Moinard, Yves and Rolland, Raymond Unexpected and unwanted results of circumscription , AIMSA'90, in Artificial Intelligence IV (methodology, systems, applications) , North-Holland , Albena, Bulg. , 61--70 , sep , 1990 Abstract Circumscription, one of the best known forms of nonmonotonic reasoning, minimizes the extension of some predicates. One problem with circumscription is that it can result in an inconsistency when applied to certain consistent theories. We give some examples proving that, even with simple theories, the second order version of circumscription is more likely to produce such an unwanted result. We give another example showing how a variable predicate may produce an inconsistency. Also, we show that the second order version may be equivalent to such an unexpected result as a finiteness axiom. The more strikingly unexpected results are the cases where the minimization of a predicate ``P'' allows to prove ``for all x, P(x)'', while the original theory did not allow to prove this formula. This may occur with first order and second order versions of circumscription. Then we precise in what meaning ``well-foundedness'' prevents such unexpected or unwanted results. This web site is maintained by René Quiniou using the Weave system from the Caravel project: http://www-caravel.inria.fr. Last modification: 10-07-2011 09:54:25