Our beliefs and opinions are shaped by others, making our social networks crucial in determining what we believe to be true. Sometimes this is for the good because our peers help us form a more accurate opinion. Sometimes it is for the worse because we are led astray. In this context, we address via agent-based computer simulations the extent to which patterns of connectivity within our social networks affect the likelihood that initially undecided agents in a network converge on a (...) true opinion following group deliberation. The model incorporates a fine-grained and realistic representation of belief and trust, and it allows agents to consult outside information sources. We study a wide range of network structures and provide a detailed statistical analysis concerning the exact contribution of various network metrics to collective competence. Our results highlight and explain the collective risks involved in an overly networked or partitioned society. Specifically, we find that 96% of the variation in collective competence across networks can be attributed to differences in amount of connectivity and clustering, which are negatively correlated with collective competence. A study of bandwagon or “group think” effects indicates that both connectivity and clustering increase the probability that the network, wholly or partly, locks into a false opinion. Our work is interestingly related to Gerhard Schurz’s work on meta-induction and can be seen as broadly addressing a practical limitation of his approach. (shrink)

Pluralistic ignorance is a socio-psychological phenomenon that involves a systematic discrepancy between people’s private beliefs and public behavior in certain social contexts. Recently, pluralistic ignorance has gained increased attention in formal and social epistemology. But to get clear on what precisely a formal and social epistemological account of pluralistic ignorance should look like, we need answers to at least the following two questions: What exactly is the phenomenon of pluralistic ignorance? And can the phenomenon arise among perfectly rational agents? In (...) this paper, we propose answers to both these questions. First, we characterize different versions of pluralistic ignorance and define the version that we claim most adequately captures the examples cited as paradigmatic cases of pluralistic ignorance in the literature. In doing so, we will stress certain key epistemic and social interactive aspects of the phenomenon. Second, given our characterization of pluralistic ignorance, we argue that the phenomenon can indeed arise in groups of perfectly rational agents. This, in turn, ensures that the tools of formal epistemology can be fully utilized to reason about pluralistic ignorance. (shrink)

This paper introduces a general logical framework for reasoning about diffusion processes within social networks. The new “Logic for Diffusion in Social Networks” is a dynamic extension of standard hybrid logic, allowing to model complex phenomena involving several properties of agents. We provide a complete axiomatization and a terminating and complete tableau system for this logic and show how to apply the framework to diffusion phenomena documented in social networks analysis.

In many social contexts, social influence seems to be inescapable: the behavior of others influences us to modify ours, and vice-versa. However, social psychology is full of examples of phenomena where individuals experience a discrepancy between their public behavior and their private opinion. This raises two central questions. First, how does an individual reason about the behavior of others and their private opinions in situations of social influence? And second, what are the laws of the resulting information dynamics? In this (...) paper, we address these questions by introducing a formal framework for representing reasoning about an individual’s private opinions and public behavior under the dynamics of social influence in social networks. Moreover, we dig deeper into the involved information dynamics by modeling how individuals can learn about each other based on this reasoning. This compels us to introduce a new formal notion of reflective social influence. Finally, we initialize the work on proof theory and automated reasoning for our framework by introducing a sound and complete tableaux system for a fragment of our logic. Furthermore, this constitutes the first tableau system for the “Facebook logic” of J. Seligman, F. Liu, and P. Girard. (shrink)

In this paper, we investigate the social herding phenomenon known as informational cascades, in which sequential inter-agent communication might lead to epistemic failures at group level, despite availability of information that should be sufficient to track the truth. We model an example of a cascade, and check the correctness of the individual reasoning of each agent involved, using two alternative logical settings: an existing probabilistic dynamic epistemic logic, and our own novel logic for counting evidence. Based on this analysis, we (...) conclude that cascades are not only likely to occur but are sometimes unavoidable by "rational" means: in some situations, the group’s inability to track the truth is the direct consequence of each agent’s rational attempt at individual truth-tracking. Moreover, our analysis shows that this is even so when rationality includes unbounded higher-order reasoning powers, as well as when it includes simpler, non-Bayesian forms of heuristic reasoning. (shrink)

We propose a new dynamic hybrid logic to reason about social networks and their dynamics building on the work of “Logic in the Community” by Seligman, Liu and Girard. Our framework distinguishes between the purely private sphere of agents, namely their mental states, and the public sphere of their observable behavior, i.e., what they seem to believe. We then show how such a distinction allows our framework to model many social phenomena, by presenting the case of pluralistic ignorance as an (...) example and discussing some of its dynamic properties. (shrink)

Throughout the last decade, there has been an increased interest in various forms of dynamic epistemic logics to model the flow of information and the effect this flow has on knowledge in multi-agent systems. This enterprise, however, has mostly been applicationally and semantically driven. This results in a limited amount of proof theory for dynamic epistemic logics. In this paper, we try to compensate for a part of this by presenting terminating tableau systems for full dynamic epistemic logic with action (...) models and for a hybrid public announcement logic. The tableau systems are extensions of already existing tableau systems, in addition to which we have used the reduction axioms of dynamic epistemic logic to define rules for the dynamic part of the logics. Termination is shown using methods introduced by Braüner, Bolander, and Blackburn. (shrink)

