判定逻辑约束问题的一般方法
A general method for deciding about logically constrained issues
摘要：
给出了一个一般的方法，用于修改程度的信念，并达成一致的决策系统的逻辑约束的问题。与其他关于信念修正的作品相比，这里的约束被假设为固定的。该方法有两个变体，彼此的对偶，其修改的置信度分别高于和低于原始的。上（上）最低的[resp.]修正的置信度被唯一地表征为最低的[resp.]。最高的，最小的，最大的，最大的，最小最小-最大]操作由逻辑约束确定。在这两种变体中，在命题的修改的置信度和其否定的置信度之间进行平衡，导致确保与逻辑约束一致的决策。这些决定被确保与应用于原始置信度的多数准则一致，只要这给出了一致的结果。它们也被确保满足关于任何特定问题的一致性的属性，以及关于原始置信度的单调性的属性。该方法在某些特殊领域的应用归结为已经建立或日益被接受的方法，如聚类分析的单链接方法和优先投票的路径方法。
英文摘要：
A general method is given for revising degrees of belief and arriving at consistent decisions about a system of logically constrained issues. In contrast to other works about belief revision, here the constraints are assumed to be fixed. The method has two variants, dual of each other, whose revised degrees of belief are respectively above and below the original ones. The upper [resp. lower] revised degrees of belief are uniquely characterized as the lowest [resp. highest] ones that are invariant by a certain max-min [resp. min-max] operation determined by the logical constraints. In both variants, making balance between the revised degree of belief of a proposition and that of its negation leads to decisions that are ensured to be consistent with the logical constraints. These decisions are ensured to agree with the majority criterion as applied to the original degrees of belief whenever this gives a consistent result. They are also also ensured to satisfy a property of respect for unanimity about any particular issue, as well as a property of monotonicity with respect to the original degrees of belief. The application of the method to certain special domains comes down to well established or increasingly accepted methods, such as the single-link method of cluster analysis and the method of paths in preferential voting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
