Inclusion logic differs from many other logics of dependence and independence in that it can only describe polynomial-time properties. In this article we examine more closely connections between syntactic fragments of inclusion logic and different complexity classes. Our focus is on two computational problems: maximal subteam membership and the model checking problem for a fixed inclusion logic formula. We show that very simple quantifier-free formulae with one or two inclusion atoms generate instances of these problems that are complete for (non-deterministic) logarithmic space and polynomial time. We also present a safety game for the maximal subteam membership problem and use it to investigate this problem over teams in which one variable is a key. Furthermore, we relate our findings to consistent query answering over inclusion dependencies, and present a fragment of inclusion logic that captures non-deterministic logarithmic space in ordered models.

包含逻辑与许多其他相关性和独立性逻辑的不同之处在于它只能描述多项式时间属性。在本文中，我们更仔细地研究了包含逻辑的句法片段与不同复杂性类别之间的联系。我们的重点是两个计算问题：最大子团队成员和固定包含逻辑公式的模型检查问题。我们展示了具有一个或两个包含原子的非常简单的无量词公式会生成这些问题的实例，这些实例对于（非确定性）对数空间和多项式时间是完整的。我们还为最大子团队成员问题提出了一个安全游戏，并用它来研究这个问题，其中一个变量是关键的团队。此外，我们将我们的发现与包含依赖关系的一致查询回答联系起来，