A Principled Approach to Reasoning about Discrete Dynamic Systems

从技术系统中的离散控制到业务流程，再到化学反应中原子改变键，离散动态现象在广泛的背景下都可以找到。尽管这些动态现象各不相同，但它们通常用离散事件或动作来概念化，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，并研究使用原则逻辑表示来对这些系统进行建模。提出的研究将侧重于一阶逻辑技术在解决大规模规划问题中的应用。特别是，有必要探索当初始知识不完整时，如何使用提升的一阶逻辑表示来解决确定性规划问题。建议的研究将集中在可以开发计算上易于处理的解决方案的情况。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，使用因果规则来指定这些效果；然而，当对间接影响的推理在计算上是可处理的，与对非可处理的情况进行区分的边界却鲜为人知。此外，当行动具有间接影响时，如何解除一阶计划的问题尚未得到探讨。这项研究的成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.