Abstract
In 1992, Moss and Parikh studied a bimodal logic of knowledge and effort called Topologic. In this current paper, Topologic is extended to the case of many agents who are assumed to have some private information at the outset, but may refine their information by acquiring information possessed by other agents, possibly via yet other agents.
Let us assume that the agents are connected by a communication graph. In the communication graph, an edge from agent i to agent j means that agent i can directly receive information from agent j. Agent i can then refine its own information by learning information that j has, including information acquired by j from another agent, k. We introduce a multi-agent modal logic with knowledge modalities and a modality representing communication among agents. We show that the validities of Topologic remain valid and that the communication graph is completely determined by the validities of the resulting logic. Applications of our logic to current political dilemmas are obvious.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Baltag, A., Moss, L.: Logics for Epistemic Programs. Knowledge, Rationality, and Action section of Synthese 139(2), 165–224 (2004)
Chopra, S., Pacuit, E., Parikh, R.: Knowledge-theoretic Properties of Strategic Voting. In: Alferes, J.J., Leite, J. (eds.) Proceedings of 9th European Conference on Logics in Artifical Intelligence. LNCS (LNAI), pp. 18–30. Springer, Heidelberg (2004)
Dabrowski, A., Moss, L., Parikh, R.: Topolgical reasoning and the logic of knowledge. Annals of Pure and Applied Logic 78, 73–110 (1996)
Georgatos, K.: Modal Logics for Topological Spaces. PhD Dissertation. Graduate School and University Center. City University of New York (1993)
Georgatos, K.: Knowledge Theoretic Properties of Topological Spaces. In: Masuch, M., Polos, L. (eds.) Logic at Work 1992. LNCS, vol. 808, pp. 147–159. Springer, Heidelberg (1994)
Georgatos, K.: Knowledge on Treelike Spaces. Studia Logica 59, 271–301 (1997)
Gerbrandy, J.: Bisimulations on Planet Kripke. Ph.D. dissertation, University of Amsterdam (1999)
Heinemann, B.: Temporal Aspects of the Modal Logic of Subset Spaces. Theoretical Computer Science 224(1-2), 135–155 (1999)
Heinemann, B.: Extending Topological Nexttime Logic. In: Goodwin, S.D., Trudel, A. (eds.) Temporal Representation and Reasoning, TIME-00, Cape Breton, Nova Scotia, Canada, pp. 87–94. IEEE Computer Society Press, Los Alamitos (2000)
Heinemann, B.: A Hybrid Treatment of Evolutionary Sets. In: Coello Coello, C.A., de Albornoz, Á., Sucar, L.E., Battistutti, O.C. (eds.) MICAI 2002. LNCS (LNAI), vol. 2313, pp. 204–213. Springer, Heidelberg (2002)
Kooi, B.: Knowledge, Chance, and Change, Ph.D. dissertation, University of Groningen (2003)
Heinemann, B.: A Hybrid Logic of Knowledge Supporting Topological Reasoning. In: Rattray, C., Maharaj, S., Shankland, C. (eds.) AMAST 2004. LNCS, vol. 3116, pp. 181–195. Springer, Heidelberg (2004) (to appear)
Moss, L., Parikh, R.: Topological Reasoning and the Logic of Knowledge. In: Moses, Y. (ed.) TARK IV. Morgan Kaufmann, San Francisco (1992)
Parikh, R.: Social Software. Synthese 132(3), 187–211 (2002)
Parikh, R., Pacuit, E., Cogan, E.: The logic of knowledge based obligation. In: Leite, J., Omicini, A., Torroni, P., Yolum, p. (eds.) DALT 2004. LNCS (LNAI), vol. 3476. Springer, Heidelberg (2005); Forthcoming in Knowledge Rationality and Action: Special Issue on the Knowledge and Games Workshop (2005)
Parikh, R., Ramanujam, R.: Distributed Processing and the Logic of Knowledge. In: Parikh, R. (ed.) Logic of Programs 1985. LNCS, vol. 193, pp. 256–268. Springer, Heidelberg (1985)
Parikh, R., Ramanujam, R.: A knowledge based semantics of messages. J. Logic, Language, and Information 12, 453–467 (2003)
Plaza, J.: Logics of public communications. In: Proceedings, 4th International Symposium on Methodologies for Intelligent Systems (1989)
van Ditmarsch, H.: Knowledge Games, Ph.D. dissertation, University of Groningen (2000)
Vickers, S.: Topology Via Logic. Cambridge University Press, Cambridge (1989)
Weiss, M.A., Parikh, R.: Completeness of Certain Bimodal Logics of Subset Spaces. Studia Logica 71(1), 1–30 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pacuit, E., Parikh, R. (2005). The Logic of Communication Graphs. In: Leite, J., Omicini, A., Torroni, P., Yolum, p. (eds) Declarative Agent Languages and Technologies II. DALT 2004. Lecture Notes in Computer Science(), vol 3476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11493402_15
Download citation
DOI: https://doi.org/10.1007/11493402_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26172-8
Online ISBN: 978-3-540-31927-6
eBook Packages: Computer ScienceComputer Science (R0)