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Journal of Logic, Language and Information

, Volume 23, Issue 2, pp 107–140 | Cite as

Dynamic Epistemic Logic for Implicit and Explicit Beliefs

  • Fernando R. Velázquez-Quesada
Article

Abstract

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are logically omniscient: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have argued that solutions of this kind are not completely adequate because they do not look at the heart of the matter: the actions that allow the agent to reach such omniscient state. Recent works have explored how acts of observation, inference, consideration and forgetting affect an agent’s implicit and explicit knowledge; the present work focuses on acts that affect an agent’s implicit and explicit beliefs. It starts by proposing a framework in which these two notions can be represented, and then it looks into their dynamics, first by reviewing the existing notion of belief revision, and then by introducing a rich framework for representing diverse forms of inference that involve both knowledge and beliefs.

Keywords

Epistemic logic Dynamic epistemic logic Knowledge Beliefs Belief revision Inference 

Notes

Acknowledgments

The author thanks the organisers and the audiences of the Workshop on Theories of Information Dynamics and Interaction and their Application to Dialogue (TIDIAD’09) and the Third Workshop on Logics for Resource-Bounded Agents (LRBA-3) as well as the anonymous referees of those workshops and of this special issue; their comments and observations have greatly improved this paper. Special thanks go to the editors of this special issue for all their work and effort. The author also thanks Johan van Benthem for the illuminating ideas that started this project, and Hans van Ditmarsch for pointing out some flaws in old versions and for the many suggestions that have helped to make this work better.

