Journal of Logic, Language and Information

, Volume 18, Issue 1, pp 23–53

Diversity of Agents and Their Interaction

Article

Abstract

Diversity of agents occurs naturally in epistemic logic, and dynamic logics of information update and belief revision. In this paper we provide a systematic discussion of different sources of diversity, such as introspection ability, powers of observation, memory capacity, and revision policies, and we show how these can be encoded in dynamic epistemic logics allowing for individual variation among agents. Next, we explore the interaction of diverse agents by looking at some concrete scenarios of communication and learning, and we propose a logical methodology to deal with these as well. We conclude with some further questions on the logic of diversity and interaction.

Keywords

Dynamic epistemic logic Belief revision Diversity Interaction 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alchourrón C., Gardenfors P., Makinson D. (1985) On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic 50: 510–530CrossRefGoogle Scholar
  2. Alechina, N., Jago, M., & Logan, B. (2006). Modal logics for communicating rule-based agents. In A. Perini, G. Brewka, S. Coradeschi, & P. Traverso (Eds.), Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006). IOS Press.Google Scholar
  3. Aucher, G. (2003). A combination system for update logic and belief revision. Master’s thesis, ILLC, University of Amsterdam.Google Scholar
  4. Aucher, G. (2005). How our beliefs contribute to interpret actions. In P. Petta, M. Pechoucek, & L. Z. Varga (Eds.), CEEMAS 2005, (pp. 276–286). Springer. LNAI 3690.Google Scholar
  5. Baltag, A., Moss, L. S., & Solecki, S. (1998). The logic of common knowledge, public announcements, and private suspicions. In I. Gilboa (Ed.), Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK 98), pp. 43–56.Google Scholar
  6. Baltag, A., van Benthem, J., Smets, S. (2007). A dynamic-logical approach to interactive epistemology. Working paper, ILLC, University of Amsterdam.Google Scholar
  7. Bonanno, G. (2007). Belief revision in a temporal framework. Working paper, University of California at Davis.Google Scholar
  8. Dechesne, F., & Wang, Y. (2007). Dynamic epistemic verifcation of security protocols: Framework and case study. In J. van Benthem, S. Ju, F. Veltman (Eds.), A Meeting of the Minds–Proceedings of the Workshop on Logic, Rationality and Interaction. King’s College Publications.Google Scholar
  9. Dung P.H. (1995) An argumentation-theoretic foundation for logic programming. Journal of Logic Programming 22: 151–177CrossRefGoogle Scholar
  10. Egre, P. (2004). Propositional Attitudes and Epistemic Paradoxes. PhD thesis, Universite Paris 1 et IHPST.Google Scholar
  11. Fagin, R., & Halpern, J. Y. (1985). Belief, awareness, and limited reasoning. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence (IJCAI-85), pp. 480–490.Google Scholar
  12. Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about Knowledge. The MIT Press.Google Scholar
  13. Gabbay, D., & Shehtman, V. (1998). Products of modal logics. Logic Journal of the IGPL, 6(1), 73–146. Part 1.Google Scholar
  14. Gardenfors, P., & Rott, H. (1995). Belief revision. In D. M. Gabbay, C. J. Hogger, & J. A. Robinson (Eds.), Handbook of Logic in Artificial Intelligence and Logic Programming, (Vol. 4). Oxford University Press.Google Scholar
  15. Gerbrandy, J. (1999). Bisimulation on Planet Kripke. PhD thesis, ILLC, University of Amsterdam.Google Scholar
  16. Gigerenzer G., Todd P., TheABC Research Group. (1999) Simple Heuristics that Make us Smart. Oxford University Press, New YorkGoogle Scholar
  17. Jago, M. (2006). Logics for Resource-Bounded Agents. PhD thesis, University of Nottingham.Google Scholar
  18. Konolige K. (1988) On the relation between default and autoepistemic logic. Artificial Intelligence 35(3): 343–382CrossRefGoogle Scholar
  19. Kurucz, A., & Zakharyaschev, M. (2003). A note on relativised products of modal logics. In F. Wolter, P. Balbiani, N.-Y. Suzuki, & M. Zakharyaschev (Eds.), Advances in Modal Logic, (Vol. 4, pp. 221–242) . King’s College Publications.Google Scholar
