Advertisement

Synthese

, Volume 192, Issue 12, pp 4071–4105 | Cite as

Syntactic awareness in logical dynamics

  • Davide Grossi
  • Fernando R. Velázquez-Quesada
Article

Abstract

The paper develops an interface between syntax-based logical models of awareness and dynamic epistemic logic. The framework is shown to be able to accommodate a variety of notions of awareness and knowledge, as well as their dynamics. This, it is argued, offers a natural formal environment for the analysis of epistemic phenomena typical of multi-agent information exchange, such as how agents become aware of relevant details, how they perform inferences and how they share their information within a group. Technically, the logics presented are all simple refinements of the logic of public announcements.

Notes

Acknowledgments

The authors would like to express their gratitude to two anonymous reviewers for their comments and observations, which have helped to improve this paper.

References

  1. Areces, C., & ten Cate, B. (2006). Hybrid logics. In P. Blackburn, J. van Benthem, & F. Wolter (Eds.), Handbook of modal logic, studies in logic and practical reasoning (Vol. 3). Amsterdam: Elsevier Science Inc.Google Scholar
  2. Artëmov, S. N., & Nogina, E. (2005). Introducing justification into epistemic logic. Journal of Logic and Computation, 15(6), 1059–1073. doi: 10.1093/logcom/exi053.CrossRefGoogle Scholar
  3. Baltag, A., Moss, L.S., & Solecki. S. (1999). The logic of public announcements, common knowledge and private suspicions. In Technical Report SEN-R9922, CWI, Amsterdam.Google Scholar
  4. Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. New York: Cambridge University Press.CrossRefGoogle Scholar
  5. Chellas, B. F. (1980). Modal logic: An introduction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  6. Duc, H. N. (1997). Reasoning about rational, but not logically omniscient, agents. Journal of Logic and Computation, 7(5), 633–648.CrossRefGoogle Scholar
  7. Dung, P. M. (1995). On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77(2), 321–358.CrossRefGoogle Scholar
  8. 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.CrossRefGoogle Scholar
  9. Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about knowledge. Cambridge: The MIT Press.Google Scholar
  10. Gerbrandy, J., & Groeneveld, W. (1997). Reasoning about information change. Journal of Logic, Language, and Information, 6(2), 147–196.CrossRefGoogle Scholar
  11. Grossi, D., Lorini, E., & Schwarzentruber, F. (2013). Ceteris paribus structure in logics of game forms. In Proceedings of TARK’13.Google Scholar
  12. Grossi, D., & Pigozzi, G. (2014). Judgment aggregation: A primer., Synthesis lectures on artificial intelligence and machine learning San Rafael: Morgan and Claypool.Google Scholar
  13. Halpern, J. (2001). Alternative semantics for unawareness. Games and Economic Behavior, 37, 321–339.CrossRefGoogle Scholar
  14. Halpern, J., & Rêgo, L. (2008). Interactive unawareness revisited. Games and Economic Behavior, 62(1), 232–262.CrossRefGoogle Scholar
  15. Hamami, Y. (2010). The interrogative model of inquiry meets dynamic epistemic logics. Master’s thesis. ILLC, Universiteit van Amsterdam, Amsterdam, The Netherlands, ILLC Master of Logic Thesis Series MoL-2010-04.Google Scholar
  16. Heifetz, A., Meier, M., & Schipper, B. (2006). Interactive unawareness. Journal of Economic Theory, 130(1), 78–94.CrossRefGoogle Scholar
  17. Hill, B. (2010). Awareness dynamics. Journal of Philosophical Logic, 39(2), 113–137.CrossRefGoogle Scholar
  18. Hintikka, J. (1962). Knowledge and belief. Ithaca: Cornell University Press.Google Scholar