References

  1. Ågotnes, T., & Alechina, N. (2007). The dynamics of syntactic knowledge. Journal of Logic and Computation, 17(1), 83–116. doi: 10.1093/logcom/exl019.CrossRefGoogle Scholar
  2. Ågotnes, T., & Alechina, N. (eds.). (2009). Special issue on logics for resource bounded agents. Journal of Logic, Language and Information, 18(1).Google Scholar
  3. Alchourrón, C. E., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50(2), 510–530. doi: 10.2307/2274239.CrossRefGoogle Scholar
  4. Aliseda A (2006) Abductive reasoning. Logical investigations into discovery and explanation, synthese library series (vol. 330). Berlin: Springer.Google Scholar
  5. Baltag, A., Moss, L. S., & Solecki, S. (1999). The logic of public announcements, common knowledge and private suspicions. Tech. Rep. SEN-R9922, CWI, Amsterdam.Google Scholar
  6. Baltag, A., & Smets, S. (2008). A qualitative theory of dynamic interactive belief revision. In G. Bonanno, W. van der Hoek, & M. Wooldridge (Eds.), Logic and the foundations of game and decision theory (LOFT7), texts in logic and games (Vol. 3, pp. 13–60). The Netherlands: Amsterdam University Press Amsterdam.Google Scholar
  7. Blackburn, P., de Rijke, M., & Venema, Y. (2001) Modal logic. No. 53 in Cambridge tracts in theoretical computer science. New York, USA: Cambridge University Press.Google Scholar
  8. Board, O. (2004). Dynamic interactive epistemology. Games and Economic Behavior, 49(1), 49–80. doi: 10.1016/j.geb.2003.10.006.CrossRefGoogle Scholar
  9. Boutilier, C. (1994). Conditional logics of normality: A modal approach. Artificial Intelligence, 68(1), 87–154.CrossRefGoogle Scholar
  10. Drapkin, J. J., & Perlis, D. (1986). Step-logics: An alternative approach to limited reasoning. In Proceedings of the European conference on artificial intelligence (pp. 160–163), Brighton, England.Google Scholar
  11. Duc, H. N. (1995). Logical omniscience vs. logical ignorance. on a dilemma of epistemic logic. In C. A. Pinto-Ferreira, N. J. Mamede (Eds.), EPIA 1995, Lecture Notes in Computer Science (vol. 990, pp 237–248). Heilderberg: Springer.Google Scholar
  12. Duc, H. N. (2001). Resource-bounded reasoning about knowledge. PhD thesis, Institut für Informatik, Universität Leipzig, Leipzig, Germany.Google Scholar
  13. Fagin, R., & Halpern, J. Y. (1988). Belief, awareness, and limited reasoning. Artificial Intelligence, 34(1), 39–76. doi: 10.1016/0004-3702(87)90003-8.Google Scholar
  14. Gärdenfors, P. (Ed.). (1992). Belief revision. No. 29 in Cambridge tracts in theoretical computer science. Cambridge: Cambridge University Press.Google Scholar
  15. Gärdenfors, P., & Makinson, D. (1988). Revisions of knowledge systems using epistemic entrenchment. In M. Y. Vardi (Ed.), TARK II (pp. 83–95), Morgan Kaufmann.Google Scholar
  16. Gärdenfors, P., & Rott, H. (1994). Belief revision. Handbook of logic in artificial intelligence and logic programming, vol Volume 4: Epistemic and temporal logics (pp. 35–132). Oxford & New York: Oxford University Press.Google Scholar
  17. Gerbrandy, J, (1999), Bisimulations on planet kripke. PhD thesis, Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam (UvA), Amsterdam, The Netherlands, ILLC Dissertation Series DS-1999-01.Google Scholar
  18. Grossi, D., & Velázquez-Quesada, F. R. (2009). Twelve angry men: A study on the fine-grain of announcements. In He et al. pp 147–160. doi: 10.1007/978-3-642-04893-7_12.
  19. Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17(2), 157–170. doi: 10.1007/BF00247909.CrossRefGoogle Scholar
  20. Halpern, J. Y. (ed.). (1986). Proceedings of the 1st conference on theoretical aspects of reasoning about knowledge, Monterey, CA/ San Francisco, CA: Morgan Kaufmann.Google Scholar
  21. Harel, D., Kozen, D., & Tiuryn, J. (2000). Dynamic logic. Cambridge, MA: MIT Press.Google Scholar
  22. He, X., Horty, J. F., & Pacuit, E. (eds.). (2009). Proceedings of the logic, rationality, and interaction, second international workshop (LORI 2009), Chongqing, China, October 8–11, 2009. Lecture Notes in Computer Science (vol. 5834). Berlin: Springer. doi: 10.1007/978-3-642-04893-7.
  23. Hintikka, J. (1962). Knowledge and belief: An introduction to the logic of the two notions. Ithaca, NY: Cornell University Press.Google Scholar
  24. Holliday, W. H., & Icard, T. F. (2010). Moorean phenomena in epistemic logic. In L. Beklemishev, V. Goranko, & V. Shehtman (Eds.), Advances in modal logic (pp. 178–199), College Publications.Google Scholar
