Synthese

, Volume 177, Supplement 1, pp 5–27 | Cite as

The dynamics of awareness

  • Johan van Benthem
  • Fernando R. Velázquez-Quesada
Open Access
Article

Abstract

Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents based on semantic information. The latter is produced by acts of observation or communication that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference—and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and hence we also need a dynamic logic of inference steps showing what effort on the part of the agent makes a conclusion explicit knowledge. Strong omniscience properties of agents should be seen not as static idealizations, but as the result of dynamic processes that agents engage in. This raises two questions: (a) how to define suitable information states of agents and matching notions of explicit knowledge, (b) how to define natural processes over these states that generate new explicit knowledge. To this end, we use a static base from the existing awareness literature, extending it into a dynamic system that includes traditional acts of observation, but also adding and dropping formulas from the current ‘awareness’ set. We give a completeness theorem, and we show how this dynamics updates explicit knowledge. Then we extend our approach to multi-agent scenarios where awareness changes may happen privately. Finally, we mention further directions and related approaches. Our contribution can be seen as a ‘dynamification’ of existing awareness logics.

Keywords

Epistemic logic Considoring dropping Obseration Awareness Dynamic epistemic logic 

References

  1. Artemov S. N., Nogina E. (2005) Introducing justification to epistemic logic. Journal of Logic and Computation 15(6): 1059–1073CrossRefGoogle Scholar
  2. Baltag, A., Moss, L. S., & Solecki, S. (1999). The logic of public announcements, common knowledge and private suspicious. Technical Report SEN-R9922. Amsterdam: CWI.Google Scholar
  3. Baltag, A., & Smets, S. (2008). A qualitative theory of dynamic interactive belief revision. In G. Bonanno, W. van der Hoek, & Wooldridge, M. (Eds.), Logic and the foundations of game and decision theory (LOFT7), texts in logic and games (Vol. 3, pp. 13–60). Amsterdam: University Press.Google Scholar
  4. Duc H. N. (1997) Reasoning about rational, but not logically omniscient, agents. Journal of Logic and Computation 7(5): 633–648CrossRefGoogle Scholar
  5. Eberle R. A. (1997) A logic of believing, knowing, and inferring. Synthese 26(3–4): 356–382Google Scholar
  6. Elgot-Drapkin J. J., Perlis D. (1990) Reasoning situation in time I: Basic concepts. Journal of Experimental and Theoretical Artificial Intelligence 2(1): 75–98CrossRefGoogle Scholar
  7. Fagin R., Halpern J. Y. (1988) Belief, awareness, and limited reasoning. Artificial Intelligence 34(1): 39–76CrossRefGoogle Scholar
  8. Gerbrandy, J. (1999). Bisimulations on planet Kripke. Ph.D. thesis, Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam (UvA), Amsterdam, The Netherlands. ILLC Dissertation Series DS-1999-01.Google Scholar
  9. Grossi, D., & Velázquez-Quesada, F. R. (2009). Twelve angry men: A study on the fine-grain of announcements. In X. He, J. F. Horty, & Pacuit, E. (Eds.), LORI, lecture notes in computer science (Vol. 5834, pp. 147–160). New York: Springer.Google Scholar
  10. Halpern J. Y. (2001) Alternative semantics for unawareness. Games and Economic Behavior 37: 321–339CrossRefGoogle Scholar
  11. Hintikka J. (1962) Knowledge and belief: An introduction to the logic of the two notions. Cornell University Press, Ithaca, NYGoogle Scholar
  12. Jago M. (2006) Rule-based and resource-bounded: A new look at epistemic logic. In: Ågotnes T., Alechina N. (eds) Proceedings of the workshop on logics for resource-bounded agents, organized as part of the 18th European summer school on logic, language and information (ESSLLI). Malaga, Spain, pp 63–77Google Scholar
