Logics for Moderate Belief-Disagreement Between Agents

  • Jia Chen
  • Tianqun Pan


A moderate belief-disagreement between agents on proposition p means that one agent believes p and the other agent does not. This paper presents two logical systems, \(\mathbf {MD}\) and \(\mathbf {MD}^D\), that describe moderate belief-disagreement, and shows, using possible worlds semantics, that \(\mathbf {MD}\) is sound and complete with respect to arbitrary frames, and \(\mathbf {MD}^D\) is sound and complete with respect to serial frames. Syntactically, the logics are monomodal, but two doxastic accessibility relations are involved in their semantics. The notion of moderate belief-disagreement, which is in accordance with the understanding of belief-disagreement in everyday life, is an epistemic one related to multiagent situations, and \(\mathbf {MD}\) and \(\mathbf {MD}^D\) are two epistemic logics.


Moderate belief-disagreement Possible worlds semantics Multiagent situation Epistemic logics 


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The authors are grateful to the anonymous reviewers of this journal and LOFT 12 for their insightful comments and revising suggestions which helped us to improve the paper.


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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhilosophyNanjing UniversityNanjingChina

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