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132
Knowledge and Common Knowledge in a Distributed Environment
 Journal of the ACM
, 1984
"... : 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 s ..."
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Cited by 499 (52 self)
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: 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...
Efficient Query Evaluation on Probabilistic Databases
, 2004
"... We describe a system that supports arbitrarily complex SQL queries with ”uncertain” predicates. The query semantics is based on a probabilistic model and the results are ranked, much like in Information Retrieval. Our main focus is efficient query evaluation, a problem that has not received attentio ..."
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Cited by 347 (38 self)
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We describe a system that supports arbitrarily complex SQL queries with ”uncertain” predicates. The query semantics is based on a probabilistic model and the results are ranked, much like in Information Retrieval. Our main focus is efficient query evaluation, a problem that has not received attention in the past. We describe an optimization algorithm that can compute efficiently most queries. We show, however, that the data complexity of some queries is #Pcomplete, which implies that these queries do not admit any efficient evaluation methods. For these queries we describe both an approximation algorithm and a MonteCarlo simulation algorithm.
An Analysis of FirstOrder Logics of Probability
 Artificial Intelligence
, 1990
"... : We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies is greater than ..."
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Cited by 272 (18 self)
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: We consider two approaches to giving semantics to firstorder logics of probability. The first approach puts a probability on the domain, and is appropriate for giving semantics to formulas involving statistical information such as "The probability that a randomly chosen bird flies is greater than .9." The second approach puts a probability on possible worlds, and is appropriate for giving semantics to formulas describing degrees of belief, such as "The probability that Tweety (a particular bird) flies is greater than .9." We show that the two approaches can be easily combined, allowing us to reason in a straightforward way about statistical information and degrees of belief. We then consider axiomatizing these logics. In general, it can be shown that no complete axiomatization is possible. We provide axiom systems that are sound and complete in cases where a complete axiomatization is possible, showing that they do allow us to capture a great deal of interesting reasoning about prob...
A Logic for Reasoning about Probabilities
 Information and Computation
, 1990
"... We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable ( ..."
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Cited by 214 (19 self)
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We consider a language for reasoning about probability which allows us to make statements such as “the probability of E, is less than f ” and “the probability of E, is at least twice the probability of E,, ” where E, and EZ are arbitrary events. We consider the case where all events are measurable (i.e., represent measurable sets) and the more general case, which is also of interest in practice, where they may not be measurable. The measurable case is essentially a formalization of (the propositional fragment of) Nilsson’s probabilistic logic. As we show elsewhere, the general (nonmeasurable) case corresponds precisely to replacing probability measures by DempsterShafer belief functions. In both cases, we provide a complete axiomatization and show that the problem of deciding satistiability is NPcomplete, no worse than that of propositional logic. As a tool for proving our complete axiomatizations, we give a complete axiomatization for reasoning about Boolean combinations of linear inequalities, which is of independent interest. This proof and others make crucial use of results from the theory of linear programming. We then extend the language to allow reasoning about conditional probability and show that the resulting logic is decidable and completely axiomatizable, by making use of the theory of real closed fields. ( 1990 Academic Press. Inc 1.
Knowledge, probability, and adversaries
 Journal of the ACM
, 1993
"... Abstract: What should it mean for an agent toknowor believe an assertion is true with probability:99? Di erent papers [FH88, FZ88a, HMT88] givedi erent answers, choosing to use quite di erent probability spaces when computing the probability that an agent assigns to an event. We showthat each choice ..."
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Cited by 72 (24 self)
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Abstract: What should it mean for an agent toknowor believe an assertion is true with probability:99? Di erent papers [FH88, FZ88a, HMT88] givedi erent answers, choosing to use quite di erent probability spaces when computing the probability that an agent assigns to an event. We showthat each choice can be understood in terms of a betting game. This betting game itself can be understood in terms of three types of adversaries in uencing three di erent aspects of the game. The rst selects the outcome of all nondeterministic choices in the system� the second represents the knowledge of the agent's opponent in the betting game (this is the key place the papers mentioned above di er) � the third is needed in asynchronous systems to choose the time the bet is placed. We illustrate the need for considering all three types of adversaries with a number of examples. Given a class of adversaries, we show howto assign probability spaces to agents in a way most appropriate for that class, where \most appropriate " is made precise in terms of this betting game. We conclude by showing how di erent assignments of probability spaces (corresponding to di erent opponents) yield di erent levels of guarantees in probabilistic coordinated attack.
