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The notion of the rational closure of a positive knowledge base K ofconditional assertions &thetas;_i |∼ &phis;_i(standing for if &thetas;_i then normally &phis;_i) was first introduced by Lehmann (1989) and developedby Lehmann and Magidor (1992). Following those authors we would also argue that the rational closure is, in a strong sense, the minimal information, or simplest, rational consequence relation satisfying K. In practice,however, one might expect a knowledge base to consist not just of positiveconditional assertions, &thetas;_i |∼ &phis;_i, but also negative conditional assertions, &thetas;__i |∼ &phis;_i (standing for{if &thetas;_i then normally &phis;_i}).Restricting ourselves to a finite language we show that the rational closure still exists for satisfiable knowledge bases containing bothpositive and negative conditional assertions and has similar properties tothose exhibited in Lehmann and Magidor (1992). In particular an algorithm in Lehmann and Magidor (1992) which constructs the rational closure can beadapted to this case and yields, in turn, completeness theorems for theconditional assertions entailed by such a mixed knowledge base.