Abstract
The bi-modal logic of subset spaces, LSS, was originally designed for revealing the intrinsic relationship between knowledge and topology. In recent years, it has been developed in several directions, not least towards a comprehensive knowledge-theoretic formalism. As to that, subset spaces have been shown to be smoothly combinable with various epistemic concepts, at least as long as attention is restricted to the single-agent case. Adjusting LSS to general multi-agent scenarios, however, has brought about few results only, presumably due to reasons inherent in the system. This is why one is led to consider more special cases. In the present paper, LSS is extended to a particular two-agent setting, where the peculiarity is given by the case that the agents are competitive in a sense; in fact, it is assumed here that one agent is always able to go ahead of another one regarding knowledge (or, the other one is possibly lagging behind in this respect), and vice versa. It turns out that such circumstances can be modeled in corresponding logical terms to a considerable extent.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Aiello, M., Pratt-Hartmann, I.E., van Benthem, J.F.A.K.: Handbook of Spatial Logics. Springer, Dordrecht (2007)
Balbiani, P., van Ditmarsch, H., Kudinov, A.: Subset space logic with arbitrary announcements. In: Lodaya, K. (ed.) Logic and Its Applications. LNCS, vol. 7750, pp. 233–244. Springer, Heidelberg (2013)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic, Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)
Dabrowski, A., Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. Annals of Pure and Applied Logic 78, 73–110 (1996)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)
Georgatos, K.: Knowledge theoretic properties of topological spaces. In: Masuch, M., Pólos, L. (eds.) Knowledge Representation and Uncertainty, Logic at Work. Lecture Notes in Artificial Intelligence, vol. 808, pp. 147–159. Springer, Heidelberg (1994)
Heinemann, B.: Topology and knowledge of multiple agents. In: Geffner, H., Prada, R., Machado Alexandre, I., David, N. (eds.) IBERAMIA 2008. LNCS (LNAI), vol. 5290, pp. 1–10. Springer, Heidelberg (2008)
Heinemann, B.: Logics for multi-subset spaces. Journal of Applied Non-Classical Logics 20(3), 219–240 (2010)
Heinemann, B.: Coming upon the classic notion of implicit knowledge again. In: Buchmann, R., Kifor, C.V., Yu, J. (eds.) KSEM 2014. LNCS, vol. 8793, pp. 1–12. Springer, Heidelberg (2014)
Lomuscio, A., Ryan, M.: Ideal agents sharing (some!) knowledge. In: Prade, H. (ed.) 13th European Conference on Artificial Intelligence, ECAI 1998, pp. 557–561. John Wiley & Sons Ltd, Chichester (1998)
Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. In: Moses, Y. (ed.) Theoretical Aspects of Reasoning about Knowledge (TARK 1992), pp. 95–105. Morgan Kaufmann, Los Altos (1992)
Wáng, Y.N., Ågotnes, T.: Subset space public announcement logic. In: Lodaya, K. (ed.) Logic and Its Applications. LNCS, vol. 7750, pp. 245–257. Springer, Heidelberg (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Heinemann, B. (2015). Subset Spaces Modeling Knowledge-Competitive Agents. In: Zhang, S., Wirsing, M., Zhang, Z. (eds) Knowledge Science, Engineering and Management. KSEM 2015. Lecture Notes in Computer Science(), vol 9403. Springer, Cham. https://doi.org/10.1007/978-3-319-25159-2_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-25159-2_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-25158-5
Online ISBN: 978-3-319-25159-2
eBook Packages: Computer ScienceComputer Science (R0)