Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 A model of distributed computations
- 3 Logical time
- 4 Global state and snapshot recording algorithms
- 5 Terminology and basic algorithms
- 6 Message ordering and group communication
- 7 Termination detection
- 8 Reasoning with knowledge
- 9 Distributed mutual exclusion algorithms
- 10 Deadlock detection in distributed systems
- 11 Global predicate detection
- 12 Distributed shared memory
- 13 Checkpointing and rollback recovery
- 14 Consensus and agreement algorithms
- 15 Failure detectors
- 16 Authentication in distributed systems
- 17 Self-stabilization
- 18 Peer-to-peer computing and overlay graphs
- Index
8 - Reasoning with knowledge
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 A model of distributed computations
- 3 Logical time
- 4 Global state and snapshot recording algorithms
- 5 Terminology and basic algorithms
- 6 Message ordering and group communication
- 7 Termination detection
- 8 Reasoning with knowledge
- 9 Distributed mutual exclusion algorithms
- 10 Deadlock detection in distributed systems
- 11 Global predicate detection
- 12 Distributed shared memory
- 13 Checkpointing and rollback recovery
- 14 Consensus and agreement algorithms
- 15 Failure detectors
- 16 Authentication in distributed systems
- 17 Self-stabilization
- 18 Peer-to-peer computing and overlay graphs
- Index
Summary
In a distributed system, processes make local decisions based on their limited view of the system state. A process learns of new facts when it receives messages from other processes, and can reason only with the additional knowledge available to it. This chapter provides a formal framework in which it is easier to understand the role of knowledge in the system, and how processes can reason with such knowledge. The first three sections are based on the book by Fagin et al. The logic of knowledge, classically termed as epistemic logic, is the formal logical analysis of reasoning about knowledge. Epistemic knowledge first received much attention from philosophers in the mid-twentieth century.
The muddy children puzzle
Consider the classical “muddy children” puzzle of Halpern and Moses and Halpern and Fagin. Imagine there are n children who return from playing outdoors, and k, k ≥ 1, of the n children have mud on their foreheads. Let Ψ denote the fact “at least one child has a muddy forehead.” Assume that each child can see all other children and their foreheads, but not their own forehead. We also assume that the children are intelligent and truthful, and answer any question asked of them, simultaneously. We now consider two scenarios.
- Type
- Chapter
- Information
- Distributed ComputingPrinciples, Algorithms, and Systems, pp. 282 - 304Publisher: Cambridge University PressPrint publication year: 2008