## What Can Machines Know? On the Properties of Knowledge in Distributed Systems (1996)

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Venue: | Journal of the ACM |

Citations: | 50 - 8 self |

### BibTeX

@ARTICLE{Fagin96whatcan,

author = {Ronald Fagin and Joseph Y. Halpern and Moshe Y. Vardi},

title = {What Can Machines Know? On the Properties of Knowledge in Distributed Systems},

journal = {Journal of the ACM},

year = {1996},

volume = {39},

pages = {328--376}

}

### Years of Citing Articles

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### Abstract

It has been argued that knowledge is a useful tool for designing and analyzing complex systems. The notion of knowledge that seems most relevant in this context is an external, information-based notion that can be shown to satisfy all the axioms of the modal logic S5. We carefully examine the properties of this notion of knowledge and show that they depend crucially, and in subtle ways, on assumptions we make about the system and about the language used for describing knowledge. We present a formal model in which we can capture various assumptions frequently made about systems, such as whether they are deterministic or nondeterministic, whether knowledge is cumulative (which means that processes never "forget"), and whether or not the "environment" affects the state transitions of the processes. We then show that under some assumptions about the system and the language, certain states of knowledge are not attainable and the axioms of S5 do not completely characterize the pr...

### Citations

1851 | Nonparametric Statistics - Savage - 1957 |

514 | Knowledge and Common Knowledge in a Distributed Environment, in Theoretical Aspects of Reasoning about Knowledge
- Halpern, Moses
- 1984
(Show Context)
Citation Context ...s perfectly consistent with S5, it is not attainable under the assumptions of [FV2]. To see that it is not attainable, it is convenient to consider the notion of distributed knowledge 1 introduced in =-=[HM1]-=- and studied in [CM, DM, FV2, MT, PR, RK]). Roughly speaking, a group has distributed knowledge of a fact if by putting all their information together, the members of the group could deduce that fact.... |

470 |
Knowledge and Belief
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- 1962
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Citation Context ...re. We begin by sketching a completeness proof for S5 n for the language L n (\Phi), since our later proofs will be in the same spirit. (The completeness result was proved by Kripke [Kr] and Hintikka =-=[Hi] for S5, a-=-nd extended by Halpern and Moses to S5 n [HM2]. The "maximal consistent sets" construction that we use is due to Makinson [Ma].) Theorem 7.1: S5 n is a sound and complete axiomatization with... |

288 | A logic of implicit and explicit belief - Levesque - 1984 |

163 |
Reasoning about knowledge and action
- Moore
- 1980
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Citation Context ... knowledge of the process cumulative? Many papers that consider reasoning about knowledge over time implicitly assume that knowledge is cumulative. Indeed, this is one of the major reasons that Moore =-=[21]-=- considers knowledge rather than belief. As Moore points out, “If we observe or perform a physical action, we generally know everything we knew before, plus whatever we have learned from the action.” ... |

151 | The complexity of reasoning about knowledge and time - Halpern, Vardi - 1989 |

136 | The synthesis of digital machines with provable epistemic properties - Rosenschein, Kaelbling - 1986 |

133 | Knowledge and common knowledge in a byzantine environment: Crash failures - Dwork, Moses - 1990 |

94 | Programming simultaneous actions using common knowledge - Moses, Tuttle |

93 |
How processes learn
- Chandy, Misra
- 1986
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Citation Context ...stent with S5, it is not attainable under the assumptions of [8]. To see that it is not attainable, it is convenient to consider the notion of distributed knowledge’ introduced in [11] and studied in =-=[2]-=-, [3], [8], [22], [23], and [26]. Roughly speaking, a group has distributed knowledge of a fact if by putting all their information together, the members of the group could deduce that fact. In the cl... |

88 | Modelling knowledge and action in distributed systems
- Halpern, Fagin
- 1989
(Show Context)
Citation Context ...ote that we have made no commitment here as to how the transitions between global states occur. There is no notion of messages or communication in our model, as there is, for example, in the model of =-=[10]-=-. While it is easy to incorporate messages and have the transitions occurring as a result of certain messages being received or sent, transitions might also be a result of physical interactions or eve... |

74 |
A Guide to the Modal Logics of Knowledge and Belief
- Halpern, Moses
- 1985
(Show Context)
Citation Context ...already had in the initial state. So this assumption, along with suitable assumptions about the initial states, will cause extra axioms to hold beyond the standard S5 axioms for common knowledge (see =-=[Le, HM2]-=- for a discussion of the S5 axioms of common knowledge). We expect to find yet other complexities if we allow the language to talk explicitly about time by adding temporal modalities (as is done in [L... |

