ask, and attempt to answer, the following question : What's Wrong with Non-Monotonic Logic? The answer, briefly' is that the motivation behind the wonderfully impressive work involved in its development is based on a confusion of proof-theoretic with epistemological issues.What's wrong with non-monotonic logic (and fo! that matter, with the logic of default reasoning)? The first question we should ask is: What's supposed to be wrong with " standard " , monotonic logic? In recent-and extremely impressive-work, Doyle and McDermott [ 1 I, McDermott C21, and Reiter C31 have argued that classical logic-in virtue of its monotoniqity-is incapable of adequately capturing or representing certain crucial features of real live reasoning and inference. In particular' they note that our knowledge is always incomplete, and is almost always known to be so ; that, in pursuing our goals-both practical and theoretical-we are forced to make assumptions or to draw conclusions on the basis of incomplete evidence ; conclusions and assumptions which we may have to withdraw in the light of either new evidence or further cogitation on what we already believe. An essential point here is that new evidence or new inference may lead us to reject previously held beliefs, especially those that we knew to be inadequately supported or merely presumptively assumed. In sum, our theories of the world are revisable; and thus our attitudes towards at least some our beliefs must likewise be revisable. Now what has all this to do with logic and its monotonicity? Both Reiter and Doyle-McDermott characterize the monotonicity of standard logic in syntactic or proof-theoretic terms. If A and B are two theories, and A is a subset of B, then the ' To remedy this lack, Doyle and McDermott introduce into an otherwise standard first order language a modal operator " M " which, they say, is to be read as " It is consistent with everything that is believed that... " (Reiter's " M " , which is not a symbol of the object language, is also supposed to be read " It is consistent to assume that.. ". I think there is some unclarity on Reiter's part about his " M ". He speaks of it in ways conducive to interpreting it as a metalinguistic predicate on sentences of the object language ; and hence not as an operator at all, either object-language or metalanguage. So his …