DS-2021-13: Formal Threads in the Social Fabric: Studies in the Logical Dynamics of Multi-Agent Interaction

DS-2021-13: Li, Dazhu (2021) Formal Threads in the Social Fabric: Studies in the Logical Dynamics of Multi-Agent Interaction. Doctoral thesis, University of Amsterdam.

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Interactions between people are a defining feature of social life. Our actions tend to be reactions to what others have done, while others again respond to our behavior. This never-ending entanglement can be observed across a wide range of settings including exchange of information, spread of opinions in social networks, cooperation and competition in economic or academic activities, and even social relationships themselves are in dynamic flux. While these phenomena have been studied in many disciplines, from sociology and economic game theory to social epistemology or philosophy of action, this dissertation pursues a logical perspective. Social interaction is a core topic in current logics of multi-agent systems at the interface of philosophy, computer science and AI, and the resulting systems have been applied to better understand human behavior, but also to design new forms of behavior by both human and artificial agents. This dissertation continues within this multi-agency tradition, especially, that of dynamic-epistemic logics, and explores two new logical perspectives that highlight two further basic properties of social interaction.

The first topic is multi-agent interaction under adverse circumstances. This arises when agents are deeply at odds, to the extent that they try to change the very setting (physical or otherwise) where their interactions take place --- as happens, for instance, when actors in some standard scenario find themselves under hostile attack. For a crisp modeling of such scenarios, we use special `graph games' where players can change the graph, i.e., their playground, during play. In our central game, one agent (the Traveler) wants to reach some region representing a goal, while the other player (the Demon) obstructs the Traveler as much as possible by removing edges from the graph. These graph games turn out to be highly amenable to logical analysis, and extending existing literature on these scenarios, we provide a complete logical analysis of graph games where obstruction consists in removing edges at the current position of the Traveler in some definable manner. This `local sabotage under a description' covers many scenarios and supports a rich logical theory of valid reasoning.

Although the above scenario may look ‘negative’, edge removal as an abstract technique can also be beneficial: we demonstrate this by next studying the interactions of agents engaged in learning and teaching. For this purpose, we consider a more realistic concrete scenario, and design richer graph games where edge removals by a Teacher represent corrections of two kinds: pointing out errors already made by a Learner, or steering the Learner away from potential future mistakes. Again we provide a logical language for analyzing these scenarios, and we show how this provides a rich framework for analyzing the dynamics of learning that goes into more procedural details than standard scenarios in formal learning theory.

One can view the role of logical methods in the preceding cases as providing more precision and detail in the analysis of social scenarios. The second part of the thesis uses logic in more or less the opposite direction: finding abstract general structures that play across many scenarios at the same time. Our particular interest here is the notion of dependence of behavior for agents engaged in social activities.

First, we explore the abstract notion of dynamic dependence over time in multi-agent systems. To capture the temporal dimension of social interaction, we develop a logical system embodying the core reasoning about functional dependence in dynamical systems. This requires extending existing modal logics of dependence with devices from temporal logic, and the result is a logic of action and dependence in dynamical systems, for which we show completeness and other properties. Moreover, since most uses of dynamical systems in the literature involve a topology on the state space, we also offer an enrichment. We introduce a topological version of the system that can describe information about social interaction when we have only imprecise (though refinable) ways of measuring the relevant variables. The result is a richer logic of what we call dynamic continuous dependence. One way of viewing these systems is as a generalization of current analyses of social behavior in evolutionary game theory.

Next, as in our first part, having developed the abstract base theory, we consider what else needs to come in to deal with more realistic social scenarios. Our case study is that of diffusion of opinions or behaviors in communities, where agents update their behavior based on what their neighbors in the social network do, according to some threshold rule. We highlight the crucial role of information in making this work, and present a logical case study of what it takes to add an epistemic dimension to our style of analysis so far.

We conclude by taking stock, and pointing at the many new issues raised by our analysis. These include many technical open problems in the logic of multi-agent systems, but also conceptual rethinking of how one should represent social entities in the first place.

Item Type: Thesis (Doctoral)
Report Nr: DS-2021-13
Series Name: ILLC Dissertation (DS) Series
Year: 2021
Subjects: Language
Depositing User: Dr Marco Vervoort
Date Deposited: 14 Jun 2022 15:17
Last Modified: 14 Jun 2022 15:17
URI: https://eprints.illc.uva.nl/id/eprint/2199

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