63 |
Semantical analysis of modal logic I, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik vol
- Kripke
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Citation Context ...ef can be found in [HM2]). Indeed, the abstract models most frequently used to capture this notion (for example, in [Ro]) have been variants of the classical Kripke-style possible-worlds model for S5 =-=[Kr]-=-. But, a priori, it is not the least bit clear that this is the appropriate abstraction for the notion of knowledge in which we are interested. Does each state of an S5 Kripke structure really corresp... |

63 |
Formal theories of knowledge in ai and robotics
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- 1985
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Citation Context ...ples). In AI, there have been two approaches to ascribing knowledge to machines or components of systems. The classical AI approach, which has been called the interpreted-symbolic-structures approach =-=[25]-=-, ascribes knowledge on the basis of the information stored in certain data structures (such as semantic nets, frames, or data structures to encode formulas of predicate logic; cf. [1]). The second, c... |

62 | Distributed processes and the logic of knowledge - Parikh, Ramanujam - 1985 |

37 | Process logic - Pratt - 1979 |

30 |
A formal model of knowledge, action, and communication in dis- tributed systems: preliminary report, ~tCM-PODC
- Halpem, Fagin
- 1985
(Show Context)
Citation Context ...ote that we have made no commitment here as to how the transitions between global states occur. There is no notion of messages or communication in our model, as there is, for example, in the model of =-=[HF]-=-. While it is easy to incorporate messages and have the transitions occurring as a result of certain messages being received or sent, transitions might also be a result of physical interactions or eve... |

26 | Foundations of knowledge for distributed systems - Fischer, Immerman - 1986 |

23 | Alternative semantics for temporal logics - Emerson - 1983 |

22 |
Semantical analysis of modal logic
- Kripke
- 1959
(Show Context)
Citation Context ...ge and belief can be found in [12]). Indeed, the abstract models most frequently used to capture this notion (e.g., [251) have been variants of the classical Kripke-style possible-worlds model for S5 =-=[16]-=-. But, a priori, it is not the least bit clear that this is the appropriate abstraction for the notion of knowledge in which we are interested. Does each state of an S5 Kripke structure really corresp... |

21 |
Formal Theories of Knowledge
- Rosenschein
(Show Context)
Citation Context ...mples). In AI there have been two approaches to ascribing knowledge to machines or components of systems. The classical AI approach, which has been called the interpretedsymbolic -structures approach =-=[Ro]-=-, ascribes knowledge on the basis of the information stored in certain data structures (such as semantic nets, frames, or data structures to encode formulas of predicate logic; cf. [BL]). The second, ... |

20 | 1986] The logic of distributed protocols
- Ladner, Reif
(Show Context)
Citation Context ... forgetting means that the set of possible runs does not increase with time, no learning means that the set of possible runs does not decrease with time. This notion was introduced by Ladner and Reif =-=[17]-=-, who viewed it as a situation where each player’s strategy is preordained and cannot be changed over time (and thus is rzonadaptfie), and studied further by Halpern and Vardi [13, 14]. In a syrzci%-o... |

18 |
On some completeness theorems in modal logic’, Zeitschrift fr mathematische Logik und Grundlagen der Mathematik 12:379–384
- Makinson
- 1966
(Show Context)
Citation Context ...(The completeness result was proved by Kripke [Kr] and Hintikka [Hi] for S5, and extended by Halpern and Moses to S5 n [HM2]. The "maximal consistent sets" construction that we use is due to=-= Makinson [Ma]-=-.) Theorem 7.1: S5 n is a sound and complete axiomatization with respect to S5 Kripke structures of n processes, for the language L n (\Phi). Sketch of proof: Soundness is straightforward, as usual, s... |

17 | Knowledge and implicit knowledge in a distributed environment
- Fagin, Vardi
- 1986
(Show Context)
Citation Context ... in surprising ways, on the assumptions made about the system and about the language used for describing knowledge. In order to explain our results, it is helpful to briefly review some material from =-=[FV2]-=-, which directly inspired our work here. In [FV2], a very restricted type of system is considered, which intuitively can be viewed as one where robots observe their external environment and then commu... |

13 | An internal semantics for modal logic - Fagin, Vardi - 1985 |

11 | Knowledge, common knowledge and related puzzles (extended summary - Lehmann - 1984 |

8 |
Reasoning about knowledge and time in asynchronous systems
- Halpern, Vardi
- 1988
(Show Context)
Citation Context ...at 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 knowledge and time =-=[13, 14]-=-. – Is the system deterministic or nondeterministic? The answer to this question might depend partly on the granularity of our analysis. A system that seems deterministic at one level of analysis may ... |

