Dynamic logics of networks: Information flow and the spread of opinion
This thesis uses logical tools to investigate a number of basic features of social networks and their evolution over time, including flow of information and spread of opinions. Part I contains the preliminaries, including an introduction to the basic phenomena in social networks that call for a logical analysis of information and reasoning, a review of background material from logic and social network theory, plus an outline of the thesis. Part II presents logical models of collective failures, and illuminates how and when sound individual microbehavior can lead to counterproductive collective macrobehavior. Part III abstracts from specific case studies to investigate the general logic of diffusion phenomena in social networks, as well as the interaction of information and diffusion dynamics. Finally, Part IV presents a summary of our findings, and some ongoing work and perspectives for future research. We discuss modal logics and related formalisms for studying network behavior under various graph properties and rules of influence. We also discuss the natural transition from network evolution by fixed rules as studied in this thesis to the study of network games where agents have choices and goals. Overall, this thesis applies tools from current logics of information update and agency to social network analysis and opinion flow over time, offering both tools for detailed modeling of specific scenarios and a better understanding of the general laws of reasoning that underlie information and diffusion dynamics in social settings.