M.I. Fischer and N. Iramerman, Foundations of knowledge for distributed systems, Theoretical Aspects of Reasoning About Knowledge: Proceedings of the  Home/Search Document Not in Database Summary Related Articles Check |
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The Complexity of Reasoning about Knowledge and Time.. - Halpern, Vardi (1989) (75 citations) Self-citation (Systems) (Correct)
....result for the language without common knowledge. We also provide a complete axiomatization for the latter language. 1. Introduction It has been argued recently that knowledge is a useful concept for analyzing the behavior and interaction of processors in a distributed system [CM,DM,FI1,Hal,HF,HM1,LR,MT,PR, RK,Ros]. When analyzing a system in terms of knowledge, not only is the current state of knowledge of the processors in the system relevant, but also how that state of knowledge changes over time. A formal propositional logic of knowledge and time was first proposed by Sato [Sa] others have since been ....
....such as messages in transit but not yet delivered, and so on (of. FHV2] The environment component plays no role in the complexity analysis, so we omit it here. This interpretation of knowledge is called a state based interpretation in [HM1] and is essentially the interpretation used in [PR,HF,Ros,RK,FI1]. We will not consider the more general ep stenuk nterpretations discussed in [HM1] 3 run r was indistinguishable from r t at all points in the past. Intuitively, a processor that cannot distinguish two runs that it could distinguish at an earlier time must have forgotten the information that ....
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M.I. Fischer and N. Iramerman, Foundations of knowledge for distributed systems, Theoretical Aspects of Reasoning About Knowledge: Proceedings of the
What Can Machines Know? On the Properties of Knowledge in.. - Fagin, Halpern, Vardi (1996) (1 citation) Self-citation (Systems) (Correct)
....assumption is 6 often made in the distributed systems literature (cf. CM, HM1, HF, Le, PR, DM] This assumption is, of course, an idealization, since cumulative knowledge in general requires unbounded memory. Bounded memory is a more realistic assumption (and has been used in papers such as [FI, RK]) But note that for limited interactions, knowledge can be cumulative even with bounded memory. We remark that Halpern and Vardi have shown that the assumption that knowledge is cumulative has a drastic effect on the complexity of the decision procedure for validity of formulas involving ....
....complete axiomatizations of knowledge for various cases of interest. 26 An interesting direction in which to extend the line of research of this paper is to consider the effect of adding to the language common knowledge and or time. 7 By results of [HM1] since reproved and generalized in [CM, FI]) we know that under certain natural assumptions, common knowledge will not be attainable. For example, if at most one process changes its state at any given time, then no common knowledge is gained beyond the common knowledge that the processes already had in the initial state. So this ....
M.J. Fischer and N. Immerman, Foundations of knowledge for distributed systems, Theoretical Aspects of Reasoning about Knowledge (ed. J.Y. Halpern), Morgan Kaufmann, 1986, pp. 171--186.
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