, Volume 195, Issue 10, pp 4343–4372 | Cite as

Knowledge, belief, normality, and introspection

  • Dominik KleinEmail author
  • Olivier Roy
  • Norbert Gratzl
S.I.: LORI - V


We study two logics of knowledge and belief stemming from the work of Stalnaker (2006), omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation underlying both models of belief, showing that neither is strong enough to support a probabilistic interpretation, nor an interpretation in terms of certainty or the “mental component” of knowledge.


Epistemic logic Doxastic logic Epistemic–doxastic logic Stalnaker Epistemology Formal epistemology 


  1. Baltag, A., Bezhanishvili, N., Özgün, A., & Smets, S. (2013). The topology of belief, belief revision and defeasible knowledge. In D. Grossi, O. Roy & H. Huang (Eds.), Logic, Rationality, and Interaction. LORI 2013. Lecture Notes in Computer Science (Vol. 8196). Berlin: Springer.Google Scholar
  2. Belnap, N. (1982). Display logic. Journal of Philosophical Logic, 11, 375–417.Google Scholar
  3. Blackburn, P., De Rijke, M., & Venema, Y. (2002). Modal logic (Vol. 53). Cambridge: Cambridge University Press.Google Scholar
  4. Chellas, B. F. (1980). Modal logic: An introduction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  5. Ciabattoni, A., Ramanayake, R., & Wansing, H. (2014). Hypersequent and display calculi-a unified perspective. Studia Logica, 102(6), 1245–1294.CrossRefGoogle Scholar
  6. Fagin, R., Geanakoplos, J., Halpern, J. Y., & Vardi, M. Y. (1999). The hierarchical approach to modeling knowledge and common knowledge. International Journal of Game Theory, 28(3), 331–365.CrossRefGoogle Scholar
  7. Galeazzi, P., & Lorini, E. (2016). Epistemic logic meets epistemic game theory: A comparison between multi-agent kripke models and type spaces. Synthese, 193(7), 2097–2127.CrossRefGoogle Scholar
  8. Gentzen, G. (1935). Untersuchungen über das logische schließen. i. Mathematische Zeitschrift, 39(1), 176–210.CrossRefGoogle Scholar
  9. Hendricks, V. F. (2003). Active agents. Journal of Logic, Language and Information, 12(4), 469–495.CrossRefGoogle Scholar
  10. Hintikka, J. (1962). Knowledge and belief: An introduction to the logic of the two notions. New York: Cornell University Press.Google Scholar
  11. Klein, D., & Pacuit, E. (2014). Changing types: Information dynamics for qualitative type spaces. Studia Logica, 102(2), 297–319.CrossRefGoogle Scholar
  12. Kracht, M. (1996). Power and weakness of the modal display calculus. In H. Wansing (Ed.), Proof theory of modal logic (pp. 95–120). Oxford: OUP.Google Scholar
  13. Leitgeb, H. (2014). The stability theory of belief. Philosophical Review, 123(2), 131–171.CrossRefGoogle Scholar
  14. Lenzen, W. (1979). Epistemologische betrachtungen zu [s4, s5]. Erkenntnis, 14(1), 33–56.CrossRefGoogle Scholar
  15. Özgün, A. (2013). Topological models for belief and belief revision. Master’s thesis, Universiteit van Amsterdam.Google Scholar
  16. Pacuit, E. (2016). Neighborhood Semantics for Modal Logic (Forthcoming).Google Scholar
  17. Poggiolesi, F. (2011). Display calculi and other modal calculi: A comparison. Synthese, 173, 259–279.CrossRefGoogle Scholar
  18. Stalnaker, R. (2006). On logics of knowledge and belief. Philosophical Studies, 128(1), 169–199.CrossRefGoogle Scholar
  19. Wansing, H. (1998). Displaying modal logic. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  20. Wansing, H. (2002). Sequent systems for modal logics. In Handbook of philosophical logic (Vol. 8, pp. 61–145). Berlin: Springer.Google Scholar
  21. Williamson, T. (2000). Knowledge and its limits. oxford: Oxford University Press.Google Scholar

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© Springer Nature B.V. 2017

Authors and Affiliations

  1. 1.Philosophy DepartmentUniversity of BayreuthBayreuthGermany
  2. 2.Department of Political ScienceUniversity of BambergBambergGermany
  3. 3.Fakultät für Philosophie, Wissenschaftstheorie und Religionswissenschaft, Munich Center for Mathematical Philosophy (MCMP)Ludwig-Maximilians-Universität MünchenMünchenGermany

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