发表机构
Jönköping University; Jönköping University Linköping University; Linköping University（约克灵根大学; 约克灵根大学-林霍姆大学; 林霍姆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究命题归结中给定解释集能否表示其他解释的问题，先从经典复杂性角度分类，再研究参数化复杂性，发现完整分类需解决编码理论中覆盖半径问题的参数化复杂性，揭示编码理论与非单调推理新联系。
AI 中文摘要
命题归结问题是一种著名的非单调推理形式，要求找到给定表现的解释。最近，出现了大量关于解空间更精细问题的研究成果，而非仅关注单个解。例如，可能有兴趣在解空间中找到彼此足够远的两个解（多样解）。本文考虑一个相关的表示问题，即给定的一组解释S是否能表示任何其他解释（即它们的对称差是否小于给定的k）。首先从经典复杂性角度研究该问题并获得完整分类。虽然只有少数情况是易处理的，但与经典归结相比，复杂性增加往往小于预期。然后研究了几个参数的参数化复杂性，得到了新的易处理和难处理情况。有趣的是，完整的参数化复杂性分类需要解决编码理论中的覆盖半径问题的参数化复杂性。据我们所知，编码理论与非单调推理之间以前未建立有用的关系，但在询问关于解空间的更复杂问题时，这种联系似乎变得很重要。
英文摘要
The propositional abduction problem is a well-known form of non-monotonic reasoning where we are asked to find an explanation of a given manifestation. Recently, there has been an influx of results asking more refined questions about the solution space rather than only individual solutions. For example, we might be interested in finding two solutions that are sufficiently far from each other (diverse solutions) in the solution space. In this paper we consider a related representation question where we ask if a given set of explanations S can represent any other explanation (that is, whether their symmetric difference is smaller than a given k). We first study this problem from a classical complexity perspective and obtain a complete classification. While only a handful of cases are tractable, the increase in complexity compared to classical abduction is often smaller than expected. We then study the parameterized complexity for several parameters and obtain new tractable and hard cases. Interestingly, a full parameterized complexity classification would require resolving the parameterized complexity of the covering radius problem from coding theory. To the best of our knowledge, no useful relationship between coding theory and non-monotonic reasoning has previously been established, but such connections seemingly become important when asking more complex questions about solution spaces.
CommentsIn Proceedings ICLP 2026, arXiv:2607.17707
Journal refEPTCS 450, 2026, pp. 1-14
