A Principled Approach to Reasoning about Discrete Dynamic Systems

离散动力学现象存在于广泛的背景下，从技术系统中的离散控制到业务流程，再到化学反应中的原子改变键。尽管它们的多样性，这些动态现象，通常概念化的离散事件或行动，可以使用共同的基本原则来描述。这些原则应该用数学语言来正式表示，以便于分析。这有助于设计通用解决方案，随后可以在各种应用程序中部署。拟议的研究计划有助于制定一般原则的表示行动及其影响，并展示这些表示可以用来执行计算上易于处理的推理行动的直接和间接影响。有几个概念和计算的挑战，阻止现有的原则表示和推理机制，使实际的贡献，解决现实世界的问题。拟议的研究计划的目标是解决其中的一些挑战。它们包括识别在实际应用中经常出现的离散动力系统的种类，并研究使用原则性逻辑表示来建模这些系统。建议的研究将集中在应用一阶逻辑技术来解决大规模规划问题。特别是，有必要探讨如何解除一阶逻辑表示可以用来解决确定性规划问题时，初始知识是不完整的。拟议的研究将集中在计算易处理的解决方案可以开发的情况下。此外，还将探讨我们如何有效地处理具有间接影响的行动。通常情况下，这些影响是使用因果规则指定的;然而，当间接影响的推理在计算上易于处理时，与不容易处理时，关于将情况分开的边界知之甚少。此外，当行动具有间接影响时，如何进行解除一阶规划的问题尚未得到探讨。这项研究的结果将是我们知识的进步和具有广泛适用性的技术的发展。

Discrete dynamic phenomena are found in a broad range of contexts from discrete control in technical systems, to business processes, to atoms changing bonds in chemical reactions. Despite their diversity, these dynamic phenomena, usually conceptualized in terms of discrete events or actions, 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 objective of the proposed research program is to address some of these challenges. They include identifying the kinds of discrete 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 first order logic techniques to solve large scale planning problems. In particular, there is a need to explore how lifted first order logic representations can be used to solve deterministic planning problems when initial knowledge is incomplete. The proposed research will concentrate on the cases where computationally tractable solutions can be developed. Also, it will be explored how can we deal efficiently with actions that have indirect effects. Often, these effects are specified using causal rules; yet, there is little known about a boundary separating the case when reasoning about indirect effects is computationally tractable from the case when it is not. Moreover, the question how lifted first order planning can be done when actions have indirect effects has not yet been explored. The outcome of this research will be advancement of our knowledge and the development of techniques with broad applicability.