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，在我们想要建立的许多系统中，参与者不能被假定为仁慈的：相反，他们必须被假定为理性的代理人，追求自己的个人目标。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，我们感兴趣的是使用模型检测技术对这些系统进行自动化分析，在过去的二十年中，这些技术已经被证明是非常有影响力的。在模型检测中，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实际上对给定系统有效。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主义不允许我们直接表示参与者的偏好或效用（即，的目标）。这个项目就是针对这个问题。其基本思想是，我们可以使用一种被称为Lukasiewicz逻辑的形式主义来表达参与者的“效用函数”，这代表了他们的偏好。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-比使用经典逻辑可能的要丰富得多。该项目将为这种新的和令人兴奋的逻辑指定的游戏类奠定理论基础，并有可能大大丰富系统类，基于逻辑的自动分析技术可以应用。

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.