## Algorithmic Knowledge (1994)

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Venue: | Proc. Second Conference on Theoretical Aspects of Reasoning about Knowledge |

Citations: | 50 - 10 self |

### BibTeX

@INPROCEEDINGS{Halpern94algorithmicknowledge,

author = {Joseph Halpern and Yoram Moses and Moshe Y. Vardi},

title = {Algorithmic Knowledge},

booktitle = {Proc. Second Conference on Theoretical Aspects of Reasoning about Knowledge},

year = {1994},

pages = {255--266},

publisher = {Morgan Kaufmann}

}

### Years of Citing Articles

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### Abstract

: The standard model of knowledge in multi-agent systems suffers from what has been called the logical omniscience problem: agents know all tautologies, and know all the logical consequences of their knowledge. For many types of analysis, this turns out not to be a problem. Knowledge is viewed as being ascribed by the system designer to the agents; agents are not assumed to compute their knowledge in any way, nor is it assumed that they can necessarily answer questions based on their knowledge. Nevertheless, in many applications that we are interested in, agents need to act on their knowledge. In such applications, an externally ascribed notion of knowledge is insufficient: clearly an agent can base his actions only on what he explicitly knows. Furthermore, an agent that has to act on his knowledge has to be able to compute this knowledge; we do need to take into account the algorithms available to the agent, as well as the "effort" required to compute knowledge. In this paper, we show...

### Citations

2902 | A method for obtaining digital signatures and public-key cryptosystems
- Rivest, Shamir, et al.
- 1978
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Citation Context ...ll is modern-day cryptography. A popular approach in cryptography these days is to use computational difficulty to guarantee the security of encryption, via public-key cryptography (see, for example, =-=[RSA78]-=-). Messages are encrypted by applying a publicized function to the original text of the message. These functions are chosen in such a way that decrypting an encrypted message is easy for an agent who ... |

1866 | P.: Randomized algorithms
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- 1997
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Citation Context ...iϕ ⇒ Evi(ϕ) ≤ 1−α 2−(α+β) if (α, β) �= (1, 1); (d) N |= ¬Xiϕ ∧ ¬Kiϕ ⇒ Evi(ϕ) = 0 if (α, β) = (1, 1). Proposition 5.3 becomes interesting in the context of well-known classes of randomized algorithms [=-=Motwani and Raghavan 1995-=-]. An RP (random polynomial-time) algorithm is a polynomial-time randomized algorithm that is (1/2, 0)-reliable. It thus follows from Proposition 5.3 that if Ai is an RP algorithm, then N |= (Xiϕ ∧ ¬K... |

1492 |
Reasoning about Knowledge
- Fagin, Halpern, et al.
- 2003
(Show Context)
Citation Context ..., vardi@cs.rice.edu 1 Introduction Representing knowledge in terms of possible-world semantics has proved quite useful. One important application has been to analyzing complex multi-agent systems. In =-=[FHMV95]-=-, a formal model of knowledge in multi-agent systems is proposed (which, in turn, is based on earlier models that appeared in [CM86, HF89, HM90, PR85, RK86]). This model of knowledge satisfies the axi... |

1032 | The Knowledge Complexity of Interactive Proof Systems - Goldwasser, Micali, et al. - 1989 |

491 | Knowledge and common knowledge in a distributed environment - Halpern, Moses - 1990 |

433 | Knowledge and Belief - Hintikka - 1962 |

406 | The inductive approach to verifying cryptographic protocols. Journal of computer security - Paulson - 1998 |

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A guide to completeness and complexity for modal logics of knowledge and belief
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- 1992
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Citation Context ...our definition makes clear that computing whether an agent knows ' has essentially nothing to do with computing whether ' is valid. The fact that checking validity is PSPACEcomplete in multi-agent S5 =-=[HM92]-=- does not indicate that computing knowledge in any particular situation will necessarily be hard. On the other hand, as we shall see, there is a connection between computing knowledge and the model-ch... |

267 |
A logic of implicit and explicit belief
- Levesque
- 1984
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Citation Context ...ould have been able to deal with Konolige's framework in its full generality. Levesque's logic of explicit belief: Levesque introduced a notion of explicit belief , captured by a modal operator B, in =-=[Lev84]-=-, with the property that the validity of formulas of the form B ) B', forsand ' propositional formulas in conjunctive normal form (CNF) can be decided in polynomial time. Moreover, he proved that if B... |

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A Deduction Model of Belief
- Konolige
- 1986
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Citation Context ...number of other papers that were concerned with the problem of computing knowledge. One of the first works in the AI literature relating knowledge and resource-bounded computation is that of Konolige =-=[Kon86]-=-. Under reasonable assumptions, Konolige's approach can be embedded in ours. The treatment of resource-bounded knowledge suggested by Moses [Mos88], and its extensions by Halpern, Moses and Tuttle [HM... |

190 | Probabilistic algorithm for testing primality - Rabin - 1980 |

145 |
Semantical analysis of modal logic I: Normal modal propositional calculi. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik
- Kripke
- 1963
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Citation Context ... can compute ϕ”). As usual, we take ϕ ∨ ψ to be an abbreviation for ¬(¬ϕ ∧ ¬ψ) and ϕ ⇒ ψ to be an abbreviation for ¬ϕ ∨ ψ. The standard possible-worlds semantics for knowledge uses Kripke structures [=-=Kripke 1963-=-]. Formally, a Kripke structure is composed of a set S of states or possible worlds, an interpretation π which associates with each state in S a truth assignment to the primitive propositions (i.e., π... |

