摘要翻译:
Bistarelli,Montanari和Rossi\cite提出的基于半环的约束满足问题(semiring CSPs)是一个非常普遍的软约束框架。本文提出了一种利用半环同态的软约束抽象方案。对于具体问题的最优解,其思想是先对抽象问题进行研究,找出其最优解,然后再用它们来解决具体问题。特别地,我们证明了映射保持最优解当且仅当它是一个反映序的半环同态。另外,对于半环同态$\alpha$和$S$上的问题$P$,如果$t$在$\alpha(P)$中是最优的,则存在$P$的最优解$\bar{t}$,使得$\bar{t}$与$\alpha(P)$中的$t$具有相同的值。
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英文标题:
《Soft constraint abstraction based on semiring homomorphism》
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作者:
Sanjiang Li and Mingsheng Ying
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最新提交年份:
2007
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分类信息:
一级分类:Computer Science 计算机科学
二级分类:Artificial Intelligence 人工智能
分类描述:Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域,除了视觉、机器人、机器学习、多智能体系统以及计算和语言(自然语言处理),这些领域有独立的学科领域。特别地,包括专家系统,定理证明(尽管这可能与计算机科学中的逻辑重叠),知识表示,规划,和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要:
The semiring-based constraint satisfaction problems (semiring CSPs), proposed by Bistarelli, Montanari and Rossi \cite{BMR97}, is a very general framework of soft constraints. In this paper we propose an abstraction scheme for soft constraints that uses semiring homomorphism. To find optimal solutions of the concrete problem, the idea is, first working in the abstract problem and finding its optimal solutions, then using them to solve the concrete problem. In particular, we show that a mapping preserves optimal solutions if and only if it is an order-reflecting semiring homomorphism. Moreover, for a semiring homomorphism $\alpha$ and a problem $P$ over $S$, if $t$ is optimal in $\alpha(P)$, then there is an optimal solution $\bar{t}$ of $P$ such that $\bar{t}$ has the same value as $t$ in $\alpha(P)$.
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PDF链接:
https://arxiv.org/pdf/0705.0734