Combining Qualitative and Quantitative Reasoning for Logic-based Games

博弈论技术在计算机科学中的应用正变得越来越普遍。其中一个原因是，在我们想要构建的许多系统中，参与者不能被假设为仁慈的：相反，他们必须被假设为理性的行动者，为追求自己的个人目标而行动。对于这样的系统，博弈论提供了一个自然的分析框架。在我们的工作中，我们对使用模型检查技术对此类系统进行自动分析感兴趣，在过去的二十年中，这种技术已被证明具有巨大的影响力。在模型检查中，其思想是将期望的系统属性表示为逻辑公式，然后检查这些属性是否确实适用于给定的系统。如果我们想将现有的验证技术扩展到博弈论设置，一个关键问题是，模型检查中使用的形式不允许我们直接表示玩家的偏好或效用（即他们的目标）。这个项目就是针对这个问题的。基本理念是，我们可以使用一种被称为Lukasiewicz逻辑的形式来表达玩家的“效用函数”，即代表他们的偏好。Lukasiewicz逻辑是一种非经典的多值逻辑，它具有吸引人的性质，即Lukasiewicz公式可以表示非常丰富的一类效用函数——比使用经典逻辑要丰富得多。该项目将为这种新的、令人兴奋的逻辑指定游戏奠定理论基础，并有可能极大地丰富基于逻辑的自动化分析技术可以应用的系统类别。

The use of game theoretic techniques in computer science is becoming ever more prevalent. One reason for this is that in many of the systems we want to build, participants cannot be assumed to be benevolent: instead, they must be assumed to be rational agents, acting in pursuit of their own personal goals. For such systems, game theory provides a natural analytical framework. In our work, we are interested in the automated analysis of such systems using techniques for model checking, which over the past two decades have proved to be enormously influential. In model checking, the idea is to express desirable system properties as logical formula, and then to check whether these properties actually hold of the given system. A key problem if we want to extend existing verification techniques to game theoretic settings is that the formalisms used in model checking do not allow us to directly represent the preferences or utilities of players (i.e., their goals). This project is directed at this problem. The basic idea is that we can use a formalism known as Lukasiewicz logic to express the "utility function" for players, which represent their preferences. Lukasiewicz logic is a non-classical, multiple-valued logic which has the attractive property that Lukasiewicz formulae can represent a very rich class of utility functions -- much richer than is possible using classical logic. The project will lay the theoretical groundwork for this new and exciting class of logically-specified games, and has the potential to greatly enrich the class of systems for which logic-based automated analysis techniques can be applied.