Topologyfree typology of beliefs
 Journal of Econ. Theory
, 1998
"... In their seminal paper, Mertens and Zamir (1985) proved the existence of a universal Harsanyi type space which consists of all possible types. Their method of proof depends crucially on topological assumptions. Whether such assumptions are essential to the existence of a universal space remained an ..."
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Cited by 38 (5 self)
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In their seminal paper, Mertens and Zamir (1985) proved the existence of a universal Harsanyi type space which consists of all possible types. Their method of proof depends crucially on topological assumptions. Whether such assumptions are essential to the existence of a universal space remained an open problem. We answer it here by proving that a universal type space does exist even when spaces are defined in pure measure theoretic terms. Heifetz and Samet (1996) showed that coherent hierarchies of beliefs, in the measure theoretic case, do not necessarily describe types. Therefore, the universal space here differs from all previously studied ones, in that it does not necessarily consist of all We study here the foundations of that part of the theory of games with incomplete information that deals with players ’ beliefs. We study it in the broadest and most natural setup, that of probability (or measure) theory without any topological notions, which have always been used for this purpose until now. We show that even under this general setup
A logical approach to multilevel security of probabilistic systems
, 1998
"... We set out a modal logic for reasoning about multilevel security of probabilistic systems. This logic contains expressions for time, probability, and knowledge. Making use of the HalpernTuttle framework for reasoning about knowledge and probability, we give a semantics for our logic and prove it i ..."
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Cited by 37 (1 self)
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We set out a modal logic for reasoning about multilevel security of probabilistic systems. This logic contains expressions for time, probability, and knowledge. Making use of the HalpernTuttle framework for reasoning about knowledge and probability, we give a semantics for our logic and prove it is sound. We give two syntactic definitions of perfect multilevel security and show that their semantic interpretations are equivalent to earlier, independently motivated characterizations. We also discuss the relation between these characterizations of security and between their usefulness in security analysis.
PSPACE bounds for rank 1 modal logics
 IN LICS’06
, 2006
"... For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank1 logics enjoy a sh ..."
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Cited by 26 (15 self)
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For lack of general algorithmic methods that apply to wide classes of logics, establishing a complexity bound for a given modal logic is often a laborious task. The present work is a step towards a general theory of the complexity of modal logics. Our main result is that all rank1 logics enjoy a shallow model property and thus are, under mild assumptions on the format of their axiomatisation, in PSPACE. This leads to a unified derivation of tight PSPACEbounds for a number of logics including K, KD, coalition logic, graded modal logic, majority logic, and probabilistic modal logic. Our generic algorithm moreover finds tableau proofs that witness pleasant prooftheoretic properties including a weak subformula property. This generality is made possible by a coalgebraic semantics, which conveniently abstracts from the details of a given model class and thus allows covering a broad range of logics in a uniform way.
Retrieval of Complex Objects Using a FourValued Logic
 Proceedings of the 19th International ACM SIGIR Conference on Research and Development in Information Retrieval
, 1996
"... The aggregated structure of documents plays a key role in fulltext, multimedia, and network Information Retrieval (IR). Considering aggregation provides new querying facilities and improves retrieval effectiveness. We present a knowledge representation for IR purposes which pays special attention t ..."
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Cited by 24 (6 self)
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The aggregated structure of documents plays a key role in fulltext, multimedia, and network Information Retrieval (IR). Considering aggregation provides new querying facilities and improves retrieval effectiveness. We present a knowledge representation for IR purposes which pays special attention to this aggregated structure of objects. In addition, further features of objects can be described. Thus, the structure of fulltext documents, the heterogeneity and the spatial and temporal relationships of objects typical for multimedia IR, and meta information for network IR are representable within one integrated framework. The model we propose allows for querying on the content of documents (objects) as well as on other features. The query result may contain objects having different types. Instead of retrieving only whole documents, the retrieval process determines the least aggregated entities that imply the query. 1 Motivation and Background New IR applications like fulltext, multime...
A Finite Model Construction For Coalgebraic Modal Logic
"... In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness result ..."
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Cited by 24 (16 self)
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In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness results for coalgebraic modal logic, which we push further by establishing that every coalgebraic modal logic admits a complete axiomatization of rank 1; it also enables us to establish a generic decidability result and a first complexity bound. Examples covered by these general results include, besides standard HennessyMilner logic, graded modal logic and probabilistic modal logic.