Abstract Reasoning about uncertainty is one of the main cornerstones of Knowledge Representation. Formal representations of uncertainty are numerous and highly varied due to different types of uncertainty intended to be modeled such as vagueness, imprecision and incompleteness. There is a rich body of theoretical results that has been generated for many of these approaches. It is often the case though, that pragmatic tools for reasoning with uncertainty lag behind this rich body of theoretical results. Rough set theory is one such approach for modeling incompleteness and imprecision based on indiscernibility and its generalizations. In this paper, we provide a pragmatic tool for constructively reasoning with generalized rough set approximations that is based on the use of Answer Set Programming ( Asp ). We provide an interpretation of answer sets as (generalized) approximations of crisp sets (when possible) and show how to use Asp solvers as a tool for reasoning about (generalized) rough set approximations situated in realistic knowledge bases. The paper includes generic Asp templates for doing this and also provides a case study showing how these techniques can be used to generate reducts for incomplete Information Systems. Complete, ready to run clingo Asp code is provided in the Appendix, for all programs considered. These can be executed for validation purposes in the clingo Asp solver.

中文翻译：

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使用答案集程序进行粗略推理

摘要 关于不确定性的推理是知识表示的主要基石之一。由于要建模的不确定性的不同类型，例如模糊性、不精确性和不完整性，不确定性的正式表示是多种多样的。许多这些方法已经产生了大量的理论结果。然而，通常情况下，用于不确定性推理的实用工具落后于这些丰富的理论结果。粗糙集理论就是这样一种基于不可分辨性及其泛化来对不完整性和不精确性进行建模的方法。在本文中，我们提供了一种实用工具，用于使用基于答案集编程 (Asp) 的广义粗糙集近似进行建设性推理。我们将答案集解释为清晰集的（广义）近似（如果可能），并展示如何使用 Asp 求解器作为推理位于现实知识库中的（广义）粗糙集近似的工具。本文包括用于执行此操作的通用 Asp 模板，还提供了一个案例研究，展示了如何使用这些技术为不完整的信息系统生成归约。对于所有考虑的程序，附录中提供了完整的、可以运行的 clingo Asp 代码。这些可以在 clingo Asp 求解器中执行以进行验证。本文包括用于执行此操作的通用 Asp 模板，还提供了一个案例研究，展示了如何使用这些技术为不完整的信息系统生成归约。对于所有考虑的程序，附录中提供了完整的、可以运行的 clingo Asp 代码。这些可以在 clingo Asp 求解器中执行以进行验证。本文包括用于执行此操作的通用 Asp 模板，还提供了一个案例研究，展示了如何使用这些技术为不完整的信息系统生成归约。对于所有考虑的程序，附录中提供了完整的、可以运行的 clingo Asp 代码。这些可以在 clingo Asp 求解器中执行以进行验证。