We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.

: Reasoning about knowledge seems to play a fundamental role in distributed systems. Indeed, such reasoning is a central part of the informal intuitive arguments used in the design of distributed protocols. Communication in a distributed system can be viewed as the act of transforming the system's state of knowledge. This paper presents a general framework for formalizing and reasoning about knowledge in distributed systems. We argue that states of knowledge of groups of processors are useful concepts for the design and analysis of distributed protocols. In particular, distributed knowledge corresponds to knowledge that is "distributed" among the members of the group, while common knowledge corresponds to a fact being "publicly known". The relationship between common knowledge and a variety of desirable actions in a distributed system is illustrated. Furthermore, it is shown that, formally speaking, in practical systems common knowledge cannot be attained. A number of weaker variants...

We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the given formula is true in that model. We discuss how to construct a model that represents an agent's knowledge in a number of different contexts, and then consider how to approach the model-checking problem.

This work applies the theory of knowledge in distributed systems to the design of efficient fault-tolerant protocols. We define a large class of problems requiring coordinated, simultaneous action in synchronous systems, and give a method of transforming specifications of such problems into protocols that are optimal in all runs: for every possible input to the system and faulty processor behavior, these protocols are guaranteed to perform the simultaneous actions as soon as any other protocol could possibly perform them. This transformation is performed in two steps. In the first step, we extract directly from the problem specification a high-level protocol programmed using explicit tests for common knowledge. In the second step, we carefully analyze when facts become common knowledge, thereby providing a method of efficiently implementing these protocols in many variants of the omissions failure model. In the generalized omissions model, however, our analysis shows that testing for common knowledge is NP-hard. Given the close correspondence between common knowledge and simultaneous actions, we are able to show that no optimal protocol for any such problem can be computationally efficient in this model. The analysis in this paper exposes many subtle differences between the failure models, including the precise point at which this gap in complexity occurs.

: We present a formal model that captures the subtle interaction between knowledge and action in distributed systems. We view a distributed system as a set of runs, where a run is a function from time to global states and a global state is a tuple consisting of an environment state and a local state for each process in the system. This model is a generalization of those used in many previous papers. Actions in this model are associated with functions from global states to global states. A protocol is a function from local states to actions. We extend the standard notion of a protocol by defining knowledge-based protocols, ones in which a process' actions may depend explicitly on its knowledge. Knowledge-based protocols provide a natural way of describing how actions should take place in a distributed system. Finally, we show how the notion of one protocol implementing another can be captured in our model. Some material in this paper appeared in preliminary form in [HF85]. An abridge...

We consider the consensus problem in asynchronous models enriched with unreliable failure detectors or partial synchrony, where processes can crash or links may fail by losing messages.

THE aim of this thesis is to investigate logical formalisms for describing, reasoning about, specifying, and perhaps ultimately verifying the properties of systems composed of multiple intelligent computational agents. There are two obvious resources available for this task. The first is the (largely AI) tradition of reasoning about the intentional notions (belief, desire, etc.). The second is the (mainstream computer science) tradition of temporal logics for reasoning about reactive systems. Unfortunately, neither resource is ideally suited to the task: most intentional logics have little to say on the subject of agent architecture, and tend to assume that agents are perfect reasoners, whereas models of concurrent systems from mainstream computer science typically deal with the execution of individual program instructions. This thesis proposes a solution which draws upon both resources. It defines a model of agents and multi-agent systems, and then defines two execution models, which ...

. This paper presents a polynomial-time protocol for reaching Byzantine agreement in t + 1 rounds whenever n ? 3t, where n is the number of processors and t is an a priori upper bound on the number of failures. This resolves an open problem presented by Pease, Shostak and Lamport in 1980. An early-stopping variant of this protocol is also presented, reaching agreement in a number of rounds that is proportional to the number of processors that actually fail. SICOMP 27-1 (1998), pp.247-290 Key words. Byzantine agreement, consensus, distributed computing, fault tolerance, computer security. AMS subject classifications. 68M10, 68M15, 68Q22, 94C12 1. Introduction. The Byzantine agreement problem (BA), introduced by Pease, Shostak and Lamport in [22], is recognized as a fundamental problem in fault-tolerant distributed computing. Over the last decade or more, the problem has received a great deal of attention in the literature, and has become a testbed for a variety of models for distrib...

Understanding knowledge is a fundamental issue in many disciplines. In computer science, knowledge arises not only in the obvious contexts (such as knowledgebased systems), but also in distributed systems (where the goal is to have each processor "know" something, as in agreement protocols). A general semantic model of knowledge is introduced, to allow reasoning about statements such as "He knows that I know whether or not she knows whether or not it is raining." This approach more naturally models a state of knowledge than previous proposals (including Kripke structures). Using this notion of model, a model theory for knowledge is developed. This theory enables one to interpret the notion of a "finite amount of information". A preliminary version of this paper appeared in Proc. 25th IEEE Symp. on Foundations of Computer Science, 1984, pp. 268--278. This version is essentially identical to the version that appears in Journal of the ACM 38:2, 1991, pp. 382--428. y Part of th...

It has been argued that knowledge is a useful tool for designing and analyzing complex systems. The notion of knowledge that seems most relevant in this context is an external, information-based notion that can be shown to satisfy all the axioms of the modal logic S5. We carefully examine the properties of this notion of knowledge and show that they depend crucially, and in subtle ways, on assumptions we make about the system and about the language used for describing knowledge. We present a formal model in which we can capture various assumptions frequently made about systems, such as whether they are deterministic or nondeterministic, whether knowledge is cumulative (which means that processes never "forget"), and whether or not the "environment" affects the state transitions of the processes. We then show that under some assumptions about the system and the language, certain states of knowledge are not attainable and the axioms of S5 do not completely characterize the pr...