Advertisement

Logics for Moderate Belief-Disagreement Between Agents

  • Jia Chen
  • Tianqun Pan
Article

Abstract

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.

Keywords

Moderate belief-disagreement Possible worlds semantics Multiagent situation Epistemic logics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

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.

References

  1. 1.
    Aumann, R.J., Agreeing to disagree, Annals of Statistics 4(6): 1236–1239, 1976.Google Scholar
  2. 2.
    Brössel, P., and A.M. Eder, How to resolve doxastic disagreement, Synthese 191(11): 2359–2381, 2014.CrossRefGoogle Scholar
  3. 3.
    Christensen, D., Epistemology of Disagreement: The Good News, The Philosophical Review 116(2): 187–217, 2007.CrossRefGoogle Scholar
  4. 4.
    Fagin, R., Y. Moses, J.Y. Halpern, and M.Y. Vardi, Reasoning about Knowledge, MIT press, Cambridge, Mass., and London, England, 2003.Google Scholar
  5. 5.
    Humberstone, I.L., The Logic of Non-contingency, Notre Dame Journal of Formal Logic 36: 214–229, 1995.CrossRefGoogle Scholar
  6. 6.
    Kuhn, S.T., Minimal Non-contingency Logic, Notre Dame Journal of Formal Logic 36: 230–234, 1995.CrossRefGoogle Scholar
  7. 7.
    Marcos, J., Logics of Essence and Accident, Bulletin of the Section of Logic 34: 43–56, 2005.Google Scholar
  8. 8.
    Pan, Tian-qun, On logic of belief-disagreement among agents, in H.P. van Ditmarsch, J. Lang, and S. Ju (eds.), Logic, Rationality, and Interaction: Third International Workshop, LORI 2011, Guangzhou, China, October 10-13, 2011. Proceedings, Springer, Berlin Heidelberg, 2011, pp. 392–293.Google Scholar
  9. 9.
    Rowbottom, D. P., What is (Dis)Agreement?, Philos Phenomenol Res. 2016. https://doi.org/10.1111/phpr.12354.
  10. 10.
    Steinsvold, C., Completeness for Various Logics of Essence and Accident, Bulletin of the Section of Logic 37: 93–101, 2008.Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of PhilosophyNanjing UniversityNanjingChina

Personalised recommendations