4 |
Reasoning about knowledge and action, Technical Note 191
- Moore
- 1980
(Show Context)
Citation Context ...nowledge of the processes cumulative? Many papers that consider reasoning about knowledge over time implicitly assume that knowledge is cumulative. Indeed, this is one of the major reasons that Moore =-=[Mo] considers-=- knowledge rather than belief. As Moore points out, "If we observe or perform a physical action, we generally know everything we knew before, plus whatever we have learned from the action." ... |

4 |
Alternative semantics for temporal logics. Theoretical computer science
- Emerson
- 1983
(Show Context)
Citation Context ...1). 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 =-=[4]-=- and [26]). 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 h... |

2 | How processes learn’, Distributed Computing 1(1 - Chandy, Misra - 1986 |

2 |
The logic of distributed protocols, Theoretical Aspects of Reasoning about Knowledge
- Ladner, Reif
- 1986
(Show Context)
Citation Context ... forgetting means that the set of possible runs does not increase with time, no learning means that the set of possible runs does not decrease with time. This notion was introduced by Ladner and Reif =-=[LR]-=-, who viewed it as a situation where each player's strategy is preordained and cannot be changed over time (and thus is nonadaptive), and studied further by Halpern and Vardi [HV1, HV2]. 11 In a synch... |

1 |
What can Machines Know? On the Epistemic
- Fagin, Halpern, et al.
- 1986
(Show Context)
Citation Context ...s false, since that would contradict the conservation principle for distributed knowledge. So p must be true. And since this argument holds for all states 1 In [HM1], a previous version of this paper =-=[FHV], and othe-=-r papers, what we are now calling distributed knowledge was called implicit knowledge. We have changed the name here to avoid conflict with the usage of the term "implicit knowledge" in pape... |

1 |
Readings uz Knowledge Representutwn
- BRACHMAN, LEVESQUE
- 1985
(Show Context)
Citation Context ...tures approach [25], ascribes knowledge on the basis of the information stored in certain data structures (such as semantic nets, frames, or data structures to encode formulas of predicate logic; cf. =-=[1]-=-). The second, called the situated-automata approach, can be viewed as ascribing knowledge on the basis of the information carried by the state of the machine [25]. This second approach describes the ... |

1 |
What can machines know? On the eplstemic properties of machines
- FAGIN, HALPERN, et al.
- 1986
(Show Context)
Citation Context ...b knows p (since he received the message) and Alice does not know whether p is true or false (since she does not know whether Bob received her message). But lIn [11], a previous version of this paper =-=[6]-=-, and other papers, what we are now calbng distributed knowledge was called wnpkclt knowledge. We have changed the name here to avoid conflict with the usage of the term “imphcit knowledge” in papers ... |

1 |
A guide to the modal Iogics of knowledge and belief
- HALPERN, MOSES
- 1985
(Show Context)
Citation Context ...our semantics is based on the standard Kripke semantics [16], we begin by reviewing the Kripke semantics for the truth of a formula at a state of a Kripke structure (where we follow Halpern and Moses =-=[12]-=- in the definition of the truth of a formula involving distributed knowledge). A Krzpke structure is a tuple (S, m, %1,..., %.), where S is a set of “states,” where m(s) is a truth assignment to the p... |

1 |
A logic of implicit and explicit belief
- LEVESOUE
- 1984
(Show Context)
Citation Context ...rs, what we are now calbng distributed knowledge was called wnpkclt knowledge. We have changed the name here to avoid conflict with the usage of the term “imphcit knowledge” in papers such as [5] and =-=[19]-=-.sWhat Can Machines Know? Distributed Systems 331 Alice does know that either p is true and Bob knows that p is true, or else p is false and Bob does not know that p is fake (since if p is false, Bob ... |

1 |
on some completeness theorems in modal logic
- MASGNSON
- 1966
(Show Context)
Citation Context ... (The completeness result was proved by Kripke [16] and Hintikka [15] for S5, and extended by Halpern and Moses to S5fl [12]. The “maximal consistent sets” construction that we use is due to Makinson =-=[20]-=-.) THEOREM A. 1. S5n is a sound and complete axiomatization with respect to S5 Kr@ke structures of n processes, for the language Y.(@). SKETCH OF PROOF. Soundness is straightforward, as usual, so we f... |

1 |
Distributed processing and the loglc of knowledge
- PARIKH, RAMANUJAM
(Show Context)
Citation Context ...not attainable under the assumptions of [8]. To see that it is not attainable, it is convenient to consider the notion of distributed knowledge’ introduced in [11] and studied in [2], [3], [8], [22], =-=[23]-=-, and [26]. Roughly speaking, a group has distributed knowledge of a fact if by putting all their information together, the members of the group could deduce that fact. In the class of systems conside... |

1 | Tlzc FozmdatLons of Starzstzcs. Wdey - SAVAGE - 1954 |