Abstract
There exists a considerable body of work on epistemic logics for bounded reasoners where the bound can be time, memory, or the amount of information the reasoners can exchange. In much of this work the epistemic logic is used as a meta-logic to reason about beliefs of the bounded reasoners from an external perspective. In this paper, we present a formal model of a system of bounded reasoners which reason about each other’s beliefs, and propose a sound and complete logic in which such reasoning can be expressed. Our formalisation highlights a problem of incorrect belief ascription in resource-bounded reasoning about beliefs, and we propose a possible solution to this problem, namely adding reasoning strategies to the logic.
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References
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)
Meyer, J.J., van der Hoek, W.: Epistemic Logic for Computer Science and Artificial Intelligence. Cambridge University Press, Cambridge (1995)
Hintikka, J.: Knowledge and belief. Cornell University Press, Ithaca (1962)
Rantala, V.: Impossible worlds semantics and logical omniscience. Acta Philosophica Fennica 35, 106–115 (1982)
Fagin, R., Halpern, J.Y., Vardi, M.Y.: A non-standard approach to the logical omniscience problem. In: Parikh, R. (ed.) Theoretical Aspects of Reasoning about Knowledge: Proceedings of the Third Conference, pp. 41–55. Morgan Kaufmann, San Francisco (1990)
Fagin, R., Halpern, J.Y.: Belief, awareness and limited reasoning: Preliminary report. In: Proceedings of the 9th International Joint Conference on Artificial Intelligence, pp. 491–501 (1985)
Konolige, K.: A Deduction Model of Belief. Morgan Kaufmann, San Francisco (1986)
Elgot-Drapkin, J.J., Perlis, D.: Reasoning situated in time I: Basic concepts. Journal of Experimental and Theoretical Artificial Intelligence 2, 75–98 (1990)
Halpern, J.Y., Moses, Y., Vardi, M.Y.: Algorithmic knowledge. In: Fagin, R. (ed.) Theoretical Aspects of Reasoning about Knowledge: Proceedings of the Fifth Conference (TARK 1994), pp. 255–266. Morgan Kaufmann, San Francisco (1994)
Pucella, R.: Deductive algorithmic knowledge. J. Log. Comput. 16(2), 287–309 (2006)
Duc, H.N.: Logical omniscience vs. logical ignorance on a dilemma of epistemic logic. In: Pinto-Ferreira, C.A., Mamede, N.J. (eds.) EPIA 1995. LNCS, vol. 990, pp. 237–248. Springer, Heidelberg (1995)
Duc, H.N.: Reasoning about rational, but not logically omniscient, agents. Journal of Logic and Computation 7(5), 633–648 (1997)
Ågotnes, T., Alechina, N.: The dynamics of syntactic knowledge. Journal of Logic and Computation 17(1), 83–116 (2007)
Sierra, C., Godo, L., de Mántaras, R.L., Manzano, M.: Descriptive dynamic logic and its application to reflective architectu res. Future Gener. Comput. Syst. 12(2-3), 157–171 (1996)
Alechina, N., Jago, M., Logan, B.: Modal logics for communicating rule-based agents. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006), pp. 322–326. IOS Press, Amsterdam (2006)
Fisher, M., Ghidini, C.: Programming resource-bounded deliberative agents. In: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence (IJCAI 1999), pp. 200–205. Morgan-Kaufmann, San Francisco (1999)
Ågotnes, T.: A Logic of Finite Syntactic Epistemic States. Ph.D. thesis, Department of Informatics, University of Bergen, Norway (2004)
Ågotnes, T., Alechina, N.: Knowing minimum/maximum n formulae. In: Brewka, G., Coradeschi, S., Perini, A., Traverso, P. (eds.) Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006), pp. 317–321. IOS Press, Amsterdam (2006)
Albore, A., Alechina, N., Bertoli, P., Ghidini, C., Logan, B., Serafini, L.: Model-checking memory requirements of resource-bounded reasoners. In: Proceedings of the Twenty-First National Conference on Artificial Intelligence (AAAI 2006), pp. 213–218. AAAI Press, Menlo Park (2006)
Alechina, N., Logan, B., Nguyen, H.N., Rakib, A.: Verifying time, memory and communication bounds in systems of reasoning agents. In: Padgham, L., Parkes, D., Müller, J., Parsons, S. (eds.) Proceedings of the Seventh International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2008), Estoril, Portugal, May 2008, vol. 2, pp. 736–743. IFAAMAS (2008)
Ågotnes, T., Walther, D.: Towards a logic of strategic ability under bounded memory. In: Proceedings of the Workshop on Logics for Resource-Bounded Agents (2007)
Adjiman, P., Chatalic, P., Goasdoué, F., Rousset, M.C., Simon, L.: Scalability study of peer-to-peer consequence finding. In: Kaelbling, L.P., Saffiotti, A. (eds.) Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI 2005), Edinburgh, Scotland, pp. 351–356. Professional Book Center (2005)
Emerson, E.A.: Temporal and modal logic. In: Handbook of Theoretical Computer Science. Formal Models and Sematics (B), vol. B, pp. 995–1072. Elsevier and MIT Press (1990)
Reynolds, M.: An axiomatization of full computation tree logic. Journal of Symbolic Logic 66(3), 1011–1057 (2001)
Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet functions for contraction and revision. Journal of Symbolic Logic 50, 510–530 (1985)
Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Proceedings of the 7th conference on Theoretical aspects of rationality and knowledge, TARK 1998 (1998)
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Alechina, N., Logan, B., Nguyen, H.N., Rakib, A. (2009). Reasoning about Other Agents’ Beliefs under Bounded Resources. In: Meyer, JJ.C., Broersen, J. (eds) Knowledge Representation for Agents and Multi-Agent Systems. KRAMAS 2008. Lecture Notes in Computer Science(), vol 5605. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05301-6_1
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DOI: https://doi.org/10.1007/978-3-642-05301-6_1
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