We introduce a general framework for reasoning about secrecy requirements in multiagent systems. Because secrecy requirements are closely connected with the knowledge of individual agents of a system, our framework employs the modal logic of knowledge within the context of the well-studied runs and systems framework. Put simply, “secrets ” are facts about a system that low-level agents are never allowed to know. The framework presented here allows us to formalize this intuition precisely, in a way that is much in the spirit of Sutherland’s notion of nondeducibility. Several well-known attempts to characterize the absence of information flow, including separability, generalized noninterference, and nondeducibility on strategies, turn out to be special cases of our definition of secrecy. However, our approach lets us go well beyond these definitions. It can handle probabilistic secrecy in a clean way, and it suggests generalizations of secrecy that may be useful for dealing with resource-bounded reasoning and with issues such as downgrading of information.

Abstract. Anonymity means that the identity of the user performing a certain action is maintained secret. The protocols for ensuring anonymity often use random mechanisms which can be described probabilistically. In this paper we propose a notion of weak probabilistic anonymity, where weak refers to the fact that some amount of probabilistic information may be revealed by the protocol. This information can be used by an observer to infer the likeliness that the action has been performed by a certain user. The aim of this work is to study the degree of anonymity that the protocol can still ensure, despite the leakage of information. We illustrate our ideas by using the example of the dining cryptographers with biased coins. We consider both the cases of nondeterministic and probabilistic users. Correspondingly, we propose two notions of weak anonymity and we investigate their respective dependencies on the biased factor of the coins. 1

Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete (or set-valued). This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently, Gr unwald and Halpern have shown that commonly used updating strategies fail in this case, except under very special assumptions. In this paper we propose a new method for updating probabilities with incomplete observations. Our approach is deliberately conservative: we make no assumptions about the so-called incompleteness mechanism that associates complete with incomplete observations. We model our ignorance about this mechanism by a vacuous lower prevision, a tool from the theory of imprecise probabilities, and we use only coherence arguments to turn prior into posterior (updated) probabilities. In general, this new approach to updating produces lower and upper posterior probabilities and previsions (expectations), as well as partially determinate decisions. This is a logical consequence of the existing ignorance about the incompleteness mechanism. As an example, we use the new updating method to properly address the apparent paradox in the `Monty Hall' puzzle. More importantly, we apply it to the problem of classification of new evidence in probabilistic expert systems, where it leads to a new, so-called conservative updating rule.

This paper presents results of the application to epistemic logic structures of the method proposed by Carnap for the development of logical foundations of probability theory. These results, which provide firm conceptual bases

This paper presents an approximate algorithm to obtain a posteriori intervals of probability, when available information is also given with intervals. The algorithm uses probability trees as a means of representing and computing with the convex sets of

We study the problem of ignorability in likelihood-based inference from incomplete categorical data. Two versions of the coarsened at random assumption (car) are distinguished, their compatibility with the parameter distinctness assumption is investigated and several conditions for ignorability that do not require an extra parameter distinctness assumption are established. It is shown that car assumptions have quite different implications depending on whether the underlying complete-data model is saturated or parametric. In the latter case, car assumptions can become inconsistent with observed data. 1. Introduction. In a sequence of papers Rubin [15], Heitjan and Rubin [11] and Heitjan [9, 10] have investigated the question under what conditions a mechanism that causes observed data to be incomplete or, more generally, coarse, can be ignored in the statistical analysis of the data. The key condition that has been identified is that the data should be missing at

We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization for the logic, and show that the satisfiability problem is NP-complete, no harder than satisfiability for propositional logic.

Abstract There are many applications where the precise time at which an event will occur (or has occurred) is uncertain. Temporal probabilistic logic programs (TPLPs) allow a programmer to express knowledge about such events. In this paper, we develop a model theory, fixpoint theory, and proof theory for TPLPs, and show that the fixpoint theory may be used to enumerate consequences of a TPLP in a sound and complete manner. Likewise the proof theory provides a sound and complete inference system. Last, but not least, we provide complexity results for TPLPs, showing in particular, that reasonable classes of TPLPs have polynomial data complexity. 1 Introduction There are a vast number of applications where uncertainty and time are indelibly intertwined. For example, the US Postal Service (USPS) as well as most commercial shippers have detailed statistics on how long shipments take to reach their destinations. Likewise, we are working on a Viennese historical land deed application where the precise time at which certain properties passed from one owner to another is also highly uncertain. Historical radio carbon dating methods are yet another source of uncertainty, providing approximate information about when a piece was created. Logical reasoning in situations involving temporal uncertainty is definitely important. For example, an individual querying the USPS express mail tracking system may want to know when he can expect his package to be delivered today-- he may then choose to stay home during the period when the probability of delivery seems very high, and leave a note authorizing the delivery official to leave the package by the door at other times.

Abstract not found

This paper reviews probabilistic approaches to rough sets in granulation, approximation, and rule induction. The Shannon entropy function is used to quantitatively characterize partitions of a universe. Both algebraic and probabilistic rough set approximations are studied. The probabilistic approximations are defined in a decision-theoretic framework. The problem of rule induction, a major application of rough set theory, is studied in probabilistic and information-theoretic terms. Two types of rules are analyzed, the local, low order rules, and the global, high order rules. 1