Skip to main content

Dynamic Epistemic Logics of Introspection

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10669))

Abstract

This work studies positive and negative introspection not as properties, but rather as actions that change the agent’s knowledge. The actions are introduced as model update operations, with matching modalities expressing their effects. Sound and complete axiom systems are provided, and some properties are explored.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    The paradigmatic example is \(p \wedge \lnot \mathop {\Box }{p}\).

  2. 2.

    Proof: http://homepages.cwi.nl/~jve/courses/lai0506/Solutions2.pdf.

References

  1. Hintikka, J.: Knowledge and Belief. Cornell University Press, Ithaca (1962)

    MATH  Google Scholar 

  2. Hendricks, V.F.: 8 bridges between formal and mainstream epistemology. Philos. Stud. 128(1), 1–5 (2006)

    Article  MathSciNet  Google Scholar 

  3. Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  4. de Bruin, B.: Explaining Games: The Epistemic Programme in Game Theory. Synthese Library, vol. 346. Springer, Dordrecht (2010). https://doi.org/10.1007/978-1-4020-9906-9

    Book  MATH  Google Scholar 

  5. van Ditmarsch, H., French, T.: Semantics for knowledge and change of awareness. J. Logic Lang. Inf. 23(2), 169–195 (2014)

    MathSciNet  MATH  Google Scholar 

  6. Grossi, D., Velázquez-Quesada, F.R.: Syntactic awareness in logical dynamics. Synthese 192(12), 4071–4105 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  7. van Benthem, J., Pacuit, E.: Dynamic logics of evidence-based beliefs. Stud. Logica 99(1), 61–92 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Velázquez-Quesada, F.R.: Explicit and implicit knowledge in neighbourhood models. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI 2013. LNCS, vol. 8196, pp. 239–252. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40948-6_19

    Chapter  Google Scholar 

  9. Balbiani, P., Fernández-Duque, D., Lorini, E.: A logical theory of belief dynamics for resource-bounded agents. In: Jonker, C.M., Marsella, S., Thangarajah, J., Tuyls, K. (eds.) Proceedings AAMAS 2016, pp. 644–652. ACM (2016)

    Google Scholar 

  10. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer, Dordrecht (2008). https://doi.org/10.1007/978-1-4020-5839-4

    MATH  Google Scholar 

  11. van Benthem, J.: Logical Dynamics of Information and Interaction. CUP, New York (2011)

    Book  MATH  Google Scholar 

  12. van Benthem, J.: Dynamic logic for belief revision. J. Appl. Non-Class. Logics 17(2), 129–155 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. van Benthem, J., Liu, F.: Dynamic logic of preference upgrade. J. Appl. Non-Class. Logics 17(2), 157–182 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  14. Ghosh, S., Velázquez-Quesada, F.R.: Agreeing to agree: reaching unanimity via preference dynamics based on reliable agents. In: Weiss, G., Yolum, P., Bordini, R.H., Elkind, E. (eds.) Proceedings AAMAS 2015, pp. 1491–1499. ACM (2015)

    Google Scholar 

  15. Ghosh, S., Velázquez-Quesada, F.R.: A note on reliability-based preference dynamics. In: van der Hoek, W., Holliday, W.H., Wang, W. (eds.) LORI 2015. LNCS, vol. 9394, pp. 129–142. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48561-3_11

    Chapter  Google Scholar 

  16. Pucella, R., Weissman, V.: Reasoning about dynamic policies. In: Walukiewicz, I. (ed.) FoSSaCS 2004. LNCS, vol. 2987, pp. 453–467. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24727-2_32

    Chapter  Google Scholar 

  17. Göller, S.: On the complexity of reasoning about dynamic policies. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 358–373. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74915-8_28

    Chapter  Google Scholar 

  18. Benthem, J.: An essay on sabotage and obstruction. In: Hutter, D., Stephan, W. (eds.) Mechanizing Mathematical Reasoning. LNCS (LNAI), vol. 2605, pp. 268–276. Springer, Heidelberg (2005). https://doi.org/10.1007/978-3-540-32254-2_16

    Chapter  Google Scholar 

  19. Areces, C., Fervari, R., Hoffmann, G.: Moving arrows and four model checking results. In: Ong, L., de Queiroz, R. (eds.) WoLLIC 2012. LNCS, vol. 7456, pp. 142–153. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32621-9_11

    Chapter  Google Scholar 

  20. Areces, C., Fervari, R., Hoffmann, G.: Swap logic. Logic J. IGPL 22(2), 309–332 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  21. Fervari, R.: Relation-Changing Modal Logics. Ph.D. thesis, Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Argentina (2014)

    Google Scholar 

  22. Areces, C., Fervari, R., Hoffmann, G.: Relation-changing modal operators. Logic J. IGPL 23(4), 601–627 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. Kooi, B., Renne, B.: Arrow update logic. Rev. Symb. Logic 4, 536–559 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)

    Book  MATH  Google Scholar 

  25. Blackburn, P., de Rijke, M., Venema, Y.: Modal logic. CUP, New York (2001)

    Book  MATH  Google Scholar 

  26. Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)

    MATH  Google Scholar 

  27. van Eijck, J., Wang, Y.: Propositional dynamic logic as a logic of belief revision. In: Hodges, W., de Queiroz, R. (eds.) WoLLIC 2008. LNCS (LNAI), vol. 5110, pp. 136–148. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69937-8_13

    Chapter  Google Scholar 

  28. Prior, A.N.: Time and Modality. Clarendon Press, Oxford (1957)

    MATH  Google Scholar 

  29. Parikh, R.: The completeness of propositional dynamic logic. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 403–415. Springer, Heidelberg (1978). https://doi.org/10.1007/3-540-08921-7_88

    Chapter  Google Scholar 

  30. Holliday, W., Icard, T.: Moorean phenomena in epistemic logic. In: Beklemishev, L., Goranko, V., Shehtman, V. (eds.) Advances in Modal Logic, College Publications, pp. 178–199 (2010)

    Google Scholar 

  31. Plaza, J.A.: Logics of public communications. In: Emrich, M.L., Pfeifer, M.S., Hadzikadic, M., Ras, Z.W. (eds.) Proceedings 4th International Symposium on Methodologies for Intelligent Systems, Oak Ridge National Laboratory, pp. 201–216 (1989)

    Google Scholar 

  32. van Benthem, J., van Eijck, J., Kooi, B.: Logics of communication and change. Inf. Comput. 204(11), 1620–1662 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was partially supported by grant ANPCyT-PICT-2013-2011, STIC-AmSud “Foundations of Graph Structured Data (FoG)”, SeCyT-UNC, the Laboratoire International Associé “INFINIS”, and the European Union’s Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No. 690974 for the project MIREL: MIning and REasoning with Legal texts.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Fernando R. Velázquez-Quesada .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Fervari, R., Velázquez-Quesada, F.R. (2018). Dynamic Epistemic Logics of Introspection. In: Madeira, A., Benevides, M. (eds) Dynamic Logic. New Trends and Applications. DALI 2017. Lecture Notes in Computer Science(), vol 10669. Springer, Cham. https://doi.org/10.1007/978-3-319-73579-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-73579-5_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73578-8

  • Online ISBN: 978-3-319-73579-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics