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Products of weighted logic programs

机译：加权逻辑程序的乘积

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Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path through a graph or a grammatical derivation, and are given a real-valued score (often interpreted as a probability) that depends on the real weights of the base axioms used in the proof. The desired output is a function over all possible proofs, such as a sum of scores or an optimal score. We describe the PRODUCT transformation, which can merge two weighted logic programs into a new one. The resulting program optimizes a product of proof scores from the original programs, constituting a scoring function known in machine learning as a "product of experts." Through the addition of intuitive constraining side conditions, we show that several important dynamic programming algorithms can be derived by applying PRODUCT to weighted logic programs corresponding to simpler weighted logic programs. In addition, we show how the computation of Kullback-Leibler divergence, an information-theoretic measure, can be interpreted using PRODUCT.
机译：加权逻辑编程是自下而上的逻辑编程的概括，是用于指定动态编程算法的合适框架。在这种设置下，证明对应于算法的输出空间，例如通过图形的路径或语法推导，并根据所使用的基本公理的实际权重获得实值得分（通常解释为概率）。在证明中。期望的输出是所有可能证明（例如分数总和或最佳分数）的函数。我们描述了PRODUCT转换，该转换可以将两个加权逻辑程序合并到一个新的逻辑程序中。生成的程序从原始程序优化了证明分数的乘积，构成了机器学习中称为“专家乘积”的评分功能。通过添加直观的约束条件，我们证明了通过将PRODUCT应用于与更简单的加权逻辑程序相对应的加权逻辑程序，可以得出几种重要的动态编程算法。此外，我们展示了如何使用PRODUCT来解释Kullback-Leibler散度的计算（一种信息理论的度量）。

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