Abstract
This paper introduces a comprehensive logical framework to reason about threshold-driven diffusion and threshold-driven link change in social networks. It considers both monotonic dynamics, where agents can only adopt new features and create new connections, and non-monotonic dynamics, where agents may also abandon features or cut ties. Three types of operators are combined: one capturing diffusion only, one capturing link change only, and one capturing both at the same time. We first characterise the models on which diffusion of a unique feature and link change stabilise, whilst discussing salient properties of stable models with multiple spreading features. Second, we show that our operators (and any combination of them) are irreplaceable, in the sense that the sequences of model updates expressed by a combination of operators cannot always be expressed using any other operators. Finally, we analyse classes of models on which some operators can be replaced.
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Acknowledgements
This research was partly funded by the project ‘Hybrid Intelligence: Augmenting Human Intellect’, a 10-year Gravitation programme funded by the Dutch Ministry of Education, Culture and Science through the Netherlands Organisation for Scientific Research, grant number 024.004.022. Zoé Christoff acknowledges support from the project ‘Social Networks and Democracy’ (VENI project number Vl.Veni.201F.032) financed by the Netherlands Organisation for Scientific Research (NWO). Edoardo Baccini would like to thank Maaike Venema-Los, Anton Chernev, and Juan Camilo Jaramillo Londoño for helpful discussions. The authors also thank the anonymous reviewers for their helpful comments, as well as the reviewers of their LOFT-2022 and TARK-2023 conference papers on which this paper builds.
Funding
Rineke Verbrugge acknowledges support from the project ‘Hybrid Intelligence: Augmenting Human Intellect’, a 10-year Gravitation programme funded by the Dutch Ministry of Education, Culture and Science through the Netherlands Organisation for Scientific Research, Grant Number 024.004.022. Zoé Christoff acknowledges support from the project ‘Social Networks and Democracy’ (VENI project number Vl.Veni.201F.032) financed by the Netherlands Organisation for Scientific Research (NWO).
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This paper is an extended version of two previous conference papers: [7], which was presented at the Logic and the Foundations of Decision Theory and Game Theory Conference 2022 held in Groningen, and [6] presented at the conference Theoretical Aspects of Rationality and Knowledge 2023 held in Oxford.
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Presented by Louwe Kuijer, Hans van Ditmarsch and Wiebe van der Hoek; Received September 29, 2023.
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Baccini, E., Christoff, Z. & Verbrugge, R. Dynamic Logics of Diffusion and Link Changes on Social Networks. Stud Logica (2024). https://doi.org/10.1007/s11225-024-10126-0
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DOI: https://doi.org/10.1007/s11225-024-10126-0