Yves Moinard and Raymond Rolland Smallest Equivalent Sets for Finite Propositional Formula Circumscription , CL'2000 (International Conference on Computational Logic) , Spinger-Verlag, LNAI , London , Vol. 1861 , 897-911 , jul , 2000 , Document Abstract Circumscription uses classical logic in order to modelize rules with exceptions and implicit knowledge. Formula circumscription is known to be easier to use in order to modelize a situation. We describe when two sets of formulas give the same result, when circumscribed. Two kinds of such equivalence are interesting: the ordinary one (two sets give the same circumscription) and the strong one (when completed by any arbitrary set, the two sets give the same circumscription) which corresponds to having the same closure for logical ``and'' and ``or''. In this paper, we focus on the smallest possible sets in these two cases. We need to revisit the characterization result of formula circumscription. Then, we are able to describe a way to get all the sets equivalent to a given set, and also a % semi-constructive way to get the smallest such sets. These results should help the automatic computation, and also the translation in terms of circumscription of complex situations. 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