  19. Holliday, W.H. (2010). Trust and the dynamics of testimony. In L. Kurzen, D. Grossi, F.R. Velázquez-Quesada (eds) Logic and Interactive RAtionality. Seminar’s yearbook 2009, ILLC (pp. 118–142). Universiteit van Amsterdam, Amsterdam, The Netherlands.Google Scholar
  20. 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). London: College Publications.Google Scholar
  21. 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
  22. List, C., Puppe, C. (2009). Judgment aggregation: A survey. In Oxford handbook of rational and social choice. Oxford: Oxford University Press.Google Scholar
  23. Meyer, J. J. C., & van Der Hoek, W. (1995). Epistemic logic for AI and computer science. New York: Cambridge University Press.CrossRefGoogle Scholar
  24. Modica, S., & Rustichini, A. (1994). Awareness and partitional information structures. Theory and Decisions, 37, 107–124.CrossRefGoogle Scholar
  25. Modica, S., & Rustichini, A. (1999). Unawareness and partitional information structures. Games and Economic Behavior, 27, 265–298.CrossRefGoogle Scholar
  26. 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 (pp. 201–216), Tennessee: Oak Ridge National Laboratory, ORNL/DSRD-24.Google Scholar
  27. Troelstra, A. S., & Schwichtenberg, H. (2000). Basic proof theory, 2nd edn. No. 43 in Cambridge tracts in theoretical computer science. Cambridge, U.K.: Cambridge University Press.Google Scholar
  28. van Benthem, J. (2008). Merging observation and access in dynamic logic. Journal of Logic Studies, 1(1), 1–17.Google Scholar
  29. 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
  30. van Benthem, J. (2011). Logical dynamics of information and interaction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  31. van Benthem, J., & Minică, S. (2012). Toward a dynamic logic of questions. Journal of Philosophical Logic, 41(4), 633–669. doi: 10.1007/s10992-012-9233-7.CrossRefGoogle Scholar
  32. van Ditmarsch, H., & French, T. (2009). Awareness and forgetting of facts and agents. In Proceedings of the 2009 IEEE/WIC/ACM International joint conference on web intelligence and intelligent agent technologies (WI-IAT 2009), Milan.Google Scholar
  33. van Ditmarsch, H.P., French, T., Velázquez-Quesada, F.R., & Wang, Y. (2013). Knowledge, awareness, and bisimulation. In Schipper BC (Ed.). TARK (pp 61–70).Google Scholar
  34. van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic (Vol. 337)., Synthese library Dordrecht: Springer.CrossRefGoogle Scholar
  35. van Ditmarsch, H., & French, T. (2011). Becoming aware of propositional variables. In M. Banerjee & A. Seth (Eds.), ICLA (pp. 204–218)., Lecture notes in computer science New Delhi: Springer. doi: 10.1007/978-3-642-18026-2-17.Google Scholar
  36. Velázquez-Quesada, F.R. (2013). Public announcements for non-omniscient agents. In Lodaya K (Ed.). Lecture notes in computer science (Vol. 7750, pp. 220–232). doi: 10.1007/978-3-642-36039-8_20
  37. Velázquez-Quesada, F. R. (2009). Inference and update. Synthese (Knowledge, Rationality and Action), 169(2), 283–300. doi: 10.1007/s11229-009-9556-2.Google Scholar
  38. Velázquez-Quesada, F. R. (2014). Dynamic epistemic logic for implicit and explicit beliefs. Journal of Logic, Language and Information, 23(2), 107–140. doi: 10.1007/s10849-014-9193-0.CrossRefGoogle Scholar
  39. Wang, Y., & Cao, Q. (2013). On axiomatizations of public announcement logic. Synthese, 190(Supplement 1), 103–134. doi: 10.1007/s11229-012-0233-5.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Davide Grossi
    • 1
  • Fernando R. Velázquez-Quesada
    • 2
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  2. 2.Departamento de Filosofía, Lógica y Filosofía de la Ciencia, Facultad de Filosofía, Universidad de SevillaUniversidad de SevillaSevilleSpain

Personalised recommendations