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Moinard, Yves and Rolland, Raymond
Ensembles de formules équivalents pour la circonscription
, RFIA'2000 : Reconnaissance des Formes et Intelligence Artificielle
, Paris
, II: 189--198
, feb
, 2000
, Document
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Abstract
Circumscription is a way to define exceptions inside classical logic. We describe when two sets of formulas give the same formula circumscription. Two equivalences 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). The strong equivalence corresponds to having the same closure for logical ``and'' and ``or''. Our study is exhaustive in the propositional case. Even for the ordinary equivalence, we show that there exists always a greatest set equivalent to a given set, and we provide a criterion for detecting equivalences, criterion which is purely syntactical when we start from an ordinary circumscription. This gives rise to various notions of ``formulas positive with respect to a given set of formulas''.
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