In the last decade, there has been increasing interest in extensions of answer set programming (ASP) that cater for quantitative information such as weights or probabilities. A wide range of quantitative reasoning tasks for ASP and logic programming, among them probabilistic inference and parameter learning in the neuro-symbolic setting, can be expressed as algebraic answer set counting (AASC) tasks, i.e., weighted model counting for ASP with weights calculated over some semiring, which makes efficient solvers for AASC desirable. In this article, we present ▪, a new solver for AASC that pushes the limits of efficient solvability. Notably, ▪ provides improved performance compared to the state of the art in probabilistic inference by exploiting three insights gained from thorough theoretical investigations in our work. Namely, we consider the knowledge compilation step in the AASC pipeline, where the underlying logical theory specified by the answer set program is converted into a tractable circuit representation, on which AASC is feasible in polynomial time. First, we provide a detailed comparison of different approaches to knowledge compilation for programs, revealing that translation to propositional formulas followed by compilation to sd-DNNF seems favorable. Second, we study how the translation to propositional formulas should proceed to result in efficient compilation. This leads to the second and third insight, namely a novel way of breaking the positive cyclic dependencies in a program, called -Unfolding, and an improvement to the Clark Completion, the procedure used to transform programs without positive cyclic dependencies into propositional formulas. Both improvements are tailored towards efficient knowledge compilation. Our empirical evaluation reveals that while all three advancements contribute to the success of ▪, -Unfolding improves performance significantly by allowing us to handle cyclic instances better.

中文翻译：

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aspmc：代数答案集计数的新领域

在过去的十年中，人们对答案集编程 (ASP) 的扩展越来越感兴趣，以适应权重或概率等定量信息。 ASP 和逻辑编程的各种定量推理任务，其中包括神经符号设置中的概率推理和参数学习，可以表示为代数答案集计数 (AASC) 任务，即计算权重的 ASP 的加权模型计数在一些半环上，这使得 AASC 的高效求解器成为理想的选择。在本文中，我们将介绍 ▪ 一种新的 AASC 求解器，它突破了高效求解的极限。值得注意的是，▪ 通过利用我们工作中彻底的理论研究中获得的三个见解，与概率推理的最新技术相比，提供了改进的性能。也就是说，我们考虑 AASC 管道中的知识编译步骤，其中答案集程序指定的底层逻辑理论被转换为易于处理的电路表示，在该表示上 AASC 在多项式时间内可行。首先，我们对程序知识编译的不同方法进行了详细比较，表明翻译为命题公式然后编译为 sd-DNNF 似乎是有利的。其次，我们研究如何翻译命题公式以实现有效的编译。这导致了第二个和第三个见解，即一种打破程序中正循环依赖关系的新方法，称为“展开”，以及对克拉克完成的改进，该过程用于将没有正循环依赖关系的程序转换为命题公式。这两项改进都是为了高效的知识编译而定制的。我们的实证评估表明，虽然所有三项进步都有助于 ▪ 的成功，但 -Unfolding 使我们能够更好地处理循环实例，从而显着提高了性能。