Reasoning About Knowledge

Fagin, Ronald; Halpern, Joseph Y.; Moses, Yoram; Vardi, Moshe Y.

doi:10.7551/mitpress/5803.001.0001

Cited by 1,277 publications

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“…It should be noted that the satisfiability of propositional logic is a subcase of satisfiability for any normal modal logic, thus for any normal modal logic the problem is NP-hard. In this paper we will focus on the standard modal logic K. For an introduction to modal logic and its complexity see [5,11].…”

Section: Introductionmentioning

confidence: 99%

Parameterized Modal Satisfiability

2011

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We investigate the parameterized computational complexity of the satisfiability problem for modal logic and attempt to pinpoint relevant structural parameters which cause the problem's combinatorial explosion, beyond the number of propositional variables v. To this end we study the modality depth, a natural measure which has appeared in the literature, and show that, even though modal satisfiability parameterized by v and the modality depth is FPT, the running time's dependence on the parameters is a tower of exponentials (unless P = NP). To overcome this limitation we propose possible alternative parameters, namely diamond dimension and modal width. We show fixed-parameter tractability results using these measures where the exponential dependence on the parameters is much milder (doubly and singly exponential respectively) than in the case of modality depth thus leading to FPT algorithms for modal satisfiability with much more reasonable running times. We also give lower bound arguments which prove that our algorithms cannot be improved significantly unless the Exponential Time Hypothesis fails.Keywords Modal logic · Parameterized complexity · Satisfiability problems A preliminary version of this paper has appeared in ICALP 2010.A. Achilleos · M. Lampis ( ) · V. Mitsou

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Section: Introductionmentioning

confidence: 99%

Parameterized Modal Satisfiability

2011

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“…We interpret programs in the runs and systems framework of Fagin et al [11], adapted to allow for names. We start with a possibly infinite set A of agents.…”

Section: Protocols Systems and Contextsmentioning

confidence: 99%

“…We do this using the framework of knowledge-based (kb) programs, proposed by Fagin et al [11,12] (FHMV from now on). Intuitively, in a kb program, an agent's actions may depend on his knowledge.…”

Section: Introductionmentioning

confidence: 99%

A knowledge-based analysis of global function computation

Halpern

Petride

2010

Distrib. Comput.

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Consider a distributed system N in which each agent has an input value and each communication link has a weight. Given a global function, that is, a function f whose value depends on the whole network, the goal is for every agent to eventually compute the value f (N ). We call this problem global function computation. Various solutions for instances of this problem, such as Boolean function computation, leader election, (minimum) spanning tree construction, and network determination, have been proposed, each under particular assumptions about what processors know about the system and how this knowledge can be acquired. We give a necessary and sufficient condition for the problem to be solvable that generalizes a number of well-known results (Attyia et al. in J ACM 35(4):845-875, 1988; Yamashita and Kameda in IEEE Trans Parallel Distrib Syst 7(1):69-89, 1996; Yamashita and Kameda in IEEE Trans Parallel Distrib Syst 10(9):878-887, 1999). We then provide a knowledge-based (kb) program (like those of Fagin et al. (Reasoning about knowledge, MIT Press,

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“…The problem is cast in terms of knowledge which provides a rigorous framework for studying this problem. Formalizing the levels of knowledge in a distributed system simplifies the analysis of various problems and the design of various protocols to solve the problems [6,10]. Knowledge analysis also provides a formal method for reasoning about distributed protocols and executions of asynchronous distributed systems [2].…”

Section: Introductionmentioning

confidence: 99%

“…Knowledge analysis also provides a formal method for reasoning about distributed protocols and executions of asynchronous distributed systems [2]. A good reference work on the theory of knowledge in distributed systems is a textbook by Fagin et al [6].…”

Section: Introductionmentioning

confidence: 99%

The power of logical clock abstractions

Kshemkalyani

2004

Distrib. Comput.

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Vector and matrix clocks are extensively used in asynchronous distributed systems. This paper asks, "how does the clock abstraction generalize?" To address this problem, the paper motivates and proposes logical clocks of arbitrary dimensions. It then identifies and explores the conceptual link between such clocks and knowledge. It establishes the necessary and sufficient conditions on the size and dimension of clocks required to attain any specified level of knowledge about the timestamp of the most recent system state for which this is possible without using any messages in the clock protocol. The paper then gives algorithms to determine the timestamp of the latest system state about which a specified level of knowledge is attainable in a given system state, and to compute the timestamp of the earliest system state in which a specified level of knowledge about a given system state is attainable. The results are applicable to applications that deal with a certain class of properties, identified as monotonic properties.

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Reasoning About Knowledge

Abstract: To my mother Maxine, who gave me a love of learning; to Susan, who is as happy and amazed as I am that The Book is finally completed; to Josh, Tim, and Teddy, who are impressed that their father is an Author; and to my late father George, who would have been proud.

Cited by 1,277 publications

References 0 publications

Parameterized Modal Satisfiability

Parameterized Modal Satisfiability

A knowledge-based analysis of global function computation

The power of logical clock abstractions

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