Logic of Interaction and Information Flow

我们目前对计算的理解已经大大超出了最初脱离环境进行数值计算的“封闭世界”的图景。在互联网和Web的时代，以及现在的普及和无处不在的计算时代，很明显，多个代理之间的交互和信息流是计算的基本特征。描述或设计的标准单位，无论是在过程调用-返回接口或硬件组件的微观尺度上，还是在Web上的软件代理的宏观尺度上，都成为一个进程或代理，其行为的本质是它如何通过某个定义的接口与其环境交互。这些发展需要引入新的交互计算数学模型。传统的观点认为程序是计算从输入到输出的函数或关系，这种观点已经不再足够：互联网计算的是什么函数？扎根的一个令人信服的想法是将系统和环境之间的交互概念化为两人游戏。一个指定系统在面对环境的所有可能动作时应该如何表现的程序，就是与系统相对应的玩家的策略。这些思想导致了游戏语义学的发展，它既为分析许多不同形式的计算提供了强大的工具，也导致了对逻辑本身的新视角。例如，考虑一下复制猫策略，根据该策略，我们可以通过逻辑的力量在国际象棋中击败大师。我们的想法是，我们在两块牌上与两位大师级选手比赛，一块是白色的，另一块是黑色的(对应于‘a or no A’)。通过简单地来回复制动作，我们最终会让一个大师对抗另一个-因此我们做得和我们的对手一样好！这是一种动态重言式：我们通过一个简单的复制过程达到很强的逻辑效果。注：只有由此产生的考虑和相关的概念才能在计算和逻辑中产生强大的应用，与几何概念、与结和辫子有关的显着联系也出现了，与纠缠量子系统中的信息流有关。因此，该提议的一个目标是建立一个涵盖所有这些例子和更多的关于相互作用和信息流的统一理论。另一种方法是将这种“动态”或“内在”方法与更传统的互动逻辑方法联系起来，并确实找到了将它们结合在一起的有用方法。

Our current understanding of computation has widened enormously beyond the original ``closed world'' picture of numerical calculation in isolation from the environment. In the age of the Internet and the Web, and now of pervasive and ubiquitous computing, it has become clear that interaction and information flow between multiple agents are essential features of computation. The standard unit of description or design, whether at a micro-scale of procedure call-return interfaces or hardware components, or a macro-scale of software agents on the Web, becomes a process or agent, the essence of whose behaviour ishow it interacts with its environment across some defined interface.These developments have required the introduction of novel mathematical models of interactive computation. The traditional view whereby a program is seen as computing a function or relation from inputs to outputs is no longer sufficient: what function does the Internet compute?One of the compelling ideas which has taken root is toconceptualize the interaction between the System and the Environment as a two-person game. A program specifying how the System should behave in the face of all possible actions by the Environment is then a strategy for the player corresponding to the System.These ideas have led to the development of Game semantics, which both provides powerful tools for analyzing many different forms of computation, and leads to new perspectives on logic itself.For example, consider the ``copy-cat strategy'', whereby we can beat a Grand-Master at chess, by the power of logic. The idea is that we play against two Grand-Masters on two boards, one as White and one as Black (corresponding to ``A or not A''). By simply copying moves back and forth, we end up playing one grand-master off against the other --- and hence do as well as our opponents! This is a kind of ``dynamic tautology'': we achieve a strong logical effect by a simple copying process. Note only do the considerations arising from this and related ideas lead to powerful applications in computation and logic, striking connections are also emerging to geometric ideas, related to knots and braids, and to information flow in entangled quantum systems.Thus one aim of the proposal is build a unified theory of interaction and information flow covering all these examples and more. Another to is to connect this ``dynamic'' or ``intrinsic'' approach to more traditional approaches to logics of interaction, and indeed to find useful ways of combining them.