What is a (non-constructive) non-monotone logical system?

Standard logical systems enjoy the properties of reflexivity, idempotence, monotony. The latter property has been dropped in artificial intelligence s ystems devoted to model drawing tentative conclusions. Up to now, all attem pts to characterizing these so-called non-monotone systems are unsatisfacto ry because these attempts either take absence of monotony as their major ch aracteristics or give a collection of properties that also tolerate monoton e systems. In contrast, we introduce in the context of non-constructive log ics a characterization that indeed furnishes necessary and sufficient condi tions for a system to be non-monotone. (C) 2000 Elsevier Science B.V. All r ights reserved.