  25. Jago, M. (2009). Epistemic logic for rule-based agents. Journal of Logic, Language and Information, 18(1), 131–158. doi: 10.1007/s10849-008-9071-8.CrossRefGoogle Scholar
  26. Konolige, K. (1984). Belief and incompleteness. Tech. Rep. 319, SRI International.Google Scholar
  27. Lakemeyer, G. (1986). Steps towards a first-order logic of explicit and implicit belief. In Halpern (1986) (pp. 325–340).Google Scholar
  28. Lamarre, P. (1991). S4 as the conditional logic of nonmonotonicity. In J. F. Allen, R. Fikes, & E. Sandewall (Eds.), KR 91 (pp. 357–367). Cambridge, MA: Morgan Kaufmann.Google Scholar
  29. Levesque, H. J. (1984). A logic of implicit and explicit belief. In Proceedings of the AAAI-84 (pp. 198–202), Austin, TX.Google Scholar
  30. Lewis, D. (1973). Counterfactuals. Cambridge, MA: Blackwell.Google Scholar
  31. Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Z. W. Ras (Eds.), Proceedings of the 4th international symposium on methodologies for intelligent systems, Oak Ridge National Laboratory (ORNL/DSRD-24) (pp. 201–216), Tennessee, USA.Google Scholar
  32. Rott, H. (2001). Change, choice and inference: A study of belief revision and nonmonotonic reasoning. No. 42 in Oxford Logic Guides, Oxford Science Publications.Google Scholar
  33. Segerberg, K. (2001). The basic dynamic doxastic logic of AGM. In Williams and Rott (2001) (pp. 57–84).Google Scholar
  34. Stalnaker, R. (2006). On logics of knowledge and belief. Philosophical Studies, 128(1), 169–199. doi: 10.1007/s11098-005-4062-y.CrossRefGoogle Scholar
  35. van Benthem, J. (2007). Dynamic logic for belief revision. Journal of Applied Non-classical Logics, 17(2), 129–155. doi: 10.3166/jancl.17.129-155.CrossRefGoogle Scholar
  36. van Benthem, J. (2008). Merging observation and access in dynamic logic. Journal of Logic Studies, 1(1), 1–17.Google Scholar
  37. van Benthem, J. (2011). Logical dynamics of information and interaction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  38. van Benthem, J., & Liu, F. (2007). Dynamic logic of preference upgrade. Journal of Applied Non-classical Logics, 17(2), 157–182. doi: 10.3166/jancl.17.157-182.CrossRefGoogle Scholar
  39. van Benthem, J., van Eijck, J., & Kooi, B. (2006). Logics of communication and change. Information and Computation, 204(11), 1620–1662. doi: 10.1016/j.ic.2006.04.006.CrossRefGoogle Scholar
  40. van Benthem, J., & Velázquez-Quesada, F. R. (2010). The dynamics of awareness. Synthese (Knowledge, Rationality and Action), 177(Supplement 1), 5–27. doi: 10.1007/s11229-010-9764-9.Google Scholar
  41. van Ditmarsch, H. (2005). Prolegomena to dynamic logic for belief revision. Synthese, 147(2), 229–275. doi: 10.1007/s11229-005-1349-7.Google Scholar
  42. van Ditmarsch, H., Herzig, A., Lang, J., & Marquis, P. (2009). Introspective forgetting. Synthese (Knowledge, Rationality and Action), 169(2), 405–423. doi: 10.1007/s11229-009-9554-4.
  43. van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic, synthese library series (vol. 337). Berlin: Springer.Google Scholar
  44. van Ditmarsch, H. P., & French, T. (2009). Awareness and forgetting of facts and agents. In Web intelligence/IAT workshops (pp. 478–483), IEEE. doi: 10.1109/WI-IAT.2009.330.
  45. van Eijck, J., & Wang, Y. (2008). Propositional dynamic logic as a logic of belief revision. In W. Hodges, R. J. G. B. de Queiroz (Eds.), WoLLIC, Lecture Notes in Computer Science (vol. 5110, pp. 136–148). Berlin: Springer. doi: 10.1007/978-3-540-69937-8_13.
  46. Vardi, M. Y. (1986). On epistemic logic and logical omniscience. In Halpern (1986) (pp. 293–305).Google Scholar
  47. Velázquez-Quesada, F. R. (2009a). Dynamic logics for explicit and implicit information. In He et al. (2009) (pp 325–326). doi: 10.1007/978-3-642-04893-7_31.
  48. Velázquez-Quesada, F. R. (2009b). Inference and update. Synthese (Knowledge, Rationality and Action), 169(2), 283–300. doi: 10.1007/s11229-009-9556-2.
  49. Velázquez-Quesada, F. R. (2011). Small steps in dynamics of information. PhD thesis, Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam (UvA), Amsterdam, The Netherlands, ILLC Dissertation series DS-2011-02.Google Scholar
  50. Veltman, F. (1985). Logics for conditionals. PhD thesis, Universiteit van Amsterdam.Google Scholar
  51. Williams, M. A., & Rott, H. (eds.). (2001). Frontiers in belief revision, no. 22 in applied logic series. Dordrecht: Kluwer.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Grupo de Lógica, Lenguaje e Información, Facultad de FilosofíaUniversidad de SevillaSevilleSpain

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