Moinard, Yves and Rolland, Raymond Equivalent sets of formulas for circumscriptions , ECAI'2000 (European Conf. on Artificial Intelligence) , IOS Press, Amsterdam , Berlin , 479-483 , aug , 2000 , Document Abstract Circumscription is a way of using classical logic in order to modelize rules with exceptions and implicit knowledge. Formula circumscription is known to be much easier to use in order to modelize a given situation. We describe precisely when two sets of formulas give the same result, when circumscribed. We show that two kinds of such equivalence are interesting: the ordinary equivalence (two sets give the same circumscription) and the strong equivalence (when completed by any arbitrary set, the two sets give the same circumscription). The strong equivalence gives the simplest result: it corresponds to having the same closure for logical ``and'' and ``or''. We give also the answer for the ordinary equivalence, showing that there exists also always a greatest set. Our answer to the problem for the case of propositional formula circumscription is exhaustive. This gives rise to various notions of formulas positive with respect to a given set of formulas. We show that for ordinary propositional circumscription, things remain simple enough to allow us to provide a syntactical definition of all these equivalent sets. 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