Abstract We consider coherent choice functions under the recent axiomatisation proposed by De Bock and de Cooman that guarantees a representation in terms of binary preferences, and we discuss how to define conditioning in this framework. In a multivariate context, we propose a notion of marginalisation, and its inverse operation called weak (cylindrical) extension. We combine this with our definition of conditioning to define a notion of irrelevance, and we obtain the irrelevant natural extension in this framework: the least informative choice function that satisfies a given irrelevance assessment.

中文翻译：

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使用选择函数建模认知无关性

摘要 我们考虑最近由 De Bock 和 de Cooman 提出的公理化下的连贯选择函数，它保证了二元偏好的表示，我们讨论了如何在这个框架中定义条件。在多元背景下，我们提出了边缘化的概念，其逆运算称为弱（圆柱）扩展。我们将其与条件的定义相结合来定义不相关的概念，并且我们在该框架中获得了不相关的自然扩展：满足给定的不相关评估的信息最少的选择函数。