改进了非单调推理的近似不动点理论，用更精细的逼近空间提升表达能力。
Approximation Fixpoint Theory with Refined Approximation Spaces
- 引入比区间更精细的逼近空间，扩展传统近似不动点理论
- 解决了原理论在简单案例中的表达局限性
- 适合研究逻辑编程与答案集编程的学者参考
近似不动点理论（AFT）是知识表示中非单调推理形式系统（如逻辑程序设计和答案集编程）的重要理论工具。许多此类形式系统的语义可表征为在特定格上非单调算子的合适不动点。传统AFT在原始格上通过区间进行近似或构造所需不动点。尽管已在多种非单调推理形式中成功应用，但对某些较简单的例子仍存在表达力不足的问题。本文通过将一致AFT扩展至更精细的逼近方式，提出更一般的逼近空间概念，展示其更强的表达能力，并研究不同逼近空间之间的关系。
原文摘要 · Abstract (English)
Approximation Fixpoint Theory (AFT) is a powerful theory covering various semantics of non-monotonic reasoning formalisms in knowledge representation such as Logic Programming and Answer Set Programming. Many semantics of such non-monotonic formalisms can be characterized as suitable fixpoints of a non-monotonic operator on a suitable lattice. Instead of working on the original lattice, AFT operates on intervals in such lattice to approximate or construct the fixpoints of interest. While AFT has been applied successfully across a broad range of non-monotonic reasoning formalisms, it is confronted by its limitations in other, relatively simple, examples. In this paper, we overcome those limitations by extending consistent AFT to deal with approximations that are more refined than intervals. Therefore, we introduce a more general notion of approximation spaces, showcase the improved expressiveness and investigate relations between different approximation spaces.
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