用线性排序解决受限选择问题，支持最小值作为备选方案。
Axiomatics of Restricted Choices by Linear Orders of Sets with Minimum as Fallback
- 通过集合上的线性序构造受限选择函数
- 即使有最小值备选，仍能保证选择函数存在
- 适用于知识更新与抽象论证等场景
我们研究如何利用线性序来实现受限选择函数，即候选集并非所有备选项的全集。在受限情形下，仅通过备选项间的二元关系构造选择函数并不总是可行。然而，我们证明可通过集合上的线性序始终构造出有效的选择函数，即使将最小元素作为默认备选也成立。本文给出了该类选择函数的一般情形及并封闭输入限制下的公理体系。受限选择结构在知识表示与推理中有应用，此处讨论其在理论更新和抽象论证中的用途。
原文摘要 · Abstract (English)
We study how linear orders can be employed to realise choice functions for which the set of potential choices is restricted, i.e., the possible choice is not possible among the full powerset of all alternatives. In such restricted settings, constructing a choice function via a relation on the alternatives is not always possible. However, we show that one can always construct a choice function via a linear order on sets of alternatives, even when a fallback value is encoded as the minimal element in the linear order. The axiomatics of such choice functions are presented for the general case and the case of union-closed input restrictions. Restricted choice structures have applications in knowledge representation and reasoning, and here we discuss their applications for theory change and abstract argumentation.
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