This paper introduces a logic to reason about a well-known model of opinion dynamics in socialnetworks initially developed by Morris DeGroot as well as Keith Lehrer and Carl Wagner. The proposed logic is an extension of Lukasiewicz' famous fuzzy logic with additional equational expressivity, modal operators, machinery from hybrid logic, and dynamic modalities. The model of opinion dynamics in social networks is simple enough to be easily grasped, but still complex enough to have interesting mathematical properties and applications. Thus, developing (...) a logic to reason about this particular model serves as a paradigmatic example of how logic can be useful in social network analysis. (shrink)

``Pluralistic ignorance'' is a phenomenon mainly studied in social psychology. Viewed as an epistemic phenomenon, one way to define it is as a situation where ``no one believes, but everyone believes that everyone else believes''. In this paper various versions of pluralistic ignorance are formalized using epistemic/doxastic logic. The motive is twofold. Firstly, the formalizations are used to show that the various versions of pluralistic ignorance are all consistent, thus there is nothing in the phenomenon that necessarily goes against logic. (...) Secondly, pluralistic ignorance, is on many occasions, assumed to be fragile. In this paper, however, it is shown that pluralistic ignorance need not be fragile to announcements of the agents' beliefs. Hence, to dissolve pluralistic ignorance in general, something more than announcements of the subjective views of the agents is needed. Finally, suggestions to further research are outlined. (shrink)

In this paper the phenomenon of pluralistic ignorance is discussed and it is argued why it is of relevance for epistemic logic and social psychology. Roughly put, pluralistic ignorance is the case when a group of interacting agents all experience a discrepancy between their private opinions and the perceived opinions of the others. After introducing the phenomenon, numerous features of pluralistic ignorance that are of interest for epistemic logic and social epistemology, are discussed. This discussion serves two purposes: It recaps (...) the existing research on pluralistic ignorance within epistemic logic and social epistemology, while at the same time stating open problems for social epistemology and epistemic logic that pertains to the study of pluralistic ignorance. Finally, it is argued that the features of pluralistic ignorance of interest to epistemic logic and social epistemology relate to general features of information dynamics in situations of social interaction. (shrink)

In this paper we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be "intermediate" logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained (...) in the paper. Our results show that many-valued hybrid logic is indeed a natural enterprise. (shrink)

In this paper we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be "intermediate" logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained (...) in the paper. Our results show that many-valued hybrid logic is indeed a natural enterprise. (shrink)

We present a logic which we call Hybrid Duration Calculus. HDC is obtained by adding the following hybrid logical machinery to the Restricted Duration Calculus : nominals, satisfaction operators, down-arrow binder, and the global modality. RDC is known to be decidable, and in this paper we show that decidability is retained when adding the hybrid logical machinery. Decidability of HDC is shown by reducing the satisfiability problem to satisfiability of Monadic Second-Order Theory of Order. We illustrate the increased expressive power (...) obtained in hybridizing RDC by showing that HDC, in contrast to RDC, can express all of the 13 possible relations between intervals. (shrink)

In this paper a first-order version of hybrid logic is presented. The language is obtained by adding nominals, satisfaction operators and the down-arrow binder to classical first-order modal logic. The satisfaction operators are applied to both formulas and terms. Moreover adding the universal modality is discussed. This first-order hybrid language is interpreted over varying domains and a sound and complete, fully internalized tableau system for this logic is given.

In this paper the machinery of Hybrid Logic and the logic of public announcements are merged. In order to bring the two logics together properly the underlying hybrid logic has been changed such that nominals only partially denote states. The hybrid logic contains nominals, satisfaction operators, the downarrow binder as well as the global modality. Following this, an axiom system for the Hybrid Public Announcement Logic is presented and using reduction axioms general completeness is proved. The general completeness allows for (...) an easy way of adding distributed knowledge. Furthermore, it turns out that distributed knowledge is definable using satisfaction operators and the downarrow binder. (shrink)

Dynamic Epistemic Logic is claimed to be a dynamic version of epistemic logic. While this being true, there are several dynamical aspects that cannot be reasoned about in Dynamic Epistemic Logic. When a scenario is fixed and a possible world model representing the scenario is constructed, the possible future ways the system can evolve are in some sense already determined. For instance no new agents can enter the scenario and no new propositional facts can become relevant. This modeling perspective is (...) the main motivation for the partial version of Dynamic Epistemic Logic introduced in this paper, which in particular, allows for the set of agents and the set of propositional variables to change. (shrink)

Knowledge on regulatory relations, in for example regulatory pathways in biology, is used widely in experiment design by biomedical researchers and in systems biology. The knowledge has typically either been represented through simple graphs or through very expressive differential equation simulations of smaller sections of a pathway. As an alternative, in this work we suggest a knowledge representation of the most basic relations in regulatory processes regulates, positively regulates and negatively regulates in logics based on a semantic analysis. We discuss (...) the usage of these relations in biology and in artificial intelligence for hypothesis development in drug discovery. (shrink)