For static lifted inference algorithms, completeness, i.e., domain liftability, is extensively studied. However, so far no domain liftability results for temporal lifted inference algorithms exist. In this paper, we close this gap. More precisely, we contribute the first completeness and complexity analysis for a temporal lifted algorithm, the socalled lifted dynamic junction tree algorithm (LDJT), which is the only exact lifted temporal inference algorithm out there. To handle temporal aspects efficiently, LDJT uses conditional independences to proceed in time, leading to restrictions w.r.t. elimination orders. We show that these restrictions influence the domain liftability results and show that one particular case while proceeding in time, has to be excluded from FO12 . Additionally, for the complexity of LDJT, we prove that the lifted width is in even more cases smaller than the corresponding treewidth in comparison to static inference.

翻译：对于静态提升推理算法，其完备性（即领域可提升性）已得到广泛研究。然而，迄今为止，尚无关于时序提升推理算法的领域可提升性结果。本文旨在填补这一空白。具体而言，我们首次对一种时序提升算法——即所谓的提升动态联结树算法（LDJT）——进行了完备性与复杂性分析，该算法是目前唯一精确的时序提升推理算法。为高效处理时序方面，LDJT利用条件独立性沿时间维度推进，这导致其在消元顺序方面存在限制。我们证明这些限制会影响领域可提升性结果，并指出在沿时间推进过程中，有一种特定情况必须从一阶二阶逻辑（FO12）中排除。此外，关于LDJT的复杂性，我们证明了相较于静态推理，提升宽度在更多情况下小于对应的树宽度。