Principled Reasoning about Dynamical Systems

从技术系统中的离散事件控制到业务流程，再到化学反应中原子改变键，动态现象在广泛的环境中都可以找到。尽管这些动态现象各不相同，但它们通常有共同的概念，要么是受行动影响的离散过渡，要么是混合系统，其中存在连续的过程和流，可以由离散的行动或事件启动或终止。重要的是，这些现象可以用共同的基本原则来描述。这些原则应该用数学语言正式表示，以方便分析。这有助于设计可随后部署在各种应用程序中的通用解决方案。提出的研究计划有助于发展行动及其影响的一般原则表示，并展示如何使用这些表示来执行关于行动的直接和间接影响的计算可处理推理。有几个概念和计算上的挑战阻碍了现有的原则表示和推理机制为解决现实世界的问题做出实际贡献。拟议的研究将解决其中一些遗留的挑战。提出的研究计划的目标是提高我们对专业推理机制的认识，这些机制可以导致开发有效的领域独立技术来解决动力系统中的问题。这包括识别在实际应用中经常出现的各种动态系统，并研究使用有原则的逻辑表示来对这些系统进行建模。建议的研究将侧重于应用专门的推理机制来解决大规模规划问题。特别是，有必要探索在初始知识不完整的情况下，如何使用提升表示来解决确定性规划问题。此外，我将探讨当行动具有间接影响时，如何进行启发式计划。这一点很重要，因为在一些现实的领域中，可以使用嵌套缩写来定义操作的前提条件，这些缩写的真值在执行操作时间接改变。提出的研究将集中在计算可处理的情况下，领域独立的技术可以开发。此外，我将探讨如何正确有效地确定观察到的效果的实际原因。这项任务不仅包括发现主要的实际原因，而且包括结果的根本原因在内的整个因果链。这项研究的结果将是我们知识的进步和具有潜在广泛适用性的技术的发展。

Dynamic phenomena are found in a broad range of contexts from discrete event control in technical systems, to business processes, to atoms changing bonds in chemical reactions. Despite their diversity, these dynamic phenomena often have common conceptualization either in terms of discrete transitions affected by actions, or in terms of hybrid systems where there are continuous processes and flows that can be initiated or terminated by discrete actions or events.  What is important these phenomena can be described using common underlying principles. These principles should be formally represented in a mathematical language that facilitates their analysis. This helps to design general solutions that can be subsequently deployed in a variety of applications. The proposed research program contributes to developing general principled representations for actions and their effects, and to demonstrating how these representations can be used to perform computationally tractable reasoning about the direct and indirect effects of actions. There are several conceptual and computational challenges that prevent the existing principled representations and reasoning mechanisms from making practical contributions to solving real-world problems. The proposed research will address some of these remaining challenges. The objective of the proposed research program is  advance our knowledge about specialized reasoning mechanisms that can lead to development of efficient domain independent techniques for solving problems in dynamical systems. This include identifying the kinds of dynamical systems that frequently occur in practical applications and investigating the use of principled logical representations to model these systems. The proposed research will focus on application of specialized reasoning mechanisms to solve large scale planning problems. In particular, there is a need to explore how lifted representations can be used to solve deterministic planning problems when initial knowledge is incomplete. Moreover, I will explore the question how lifted heuristic planning can be done when actions have indirect effects. This is important since in some realistic domains preconditions of actions can be defined using nested abbreviations whose truth values change indirectly when actions are executed. The proposed research will concentrate on the cases where computationally tractable, domain independent techniques can be developed.  Also, I will explore how can we correctly and efficiently determine the actual causes of an observed effect. This task includes finding  not only the primary actual cause, but also the whole causal chain including the root cause of an effect. The outcome of this research will be advancement of our knowledge and the development of techniques with potentially broad applicability.