探索二维空间：一种动态逻辑观点
Exploring the bidimensional space: A dynamic logic point of view
摘要：
我们提出了一个家庭的逻辑推理代理的位置和运动在平面上有几个潜在的应用领域的多智能体系统（MAS），如多智能体规划和机器人。最一般的逻辑包括（i）原子公式，用于表示给定事实的真实性或给定代理在平面的某个位置的存在，（ii）原子程序，对应于平面中的四个基本方向（上，下，左，右）以及命题动态逻辑的四个程序构造（顺序组合，非确定性组合，迭代和测试）。由于这种逻辑是不可计算的，我们研究了它的一些有趣的可判定和可公理化的片段，并给出了一个可判定的扩展，它的无迭代片段通过表示智能体在平面上运动的特殊程序来实现。
英文摘要：
We present a family of logics for reasoning about agents' positions and motion in the plane which have several potential applications in the area of multi-agent systems (MAS), such as multi-agent planning and robotics. The most general logic includes (i) atomic formulas for representing the truth of a given fact or the presence of a given agent at a certain position of the plane, (ii) atomic programs corresponding to the four basic orientations in the plane (up, down, left, right) as well as the four program constructs of propositional dynamic logic (sequential composition, nondeterministic composition, iteration and test). As this logic is not computably enumerable, we study some interesting decidable and axiomatizable fragments of it. We also present a decidable extension of the iteration-free fragment of the logic by special programs representing motion of agents in the plane.
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