Quantitative extensions of logic programming often require the solution of so called second level inference tasks, i.e., problems that involve a third operation, such as maximization or normalization, on top of addition and multiplication, and thus go beyond the well-known weighted or algebraic model counting setting of probabilistic logic programming under the distribution semantics. We introduce Second Level Algebraic Model Counting (2AMC) as a generic framework for these kinds of problems. As 2AMC is to (algebraic) model counting what forall-exists-SAT is to propositional satisfiability, it is notoriously hard to solve. First level techniques based on Knowledge Compilation (KC) have been adapted for specific 2AMC instances by imposing variable order constraints on the resulting circuit. However, those constraints can severely increase the circuit size and thus decrease the efficiency of such approaches. We show that we can exploit the logical structure of a 2AMC problem to omit parts of these constraints, thus limiting the negative effect. Furthermore, we introduce and implement a strategy to generate a sufficient set of constraints statically, with a priori guarantees for the performance of KC. Our empirical evaluation on several benchmarks and tasks confirms that our theoretical results can translate into more efficient solving in practice. Under consideration for acceptance in TPLP.

本文介绍了用于解决量化扩展逻辑编程中的第二级推理任务的算法框架Second Level Algebraic Model Counting (2AMC)，探讨了使用知识编译技术降低处理效率时的需要考虑变量阶数限制问题，进一步提出并实现了一种静态生成约束的策略，并在多个任务和基准测试上评估了有效性。

高效知识编译: 超越带权模型计数