DeepAI AI Chat
Log In Sign Up

Reasoning About Common Knowledge with Infinitely Many Agents

by   Joseph Y. Halpern, et al.

Complete axiomatizations and exponential-time decision procedures are provided for reasoning about knowledge and common knowledge when there are infinitely many agents. The results show that reasoning about knowledge and common knowledge with infinitely many agents is no harder than when there are finitely many agents, provided that we can check the cardinality of certain set differences G - G', where G and G' are sets of agents. Since our complexity results are independent of the cardinality of the sets G involved, they represent improvements over the previous results even with the sets of agents involved are finite. Moreover, our results make clear the extent to which issues of complexity and completeness depend on how the sets of agents involved are represented.


page 1

page 2

page 3

page 4


The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics

We study the complexity of the combination of the Description Logics ALC...

Complete Axiomatizations for Reasoning About Knowledge and Time

Sound and complete axiomatizations are provided for a number of differen...

Subjective Knowledge and Reasoning about Agents in Multi-Agent Systems

Though a lot of work in multi-agent systems is focused on reasoning abou...

Two's Company, Three's a Crowd: Consensus-Halving for a Constant Number of Agents

We consider the ε-Consensus-Halving problem, in which a set of heterogen...

On cardinality of the lower sets and universal discretization

A set Q in ℤ_+^d is a lower set if (k_1,…,k_d)∈ Q implies (l_1,…,l_d)∈ Q...

Credibility Discounting in the Theory of Approximate Reasoning

We are concerned with the problem of introducing credibility type inform...

Few self-involved agents among BC agents can lead to polarized local or global consensus

Social issues are generally discussed by highly-involved and less-involv...