In this paper, we study two problems: determining action model equivalence and minimizing the event space of an action model under certain structural relationships. The Kripke model equivalence is perfectly caught by the structural relationship called bisimulation. In this paper, we propose the generalized action emulation perfectly catching the action model equivalence. Previous structural relationships sufficient for the action model equivalence, i.e. the bisimulation, the propositional action emulation, the action emulation, and the action emulation of canonical action models, can be described by various restricted versions of the generalized action emulation. We summarize four critical properties of the atom set over preconditions, and prove that any formula set satisfying these properties can be used to restrict the generalized action emulation to determine the action model equivalence by an iteration algorithm. We also construct a new formula set with these four properties, which is generally more efficient than the atom set. The technique of the partition refinement has been used to minimize the world space of a Kripke model under the bisimulation. Applying the partition refinement to action models allows one to minimize their event spaces under the bisimulation. The propositional action emulation is weaker than bismulation but still sufficient for the action model equivalence. We prove that it is PSPACE-complete to minimize the event space of an action model under the propositional action emulation, and provide a PSPACE algorithm for it. Finally, we prove that minimize the event space under the action model equivalence is PSPACE-hard, and propose a computable method based on the canonical formulas of modal logics to solve this problem.
翻译:在本文中,我们研究了两个问题:确定行动模型等同,并在某些结构关系下将行动模型的事件空间最小化。 Kripke 模型等同完全被称为“ 刺激” 的结构关系完全抓住。 在本文中,我们建议普遍行动模拟,完全赶上行动模型等同。 先前的结构关系足以满足行动模型等同, 即: 刺激、 提议行动模拟、 行动模拟, 以及弹道行动模型的模拟等同, 可以用各种限制版本的普遍行动模拟来描述。 我们总结了原子组的四种关键属性, 并证明任何符合这些属性的公式组可以用来限制通用行动模拟, 以便用迭代算算算来确定行动模型等等同。 我们还用这四种等等等等等等等等等等等的新的结构关系构建了一个新的公式。 精细化的分区技术已经用来最大限度地减少平价模型的可折算空间模型的世界空间空间空间空间空间空间空间空间空间空间空间空间空间空间空间空间空间空间空间空间空间空间模型空间模型。 我们的平级计算行动模型比最后的平级行动要更弱化, 我们的平整的平整的平级行动是证明一个最弱的行动。