61651080
I'm OK if You're OK: On the Notion of Trusting Communication
We consider the issue of what an agent or a processor needs to know in order to know that its messages are true. This may be viewed as a first step to a general theory of cooperative communication in distributed systems. An honest message is one that is known to be true when it is sent (or said). If every message that is sent is honest, then of course every message that is sent is true. Various weaker considerations than honesty are investigated with the property that provided every message sent satisfies the condition, then every message sent is true.
152014
Causality, Responsibility, and Blame: A Structural-Model Approach
This talk provides an overview of work that I have done with Hana Chockler, Orna Kupferman, and Judea Pearl (H. Chockler and J. Y. Halpern, 2004), (H. Chockler, et al., 2003), (J. Y. Halpern and J. Pearl, 2005), on defining notions such as causality, explanation, responsibility, and blame. I first review the Halpern-Pearl definition of causality, what it means that A is a cause of B, and show how it handles well some standard problems of causality. This definition of causality (like most in the literature) views causality as an all-or-nothing concept. Either A is a cause of B or it is not. I show how it can be extended to take into account the degree of responsibility of A for B. For example, if someone wins an election 11-0, each person is less responsible for his victory than if he had won 6-5. Finally, I show how this notion of degree of responsibility can be used to provide insight into model checking notions such as coverage
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»
47316226
Equations Between Regular Terms and an Application to Process Logic
Regular terms with the Kleene operations $ \cup $, ; and $ * $ can be thought of as operators on languages, generating other languages. An equation $\tau _1 = \tau _2 $ between two such terms is said to be satisfiable just in case languages exist which make this equation true. We show that the satisfiability problem even for $ * $-free regular terms is undecidable. Similar techniques are used to show that a very natural extension of the Process Logic of Harel, Kozen and Parikh is undecidable.
215949262
Knowledge, probability, and adversaries
What should it mean for an agent to know or believe an assertion is true with probability 9.99? Different papers [2, 6, 15] give different answers, choosing to use quite different probability space...
15233558
A new look at fault tolerant network routing
Consider a communication network G in which a limited number of link and/or node faults F might occur. A routing &rgr; for the network (a fixed path between each pair of nodes) must be chosen without any knowledge of which components might become faulty. Choosing a good routing corresponds to bounding the diameter of the surviving route graph R(G,&rgr;)/F, where two nonfaulty nodes are joined by an edge if there are no faults on the route between them. We prove a number of results concerning the diameter of surviving route graphs. We show that if &rgr; is a minimal length routing, then the diameter of R(G,&rgr;)/F can be on the order of the number of nodes of G, even if F consists of only a single node. However, if G is the n-dimensional cube, the diameter of R(G,&rgr;)/F≤3 for any minimal length routing &rgr; and any set of faults F with |F|<n. We also show that if F consists only of edges and does not disconnect G, then the diameter of R(G,&rgr;)/F is ≤ 3|F|+1, while if F consists only of nodes and does not disconnect G, then the diameter of R(G,&rgr;)/F is ≤ the sum of the degrees of the nodes in F, where in both cases &rgr; is an arbitrary minimal length routing. We conclude with one of the most important contributions of this paper: a list of interesting and apparently difficult open problems.
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.
7572747
Set-theoretic completeness for epistemic and conditional logic
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of formulas in the language (the semantics), a collection of axioms and rules of inference characterizing reasoning (the proof theory), and then relate the proof theory to the semantics via soundness and completeness results. Here we consider an approach that is more common in the economics literature, which works purely at the semantic, set-theoretic level. We provide set-theoretic completeness results for a number of epistemic and conditional logics, and contrast the expressive power of the syntactic and set-theoretic approaches.
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.
35307334
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 first has moderate costs in the remaining two parameters, sends $O(t\sqrt{t})$ messages, and takes O(n+t) time. This protocol can be easily modified to run in any completely asynchronous system equipped with a failure detection mechanism. The second sends only O(t log t) messages, but its running time is large (O(t2(n+t) 2n+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.
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.