测度论加权模型积分
Measure Theoretic Weighted Model Integration
摘要：
加权模型计数（WMC）是一个流行的框架，执行概率推理与离散随机变量。最近，WMC已扩展到加权模型集成（WMC），以额外处理连续变量。在它们的核心，计算问题包括加权逻辑公式的积分和求和。从理论的角度来看，WMC中已经存在的加权求和公式与黎曼积分相结合，从而制定了WMC。一个更有原则的方法来整合，这是植根于测度理论，是勒贝格积分。勒贝格积分允许一个对待离散和连续变量在平等的基础上的原则方式。我们提出了一个理论上健全的措施理论制定加权模型集成，这自然减少到加权模型计数连续变量的情况下。而不是把加权模型集成作为加权模型计数的扩展，WMC出现在我们的配方中作为一个特殊的情况下的计数。
英文摘要：
Weighted model counting (WMC) is a popular framework to perform probabilistic inference with discrete random variables. Recently, WMC has been extended to weighted model integration (WMI) in order to additionally handle continuous variables. At their core, WMI problems consist of computing integrals and sums over weighted logical formulas. From a theoretical standpoint, WMI has been formulated by patching the sum over weighted formulas, which is already present in WMC, with Riemann integration. A more principled approach to integration, which is rooted in measure theory, is Lebesgue integration. Lebesgue integration allows one to treat discrete and continuous variables on equal footing in a principled fashion. We propose a theoretically sound measure theoretic formulation of weighted model integration, which naturally reduces to weighted model counting in the absence of continuous variables. Instead of regarding weighted model integration as an extension of weighted model counting, WMC emerges as a special case of WMI in our formulation.
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