Delgrande's knowledge level account of forgetting provides a general approach to forgetting syntax elements from sets of formulas with links to many other forgetting operations, in particular, to Boole's variable elimination. On the other hand, marginalisation of epistemic states is a specific approach to actively reduce signatures in more complex semantic frameworks, also aiming at forgetting atoms that is very well known from probability theory. In this paper, we bring these two perspectives of forgetting together by showing that marginalisation can be considered as an extension of Delgrande's approach to the level of epistemic states. More precisely, we generalize Delgrande's axioms of forgetting to forgetting in epistemic states, and show that marginalisation is the most specific and informative forgetting operator that satisfies these axioms. Moreover, we elaborate suitable phrasings of Delgrande's concept of forgetting for formulas by transferring the basic ideas of the axioms to forgetting formulas from epistemic states. However, here we show that this results in trivial approaches to forgetting formulas. This finding supports the claim that forgetting syntax elements is essentially different from belief contraction, as e.g. axiomatized in the AGM belief change framework.
翻译:Delgrande 的知识水平的遗忘说明提供了一种一般性的方法,将一系列公式中的语法要素与许多其他忘记行动相联系,尤其是布勒的变数消除。另一方面,在更复杂的语义框架里,迷信国家的边缘化是一种具体的方法,目的是积极减少签名,目的也是要忘记从概率理论中非常广为人知的原子。在本文件中,我们通过显示边缘化可被视为Delgrande方法向认知状态水平的延伸,将这两种观点结合起来。更确切地说,我们概括了Delgrande忘记在认知状态中遗忘的原教旨,并表明边缘化是最具体和知情地忘记满足这些原教义的操作者。此外,我们拟订了Delgrande的忘记公式概念的适当语句,将轴的基本思想转移给记忆状态国家的公式。然而,我们在这里展示了这种忽略公式的琐碎方法的结果。这种发现支持了放弃原教法框架的信念,即放弃原教法框架是不同的。