The expressive power of interval temporal logics (ITLs) makes them really fascinating, and one of the most natural choices as specification and planning language. However, for a long time, due to their high computational complexity, they were considered not suitable for practical purposes. The recent discovery of several computationally well-behaved ITLs has finally changed the scenario. In this paper, we investigate the finite satisfiability and model checking problems for the ITL D featuring the sub-interval relation, under the homogeneity assumption (that constrains a proposition letter to hold over an interval if and only if it holds over all its points). First we prove that the satisfiability problem for D, over finite linear orders, is PSPACE-complete; then we show that its model checking problem, over finite Kripke structures, is PSPACE-complete as well. The paper enrich the set of tractable interval temporal logics with a meaningful representative.

中文翻译：

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同质性假设下子区间逻辑的可满足性及模型检验

间隔时间逻辑 (ITL) 的表达能力使它们非常迷人，并且是作为规范和规划语言的最自然的选择之一。然而，长期以来，由于它们的高计算复杂度，它们被认为不适合实际用途。最近发现的几个计算性能良好的 ITL 终于改变了这种情况。在本文中，我们研究了具有子区间关系的 ITL D 的有限可满足性和模型检查问题，在同质性假设下（约束一个命题字母在一个区间上成立当且仅当它在所有点上成立） . 首先我们证明 D 的可满足性问题在有限线性阶数上是 PSPACE 完全的；然后我们证明它的模型检查问题，在有限 Kripke 结构上，也是 PSPACE 完备的。这篇论文用一个有意义的代表丰富了一组易处理的区间时间逻辑。