演绎非单调推理运算：反序表示
Deductive Nonmonotonic Inference Operations: Antitonic Representations
摘要：
我们提供了那些非单调推理操作C的特征，对于这些非单调推理操作C，C（X）可以被描述为X的所有逻辑后果的集合以及反单调地依赖于X的一些附加假设S（X）的集合（即，X是Y的子集意味着S（Y）是S（X）的子集）。所表示的操作的确切特征在于性质，其中大部分已在Freund-Lehmann（cs.AI/0202031）研究。还提供了类似的右吸收和累积操作的特征。对于累积操作，我们的结果与弗罗因德的结果非常吻合。然后，我们讨论了扩展有限操作无穷操作的一个典型的方式，并讨论了共紧性。我们的结果提供了一个令人满意的概念，伪紧性，推广到演绎非单调操作的概念，紧凑的单调操作。它们还提供了一个替代的，更优雅和更一般的，证明存在一个无穷演绎扩展的任何有限演绎操作（定理7.9弗罗因德-莱曼）。
英文摘要：
We provide a characterization of those nonmonotonic inference operations C for which C(X) may be described as the set of all logical consequences of X together with some set of additional assumptions S(X) that depends anti-monotonically on X (i.e., X is a subset of Y implies that S(Y) is a subset of S(X)). The operations represented are exactly characterized in terms of properties most of which have been studied in Freund-Lehmann(cs.AI/0202031). Similar characterizations of right-absorbing and cumulative operations are also provided. For cumulative operations, our results fit in closely with those of Freund. We then discuss extending finitary operations to infinitary operations in a canonical way and discuss co-compactness properties. Our results provide a satisfactory notion of pseudo-compactness, generalizing to deductive nonmonotonic operations the notion of compactness for monotonic operations. They also provide an alternative, more elegant and more general, proof of the existence of an infinitary deductive extension for any finitary deductive operation (Theorem 7.9 of Freund-Lehmann).
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