提出支持数值前提的提升式后继生成方法，解决规划状态爆炸问题。
Lifted Successor Generation in Numeric Planning
- 通过最大团枚举实现变量替换，生成无歧义的地面动作。
- 在23个基准领域中完全正确，仅1个领域存在少量无效动作。
- 首个支持数值前提的提升式生成器，适合研究复杂规划系统。
大多数规划器将用类似一阶语言表述的数值规划任务转化为地面任务表示，但可能导致任务规模指数级膨胀，尤其在难以地面化的任务中。本文扩展了经典规划中的先进提升式后继生成器，以支持数值前提的适用性判断。该方法在替换一致性图中枚举最大团，每个最大团对应一个动作模式的变量替换，生成一个地面动作。通过引入数值前提扩展该图，并在形式化条件下证明生成器的精确性。当条件不满足时，生成器可能包含不适用的地面动作，但可通过最终适用性检查剔除，且不影响完备性。在25个基准领域中，仅有1个领域出现此类情况。据作者所知，当前尚无其他提升式后继生成器支持数值前提，本方法为未来在丰富规划片段上的提升式规划研究提供了可能。
原文摘要 · Abstract (English)
Most planners ground numeric planning tasks, given in a first-order-like language, into a ground task representation. However, this can lead to an exponential blowup in task representation size, which occurs in practice for hard-to-ground tasks. We extend a state-of-the-art lifted successor generator for classical planning to support numeric precondition applicability. The method enumerates maximum cliques in a substitution consistency graph. Each maximum clique represents a substitution for the variables of the action schema, yielding a ground action. We augment this graph with numeric action preconditions and prove the successor generator is exact under formally specified conditions. When the conditions fail, our generator may list inapplicable ground actions; a final applicability check filters these without affecting completeness. However, this cannot happen in 23 of 25 benchmark domains, and it occurs only in 1 domain. To the authors' knowledge, no other lifted successor generator supports numeric action preconditions. This enables future research on lifted planning for a very rich planning fragment.
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