Abstract
In this paper we present an agent-based approach to formalising information diffusion using Markov models which attempts to account for the internal informational state of the agent and investigate the use of probabilistic model-checking for analysing these models. We model information diffusion as both continuous and discrete time Markov chains, using the latter to provide an agent-centred perspective. We present a negative result - we conclude that current model-checking technology is inadequate for analysing such systems in an interesting way.
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Notes
- 1.
This is detailed in http://www.prismmodelchecker.org/doc/semantics.pdf.
- 2.
Ernst Moritz Hahn, private communication.
References
Bailey, N.: The Mathematical theory of Infectious Diseases and its applications. Charles Griffin and Company Ltd., London (1975)
Belardinelli, F., Grossi, D.: On the formal verification of diffusion phenomena in open dynamic agent networks. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, pp. 237–245. AAMAS 2015, International Foundation for Autonomous Agents and Multiagent Systems, Richland, SC (2015). http://dl.acm.org/citation.cfm?id=2772879.2772912
Bolzern, P., Colaneri, P., Nicolao, G.D.: Opinion influence and evolution in social networks: a markovian agents model. Automatica 100, 219–230 (2019). https://doi.org/10.1016/j.automatica.2018.11.023, http://www.sciencedirect.com/science/article/pii/S0005109818305557
Christoff, Z., Hansen, J.U.: A two-tiered formalization of social influence. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI 2013. LNCS, vol. 8196, pp. 68–81. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40948-6_6
Christoff, Z., Hansen, J.U.: A logic for diffusion in social networks. J. Appl. Logic 13(1), 48–77 (2015). https://doi.org/10.1016/j.jal.2014.11.011
Christoff, Z., Hansen, J.U., Proietti, C.: Reflecting on social influence in networks. J. Logic Lang. Inform. 25(3), 299–333 (2016). https://doi.org/10.1007/s10849-016-9242-y
Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)
Dennis, L.A., Slavkovik, M., Fisher, M.: “How Did They Know?”—model-checking for analysis of information leakage in social networks. In: Cranefield, S., Mahmoud, S., Padget, J., Rocha, A.P. (eds.) COIN -2016. LNCS (LNAI), vol. 10315, pp. 42–59. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66595-5_3
Duflot, M., et al.: Practical applications of probabilistic model checking to communication protocols. In: Gnesi, S., Margaria, T. (eds.) FMICS Handbook on Industrial Critical Systems, pp. 133–150. IEEE Computer Society Press, Los Alamitos (2010)
Fisher, M., Dennis, L.A., Webster, M.: Verifying autonomous systems. Commun. ACM 56(9), 84–93 (2013)
Grandi, U., Lorini, E., Novaro, A., Perrussel, L.: Strategic disclosure of opinions on a social network. In: Proceedings of the 16th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS-2017) (2017)
Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978). https://doi.org/10.1086/226707
Jackson, M.O.: Social and Economic Networks. Princeton University Press, Princeton, NJ, USA (2008)
Jackson, M.O., Rogers, B.W., Zenou, Y.: The economic consequences of social-network structure. J. Econ. Lit. 55(1), 49–95 (2017). https://doi.org/10.1257/jel.20150694
Kouvaros, P., Lomuscio, A.: Formal verification of opinion formation in swarms. In: Proceedings of the 2016 International Conference on Autonomous Agents & #38; Multiagent Systems, pp. 1200–1208. AAMAS 2016, International Foundation for Autonomous Agents and Multiagent Systems, Richland, SC (2016). http://dl.acm.org/citation.cfm?id=2936924.2937099
Kwiatkowska, M., Norman, G., Parker, D.: Stochastic model checking. In: Bernardo, M., Hillston, J. (eds.) SFM 2007. LNCS, vol. 4486, pp. 220–270. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72522-0_6
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_47
Kwiatkowska, M., Thachuk, C.: Probabilistic model checking for biology. In: Software Safety and Security. NATO Science for Peace and Security Series - D: Information and Communication Security, IOS Press (2014), to appear
Lamberson, P.J.: Linking network structure and diffusion through stochastic dominance. In: Complex Adaptive Systems and the Threshold Effect, Papers from the 2009 AAAI Fall Symposium, Arlington, Virginia, USA, November 5–7, 2009 (2009)
Li, M., Wang, X., Gao, K., Zhang, S.: A survey on information diffusion in online social networks: models and methods. Information 8(4), 118 (2017). https://doi.org/10.3390/info8040118
Liu, F., Seligman, J., Girard, P.: Logical dynamics of belief change in the community. Synthese 191(11), 2403–2431 (2014). https://doi.org/10.1007/s11229-014-0432-3
Mercier, H., Sperber, D.: The Enigma of Reason. Harvard University Press, London, UK (2017)
Newman, M.E.J., Watts, D.J., Strogatz, S.H.: Random graph models of social networks. Proc. Nat. Acad. Sci. 99(suppl 1), 2566–2572 (2002). https://doi.org/10.1073/pnas.012582999
Pardo, R., Schneider, G.: Model checking social network models. In: Proceedings Eighth International Symposium on Games, Automata, Logics and Formal Verification, GandALF 2017, Roma, Italy, 20–22 September 2017, pp. 238–252 (2017). https://doi.org/10.4204/EPTCS.256.17, https://doi.org/10.4204/EPTCS.256.17
Pedersen, T., Slavkovik, M.: Formal models of conflicting social influence. In: An, B., Bazzan, A., Leite, J., Villata, S., van der Torre, L. (eds.) PRIMA 2017. LNCS (LNAI), vol. 10621, pp. 349–365. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69131-2_21
Rapoport, A.: Spread of information through a population with socio-structural bias: I. assumption of transitivity. Bull. Math. Biophys. 15(4), 523–533 (1953). https://doi.org/10.1007/BF02476440, https://doi.org/10.1007/BF02476440
Schelling, T.C.: Dynamic models of segregation. J. Math. Sociol. 1(2), 143–186 (1971)
Smets, S., Velázquez-Quesada, F.R.: How to make friends: a logical approach to social group creation. In: Baltag, A., Seligman, J., Yamada, T. (eds.) LORI 2017. LNCS, vol. 10455, pp. 377–390. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-55665-8_26
Winship, C.: Threshold models of social influence. In: Bearman, P., Hedström, P. (eds.) The Oxford Handbook of Analytical Sociology. Oxford University Press, Oxford (2011). https://doi.org/10.1093/oxfordhb/9780199215362.013.20
Zonghao, G., Ou, W., Peng, Y., Lansheng, H., Weiming, W.: Model checking probabilistic network propagation protection strategies. In: 2016 IEEE Trustcom/BigDataSE/ISPA, pp. 354–361 (August 2016). https://doi.org/10.1109/TrustCom.2016.0084
Acknowledgements
The research was partly supported by the project “Better Video workflows via Real-Time Collaboration and AI-Techniques in TV and New Media”, funded by the Research Council of Norway under Grant No.:269790.
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Dennis, L.A., Slavkovik, M. (2020). Model-Checking Information Diffusion in Social Networks with PRISM. In: Bassiliades, N., Chalkiadakis, G., de Jonge, D. (eds) Multi-Agent Systems and Agreement Technologies. EUMAS AT 2020 2020. Lecture Notes in Computer Science(), vol 12520. Springer, Cham. https://doi.org/10.1007/978-3-030-66412-1_30
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