  20. Levesque H.J. (1990) All I know: A study in autoepistemic logic. Artificial Intelligence Journal 42: 381–386CrossRefGoogle Scholar
  21. Liu, F. (2004). Dynamic variations: Update and revision for diverse agents. Master’s thesis, ILLC, University of Amsterdam.Google Scholar
  22. Liu, F. (2006). Preference change and information processing. In Proceedings of the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT 06), Liverpool. Research Report, PP-2006-41, ILLC, University of Amsterdam.Google Scholar
  23. Parikh R., Ramanujam R. (2003) A knowledge-based semantics of messages. Journal of Logic, Language and Information 12: 453–467CrossRefGoogle Scholar
  24. Plaza, J. A. (1989). Logics of public announcements. In Proceedings 4th International Symposium on Methodologies for Intelligent Systems.Google Scholar
  25. Rott, H. (2006). Shifting priorities: Simple representations for 27 iterated theory change operators. In H. Langerlund, S. Lindström, & R. Sliwinski (Eds.), Modality Matters: Twenty-five Essays in Honour of Krister Segerberg, (pp. 359–384). Uppsala Philosophical Studies 53.Google Scholar
  26. Silberschatz A., Galvin P.B., Gagne G. (2003) Operating System Concepts. Wiley, New York, NY, USAGoogle Scholar
  27. Snyder, J. (2004). Product update for agents with bounded memory. Manuscript, Department of Philosophy, Stanford University.Google Scholar
  28. Spohn, W. (1988). Ordinal conditional functions: A dynamic theory of epistemic states. In W. L. Harper et al. (Ed.), Causation in Decision, Belief Change and Statistics II, (pp. 105–134). Dordrecht: Kluwer.Google Scholar
  29. van Benthem J. (1996) Exploring Logical Dynamics. CSLI Publication, StanfordGoogle Scholar
  30. van Benthem, J. (2006). ‘One is a lonely number’: On the logic of communication. In P. Koepke, Z. Chatzidakis, & W. Pohlers (Eds.), Logic Collquium, ASL Lecture Notes in Logic 27. AMS Publications, Providence (R.I.). Research Report, PP-2002-27, ILLC, University of Amsterdam.Google Scholar
  31. van Benthem J. (2007) Dynamic logic for belief revision. Journal of Applied Non-Classical Logic 17(2): 129–156CrossRefGoogle Scholar
  32. van Benthem J. (2008) Rational animals, a logical jungle?. Journal of Peking University (Humanities and Social Sciences) 45(1): 80–90Google Scholar
  33. van Benthem, J., Gerbrandy, J., & Kooi, B. (2006). Dynamic update with probabilities. Research Report, PP-2006-21, ILLC, University of Amsterdam.Google Scholar
  34. van Benthem, J., Gerbrandy, J., & Pacuit, E. (2007). Merging frameworks for interaction: DEL and ETL. In D. Samet (Ed.), Proceedings of TARK.Google Scholar
  35. van Benthem J., Liu F. (2004) Diversity of logical agents in games. Philosophia Scientiae 8(2): 163–178Google Scholar
  36. van Benthem J., Liu F. (2007) Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logic 17(2): 157–182CrossRefGoogle Scholar
  37. van Benthem, J., & Pacuit, E. (2006). The tree of knowledge in action: Towards a common perspective. In I. Hodkinson, G. Governatori, & Y. Venema (Eds.), Proceedings of Advances in Modal Logic (AiML 2006). Uppsala Philosophical Studies 53.Google Scholar
  38. van der Hoek, W., Jaspars, J., & Thijsse, E. (1990). A general approach to multi-agent minimal knowledge. In M. Ojeda-Aciego, I. P. Guzman, G. Brewka, & L. M. Pereira (Eds.), Proceedings of the 7th European Workshop on Logics in Artificial Intelligence (JELIA 2000), (pp. 254–268). Heidelberg: Springer-Verlag. LNAI 1919.Google Scholar
  39. van Ditmarsch H., van der Hoek W., Kooi B. (2007) Dynamic Epistemic Logic. Springer, BerlinGoogle Scholar
  40. Wassermann, R. (2000). Resource Bounded Belief Revision. PhD thesis, ILLC, University of Amsterdam.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Philosophy, School of Humanities and Social SciencesTsinghua UniversityBeijingChina
  2. 2.Institute for Logic, Language and Computation (ILLC)University of AmsterdamAmsterdarmNetherlands

Personalised recommendations