  13. Jago M. (2009) Epistemic logic for rule-based agents. Journal of Logic, Language and Information 18(1): 131–158CrossRefGoogle Scholar
  14. Konolige, K. (1984). Belief and incompleteness. Technical Report 319. Menlo Park, California: SRI International.Google Scholar
  15. Lakemeyer G. (1986) Steps Towards a first-order logic of explicit and implicit belief. In: Halpern J.Y. (eds) Proceedings of 1986 conference on theoretical aspects of reasoning about knowledge. Morgan Kaufmann Publishers Inc, San Francisco, CA, pp 325–340Google Scholar
  16. Levesque, H. J. (1984). A logic of implicit and explicit belief. In Proceedings of AAAI-84 (pp. 198–202). Austin, TXGoogle Scholar
  17. Moore, R. C., & Hendrix, G. (1979). Computational models of beliefs and the semantics of belief sentences. Technical Report 187. Menlo Park, California: SRI International.Google Scholar
  18. Moreno A. (1998) Avoiding logical omniscience and perfect reasoning: A survey. AI Communications 11(2): 101–122Google Scholar
  19. Plaza, J. A. (1989). Logics of public communications. In M. L. Emrich, M. S. Pfeifer, M. Hadzikadic, & Ras, Z. W. (Eds.), Proceedings of the 4th international symposium on methodologies for intelligent systems (pp. 201–216). Tennessee, USA: Oak Ridge National Laboratory, ORNL/DSRD-24.Google Scholar
  20. Sim K. M. (1997) Epistemic logic and logical omniscience. A survey. International Journal of Intelligent Systems 12(1): 57–81CrossRefGoogle Scholar
  21. van Benthem J. (2007) Dynamic logic for belief revision. Journal of Applied Non-Classical Logics 17(2): 129–155CrossRefGoogle Scholar
  22. van Benthem J. (2008) Merging observation and access in dynamic logic. Journal of Logic Studies 1(1): 1–17Google Scholar
  23. van Benthem J. (2009) Logic, mathematics, and general agency. In: Bour P., Rebuschi M., Rollet L. (eds) Festschrift for Gerhard Heinzmann. Laboratoire d’histoire des ceinces et de la philosophie, NancyGoogle Scholar
  24. van Benthem, J. (2010). Logical dynamics of information and interaction. Cambridge: Cambridge University Press (to appear).Google Scholar
  25. van Benthem J., Liu F. (2007) Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics 17(2): 157–182CrossRefGoogle Scholar
  26. van Benthem J., Martínez M. (2008) The stories of logic and information. In: Adriaans P., Benthem J. (eds) Philosophy Of information, handbook of the philosophy of science. North-Holland, Amsterdam, pp 217–280CrossRefGoogle Scholar
  27. van Benthem J., van Eijck J., Kooi B. (2006) Logics of communication and change. Information and Computation 204(11): 1620–1662CrossRefGoogle Scholar
  28. 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
  29. van Ditmarsch H., Herzig A., Lang J., Marquis P. (2009) Introspective forgetting. Synthese (Knowledge, Rationality and Action) 169(2): 405–423Google Scholar
  30. Vardi M.Y. (1986) On epistemic logic and logical omniscience. In: Halpern J. (eds) Proceedings of the 1986 conference. Morgan Kaufmann Publishers Inc., Los Altos, CA, pp 293–305Google Scholar
  31. Velázquez-Quesada F. R. (2009) Inference and update. Synthese (Knowledge, Rationality and Action) 169(2): 283–300Google Scholar
  32. Velázquez-Quesada, F. R. (2011). Small steps in dynamics of information. Ph.D. thesis, Institute for Logic, Language and Computation (ILLC), Universiteit van Amsterdam (UvA), Amsterdam, The Netherlands (to appear).Google Scholar

Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Johan van Benthem
    • 1
    • 2
  • Fernando R. Velázquez-Quesada
    • 1
  1. 1.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.Department of PhilosophyStanford UniversityPalo, AltoUSA

Personalised recommendations