为混合约束求解提供理论基础，提升ASP在真实问题中的表达能力
Hybrid Answer Set Programming: Foundations and Applications
- 基于HT_c逻辑扩展，构建混合ASP的统一理论框架
- 首次系统定义混合约束逻辑的语义与推理机制
- 适用于产品配置等含数值约束的实际场景
答案集编程（ASP）是解决现实世界问题的强大工具，但许多问题涉及数值变量和复杂约束，超出标准ASP求解器的能力。混合求解器如CLINGCON和CLINGO[DL]通过针对特定约束使用专门方法来应对，但缺乏坚实的理论基础。本文通过引入带约束的这里-那里逻辑（HT_c），作为传统这里-那里逻辑（HT）及其非单调扩展均衡逻辑的延伸，首次建立了混合ASP的理论基础。目前HT已成为ASP的逻辑根基，而HT_c等扩展对混合ASP具有类似作用。然而，这些逻辑在基本性质及求解器实现中的应用仍存在诸多未解问题。具备对这些混合逻辑的正式理解，有助于揭示实际问题的内在结构，改进其在ASP中的建模方式。以产品配置为例，展示了该理论的实际应用价值。
原文摘要 · Abstract (English)
Answer Set Programming (ASP) is a powerful tool for solving real-world problems. However, many problems involve numeric values and complex constraints beyond the capabilities of standard ASP solvers. Hybrid solvers like CLINGCON and CLINGO[DL] address this by using specialized methods for specific constraints. However, these solvers lack a strong theoretical foundation. This issue has first been addressed by introducing the Logic of Here-and-There with constraints (HT_c) as an extension of the Logic of Here-and-There (HT) and its non-monotone extension Equilibrium Logic. Nowadays, HT serves as a logical foundation for ASP and has facilitated a broader understanding of this paradigm. The idea is that HTC (and other extensions) play an analogous role for hybrid ASP. There remain many open questions about these logics regarding their fundamental characteristics as well as their practical use in solvers, ie. how they can guide the implementation. Having a formal understanding of these hybrid logics is also needed to better understand the inherent structure of the (real-world) problems they are applied to and to improve their representations in ASP. As an example of an application of ASP we use product configuration.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。