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130 |
AOP: Agent Oriented Programming
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- 1993
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Citation Context ...`does ' hold?' and K i ' do say `Yes"'. (Knowledgebased programs are related in spirit to the knowledge-based protocols of [HF89], and to the notion of agent-oriented programming introduced by Sh=-=oham [Sho93]-=-.) Such a program contains only a finite number of knowledge tests. Thus, in order to implement such a program, we need an algorithm that is complete only with respect to the tests in the program. Mor... |

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

117 | Model checking vs. theorem proving: A manifesto
- Halpern, Vardi
- 1991
(Show Context)
Citation Context ...hand, as we shall see, there is a connection between computing knowledge and the model-checking problem, that is, the problem of checking whether a formula is true at a particular point in the system =-=[HV91]-=-. While the definition of algorithmic knowledge draws a direct connection between an agent's explicit knowledge and the need to compute this knowledge, X i ' as defined is a notion of belief. An algor... |

102 | Bounded complexity justifies cooperation in the finitely repeated prisoners’ dilemma - Neyman - 1985 |

96 |
A probabilistic PDL
- Kozen
- 1983
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Citation Context ...extend the logic to distinguish them. 4To get around this particular problem, some approaches that combine logic and probability give semantics to formulas by viewing them as random variables (e.g., [=-=Kozen 1985-=-]).s6 J. Y. HALPERN AND R. PUCELLA with probability α at a state by considering the probability of those sequences of coin tosses at the state that make the algorithm answer “Yes”. Formally, we start ... |

93 | Reasoning situated in time I: Basic concepts - Elgot-Drapkin, Perlis - 1990 |

93 |
awareness and limited reasoning
- Belief
- 1987
(Show Context)
Citation Context ...ledge. As expected, a model that takes computation into account does not suffer from the logical omniscience problem. Indeed, the solution we propose here is closely related to a solution proposed in =-=[FH88]-=- for dealing with the logical omniscience problem, namely, to include an awareness function. And, just like that solution, it has a syntactic component. There have been a number of other papers that w... |

88 | How processes learn - Chandy, Misra - 1986 |

86 |
Impossible Possible Worlds Vindicated
- Hintikka
- 1975
(Show Context)
Citation Context ...arlier models that appeared in [CM86, HF89, HM90, PR85, RK86]). This model of knowledge satisfies the axioms of S5. In particular, it suffers from what has been called the logical omniscience problem =-=[Hin75]-=-: agents know all tautologies, and know all the logical consequences of their knowledge. This was not viewed as a problem in the context of those papers, since knowledge is viewed as being ascribed by... |

85 | Modelling knowledge and action in distributed systems
- Halpern, Fagin
- 1989
(Show Context)
Citation Context ...ledge and action. Such programs can contain statements of the form "if asked `does ' hold?' and K i ' do say `Yes"'. (Knowledgebased programs are related in spirit to the knowledge-based pro=-=tocols of [HF89]-=-, and to the notion of agent-oriented programming introduced by Shoham [Sho93].) Such a program contains only a finite number of knowledge tests. Thus, in order to implement such a program, we need an... |

71 | Knowledge, probability, and adversaries - Halpern, Tuttle - 1993 |

65 | Using reasoning about knowledge to analyze distributed systems - Halpern - 1987 |

60 |
Essays on the foundations of game theory
- Binmore
- 1990
(Show Context)
Citation Context ...cantly different, it is in the spirit of [Mos88, HMT88]. There have also been many attempts in the game-theoretical literature to model resource-bounded agents, e.g., [Meg89, MW86, Ney85, Rub85] (see =-=[Bin90]-=-(Chapters 5-6) for a foundational discussion); our formal model is much different from any proposed in this literature. 2 Knowledge in multi-agent systems We briefly review the framework of [FHMV95] f... |

55 | Distributed processing and the logic of knowledge - Parikh, Ramanujam - 1985 |

34 |
Towards optimal distributed consensus
- Berman, Garay, et al.
- 1989
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Citation Context ...g in terms of algorithmic knowledge may be necessary as well. One example where algorithmic knowledge has been found to be useful is in the design and description of protocols for Byzantine agreement =-=[BGP89]-=-. Although the notion of algorithmic knowledge was not explicitly used in [BGP89], the reasoning done there can be embedded directly in our framework. 5 Conclusions We have presented a conceptually si... |

26 | A knowledge-based analysis of zero knowledge
- Halpern, Moses, et al.
- 1988
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Citation Context ...86]. Under reasonable assumptions, Konolige's approach can be embedded in ours. The treatment of resource-bounded knowledge suggested by Moses [Mos88], and its extensions by Halpern, Moses and Tuttle =-=[HMT88]-=- to treat aspects of interactive proofs and zero knowledge proofs [GMR89], can be viewed as precursors of this work. Although our model is significantly different, it is in the spirit of [Mos88, HMT88... |

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20 |
Recent work in inductive logic
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- 1983
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Citation Context ...THMIC KNOWLEDGE 3 as evidence that ϕ is true; the probability that ϕ is true also depends in part on the prior probability of ϕ. Evidence has been widely studied in the literature on inductive logic [=-=Kyburg 1983-=-]. We focus on the evidence contributed specifically by a randomized knowledge algorithm. In a companion paper [Halpern and Pucella 2003], we consider a formal logic for reasoning about evidence. The ... |

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11 | On computable beliefs of rational machines - Megiddo - 1989 |

7 | View-based explicit knowledge - Ramanujam - 1999 |

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5 | A Favorable Strategy for Twenty-One - Thorp - 1961 |

1 | Beat the dealer. Vintage - Thorp - 1966 |