Solving a decision theory problem usually involves finding the actions, among a set of possible ones, which optimize the expected reward, possibly accounting for the uncertainty of the environment. In this paper, we introduce the possibility to encode decision theory problems with Probabilistic Answer Set Programming under the credal semantics via decision atoms and utility attributes. To solve the task we propose an algorithm based on three layers of Algebraic Model Counting, that we test on several synthetic datasets against an algorithm that adopts answer set enumeration. Empirical results show that our algorithm can manage non trivial instances of programs in a reasonable amount of time. Under consideration in Theory and Practice of Logic Programming (TPLP).

翻译：解决决策理论问题通常涉及在一组可能的行动中，找到能够优化期望奖励的行动，并可能需要考虑环境的不确定性。本文提出了一种通过决策原子和效用属性，在置信语义下使用概率答案集编程对决策理论问题进行编码的方法。为解决该任务，我们提出了一种基于三层代数模型计数的算法，并在多个合成数据集上，将其与采用答案集枚举的算法进行了对比测试。实验结果表明，我们的算法能够在合理时间内处理非平凡的程序实例。本文已提交至《逻辑编程理论与实践》（TPLP）期刊审议。