In this paper we present a duality between nonmonotonic consequence relations and well-founded convex geometries. On one side of the duality we consider nonmonotonic consequence relations satisfying the axioms of an infinitary variant of System P, which is one of the most studied axiomatic systems for nonmonotonic reasoning, conditional logic and belief revision. On the other side of the duality we consider well-founded convex geometries, which are infinite convex geometries that generalize well-founded posets. Since there is a close correspondence between nonmonotonic consequence relations and path independent choice functions one can view our duality as an extension of an existing duality between path independent choice functions and convex geometries that has been developed independently by Koshevoy and by Johnson and Dean.

中文翻译：

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非单调结果关系和凸几何之间的离散对偶性

在本文中，我们提出了非单调结果关系和有根据的凸几何之间的对偶性。在二元性的一方面，我们考虑满足系统 P 无限变体公理的非单调结果关系，系统 P 是用于非单调推理、条件逻辑和信念修正的研究最多的公理系统之一。在对偶的另一边，我们考虑了有据可查的凸几何，它们是无限的凸几何，可以推广有根据的偏序集。由于非单调结果关系和路径无关选择函数之间存在密切的对应关系，因此我们可以将我们的对偶性视为路径无关选择函数和由 Koshevoy 和 Johnson 和 Dean 独立开发的凸几何之间现有对偶性的扩展。