布尔函数限制集命题溯因的复杂性
Complexity of Propositional Abduction for Restricted Sets of Boolean Functions
摘要：
溯因推理是非单调推理的一种基本而重要的形式。给定一个解释世界如何运行的知识库，它旨在为一些观察到的现象找到解释。在本文中，我们专注于命题溯因，其中的知识库和表现形式表示的命题公式。决定是否存在解释的问题一般被证明是SigmaP 2-完全的。我们考虑通过限制允许的连接词在公式中的某些集合的布尔函数的变体。我们给出了一个完整的分类的复杂性的所有可观的布尔函数集。通过这种方式，我们确定更容易的情况下，即NP完全和多项式的情况下，我们突出的棘手的来源。此外，我们解决的问题，计数的解释，并绘制一个完整的图片计数的复杂性。
英文摘要：
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional abduction, where the knowledge base and the manifestation are represented by propositional formulae. The problem of deciding whether there exists an explanation has been shown to be SigmaP2-complete in general. We consider variants obtained by restricting the allowed connectives in the formulae to certain sets of Boolean functions. We give a complete classification of the complexity for all considerable sets of Boolean functions. In this way, we identify easier cases, namely NP-complete and polynomial cases; and we highlight sources of intractability. Further, we address the problem of counting the explanations and draw a complete picture for the counting complexity.
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。
