A Principled Approach to Reasoning about Discrete Dynamic Systems

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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.