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Do inferential processes affect uncertainty frameworks? (English) Zbl 1315.68235
Summary: This paper studies the connections among different (comparative or numerical) degrees of belief. In particular we consider, in turn, a comparative probability or possibility on a given Boolean algebra and we prove that their upper extensions to a different Boolean algebra are, respectively, a comparative plausibility or possibility. On the other hand, in general the upper extension of a comparative necessity is simply a comparative capacity. Moreover, by considering a suitable condition of weak logical independence between the two Boolean algebras, we prove that the upper ordinal relation is a comparative possibility in all the aforementioned cases. We consider specifically also the lower ordinal relations, since they may not be the comparative dual relation of the upper ones.

68T37 Reasoning under uncertainty in the context of artificial intelligence
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