Abstract
We introduce Multimodal Logics of Normative Systems as a contribution to the development of a general logical framework for reasoning about normative systems over logics for Multi-Agent Systems. Given a multimodal logic L, for every modality \(\Box_{i}\) and normative system η, we expand the language adding a new modality \(\Box_{i}^{\eta}\) with the intended meaning of \(\Box_{i}^{\eta}\phi\) being “φ is obligatory in the context of the normative system η over the logic L”. In this expanded language we define the Multimodal Logic of Normative Systems over L, for any given set of normative systems N, and we give a sound and complete axiomatisation for this logic, proving transfer and model checking results. The special case when L and N are axiomatised by sets of Sahlqvist or shallow modal formulas is studied.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
References
Noriega, P.: Fencing the Open Fields: Empirical Concerns on Electronic Institutions. In: Boissier, O., Padget, J.A., Dignum, V., Lindemann, G., Matson, E., Ossowski, S., Sichman, J.S., Vázquez-Salceda, J. (eds.) ANIREM 2005 and OOOP 2005. LNCS (LNAI), vol. 3913, pp. 82–98. Springer, Heidelberg (2006)
van der Hoek, W., Wooldridge, M.: On obligations and normative ability: towards a logical analysis of the social contract. Journal of Applied Logic 3, 396–420 (2005)
Ågotnes, T., van der Hoek, W., Rodríguez-Aguilar, J.A., Sierra, C., Wooldridge, M.: On the Logic of Normative Systems. Twentieth International Joint Conference on AI, IJCAI 2007, pp. 1175–1180. AAAI Press, Menlo Park (2007)
Gabbay, D.M.: Fibring Logics. Oxford Logic Guides, 38 (1999)
Kurucz, A.: Combining Modal Logics. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, vol. 15, pp. 869–928. Elsevier, Amsterdam (2007)
Blackburn, P., van Benthem, J., Wolter, F.: Handbook of Modal Logic, vol. 15. Elsevier, Amsterdam (2007)
Ramchurn, S.D., Sierra, C., Godo, L., Jennings, N.R.: Negotiating using rewards. In: Proceedings of the Fifth international Joint Conference on Autonomous Agents and Multiagent Systems. AAMAS 2006, Hakodate, Japan, May 08–12, 2006, pp. 400–407. ACM Press, New York (2006)
Gabbay, D.M.: What is a Logical System? Oxford University Press, Inc, Oxford (1994)
Thomason, S.K.: Independent Propositional Modal Logics. Studia Logica 39, 143–144 (1980)
Baader, F., Ghilardi, S., Tinelli, C.: A new combination procedure for the word problem that generalizes fusion decidability results in modal logics. Information and Computation 204, 1413–1452 (2006)
Finger, M., Weiss, M.A.: The Unrestricted Combination of Temporal Logic Systems. Logic Journal of the IGPL 10, 165–189 (2002)
Franceschet, M., Montanari, A., de Rijke, M.: Model Checking for Combined Logics with an Application to Mobile Systems. Automated Software Engineering 11, 289–321 (2004)
Wolter, F.: Fusions of modal logics revisited. In: Kracht, M., de Rijke, M., Wansing, H., Zakharyashev, M. (eds.) Advances in Modal Logic, CSLI, Stanford (1998)
Cate, B.D.T.: Model Theory for extended modal languages. Ph.D Thesis, Institute for Logic, Language and Computation, Universiteit van Amsterdam. ILLC Dissertation, Series DS-2005-01 (2005)
Goranko, V., Vakarelov, D.: Elementary Canonical Formulae: extending Sahlqvist’s Theorem. Annals of Pure and Applied Logic 141, 180–217 (2006)
Moses, Y., Tennenholtz, M.: Artificial social systems. Computers and AI 14, 533–562 (1995)
Shoham, Y., Tennenholtz, M.: On the synthesis of useful social laws for artificial agent societies. In: Proceedings of the Tenth National Conference on Artificial Intelligence (AAAI 1992), San Diego, CA (1992)
Shoham, Y., Tennenholtz, M.: On social laws for artificial agent societies: Off-line design. In: Agre, P.E., Rosenschein, S.J. (eds.) Computational Theories of Interaction and Agency, pp. 597–618. MIT Press, Cambridge (1996)
Shoham, Y., Tennenholtz, M.: On the emergence of social conventions: Modelling, analysis, and simulations. Artificial Intelligence 94(1–2), 139–166 (1997)
Fitoussi, D., Tennenholtz, M.: Choosing social laws for multi-agent systems: Minimality and simplicity. Artificial Intelligence 119(1–2), 61–101 (2000)
Lomuscio, A., Sergot, M.: Deontic interpreted systems. Studia Logica 75(1), 63–92 (2003)
Viganò, F., Colombetti, M.: Model Checking Norms and Sanctions in Institutions. In: Sichman, J.S., et al. (eds.) COIN 2007 Workshops. LNCS (LNAI), vol. 4870, pp. 261–274. Springer, Heidelberg (2008)
Cliffe, O., De Vos, M., Padget, J.: Embedding Landmarks and Scenes in a Computational Model of Institutions. In: Sichman, J.S., et al. (eds.) COIN 2007 Workshops. LNCS (LNAI), vol. 4870, pp. 262–275. Springer, Heidelberg (2008)
García-Camino, A., Rodríguez-Aguilar, J.A., Vasconcelos, W.: A Distributed Architecture for Norm Management in Multi-Agent Systems. In: Sichman, J.S., Padget, J., Ossowski, S., Noriega, P. (eds.) COIN 2007. LNCS(LNAI), vol. 4870, pp. 275–286. Springer, Heidelberg (2008)
Joseph, S., Sierra, C., Schorlemmer, M.: A coherence based framework for institutional agents. In: Sichman, J.S., Padget, J., Ossowski, S., Noriega, P. (eds.) COIN 2007. LNCS(LNAI), vol. 4870, pp. 287–300. Springer, Heidelberg (2008)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dellunde, P. (2008). On the Multimodal Logic of Normative Systems. In: Sichman, J.S., Padget, J., Ossowski, S., Noriega, P. (eds) Coordination, Organizations, Institutions, and Norms in Agent Systems III. COIN 2007. Lecture Notes in Computer Science(), vol 4870. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79003-7_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-79003-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79002-0
Online ISBN: 978-3-540-79003-7
eBook Packages: Computer ScienceComputer Science (R0)