23268703
A knowledge-theoretic analysis of uniform distributed coordination and failure detectors
It is shown that, in a precise sense, if there is no bound on the number of faulty processes in a system with unreliable but fair communication, Uniform Distributed Coordination (UDC) can be attained if and only if a system has perfect failure detectors. This result is generalized to the case where there is a bound t on the number of faulty processes. It is shown that a certain type of generalized failure detector is necessary and sufficient for achieving UDC in a context with at most t faulty processes. Reasoning about processes’ knowledge as to which other processes are faulty plays a key role in the analysis.
1225089
Defining Explanation in Probabilistic Systems
As probabilistic systems gain popularity and are coming into wider use, the need for a mechanism that explains the system's findings and recommendations becomes more critical. The system will also need a mechanism for ordering competing explanations. We examine two representative approaches to explanation in the literature-- one due to Gardenfors and one due to Pearl--and show that both suffer from significant problems. We propose an approach to defining a notion of "better explanation" that combines some of the features of both together with more recent work by Pearl and others on causality.
3055934
A knowledge-theoretic analysis of uniform distributed coordination and failure detectors
Abstract.It is shown that, in a precise sense, if there is no bound on the number of faulty processes in a system with unreliable but fair communication, Uniform Distributed Coordination (UDC) can be attained if and only if a system has perfect failure detectors. This result is generalized to the case where there is a bound t on the number of faulty processes. It is shown that a certain type of generalized failure detector is necessary and sufficient for achieving UDC in a context with at most t faulty processes. Reasoning about processes’ knowledge as to which other processes are faulty plays a key role in the analysis.
12474954
Modeling Belief in Dynamic Systems, Part II: Revisions and Update
The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.
2990183
Performing work efficiently in the presence of faults
We consider a system of t synchronous processes that communicate only by sending messages to one another, and together the processes must perform n independent units of work. Processes may fail by crashing; we want to guarantee that in every execution of the protocol in which at least one process survives, all n units of work will be performed. We consider three parameters: the number of messages sent, the total number of units of work performed (including multiplicities), and time. We present three protocols for solving the problem. All three are work optimal, doing O(n+t) work. The rst has moderate costs in the remaining two parameters, sends O(t p t) messages, and takes O(n+t) time. This protocol can be easily modied to run in any completely asynchronous system equipped with a failure detection mechanism. The second sends only O(tlogt) messages, but its running time is large (O(t 2 (n+t)2 n+t )). The third is essentially time optimal in the (usual) case in which there are no failures, and its time complexity degrades gracefully as the number of failures increases.
8145017
Characterizing the Common Prior Assumption
Abstract Logical characterizations of the common prior assumption (CPA) are investigated. Two approaches are considered. The first is called frame distinguishability , and is similar in spirit to the approaches considered in the economics literature. Results similar to those obtained in the economics literature are proved here as well, namely, that we can distinguish finite spaces that satisfy the CPA from those that do not in terms of disagreements in expectation. However, it is shown that, for the language used here, no formulas can distinguish infinite spaces satisfying the CPA from those that do not. The second approach considered is that of finding a sound and complete axiomatization. Such an axiomatization is provided; again, the key axiom involves disagreements in expectation. The same axiom system is shown to be sound and complete both in the finite and the infinite case. Thus, the two approaches to characterizing the CPA behave quite differently in the case of infinite spaces. Journal of Economic Literature Classification Numbers: C70, D80.
439524
A Nonstandard Approach to the Logical Omniscience Problem
We introduce a new approach to dealing with the well-known logical omniscience problem in epistemic logic. Instead of taking possible worlds where each world is a model of classical propositional logic, we take possible worlds which are models of a nonstandard propositional logic we call NPL, which is somewhat related to relevance logic. This approach gives new insights into the logic of implicit and explicit belief considered by Levesque and Lakemeyer. In particular, we show that in a precise sense agents in the structures considered by Levesque and Lakemeyer are perfect reasoners in NPL.
35977937
Reasoning about Procedures as Parameters in the Language L4
Abstract We provide a sound and relatively complete axiom system for partial correctness assertions in an Algol-like language with procedures passed as parameters, but with no global variables (traditionally known as the language L4). The axiom system allows us to reason syntactically about programs and to construct proofs for assertions about complicated programs from proofs of assertions about their components. Such an axiom system for a language with these features had been sought by a number of researchers, but no previously published solution has been entirely satisfactory. Our axiom system extends the natural style of reasoning used in previous Hoare axiom systems to programs with procedures of higher type. The details of the proof that our axiom system is relatively complete in the sense of Cook may be of independent interest, because we introduce results about expressiveness for programs with higher types that are useful beyond the immediate problem of the language L4. We also prove a new incompleteness result that applies to our logic and to similar Hoare logics.
7772927
What can machines know?: On the properties of knowledge in distributed systems
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, zrzforrnatzorr-based notion that can be shown to satisfy all the axioms of the modal logic S5. The properties of this notion of knowledge are examined, and it is shown that they depend crucially. and in subtle ways, on assumptions made about the system and about the language used for describing knowledge. A formal model is presented in which one 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. It 1s then shown 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 properties of knowledge; extra axioms are needed. Complete axiomatlzations for knowledge in a number of cases of interest are provided.
14995360
A model-theoretic analysis of knowledge
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»
52151232
Knowledge and common knowledge in a distributed environment
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. It is shown 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 of common knowledge that are attainable in many cases of interest are introduced and investigated.