Jens Ulrik Hansen

Normal Gait of Young and Old Men and Women: Ground Reaction Force Measurement on a Treadmill

Forty normal persons had their gait tested using an instrumented treadmill. All were tested at the same speed of gait. The temporal factors of gait, the ataxia, and the external work of the gait were all calculated from the ground reaction forces. Ten women and ten men 20-29 years and ten women and ten men aged 60-69 were tested. The study demonstrated a constant pattern of gait independent of age and sex.

Decidability of a Hybrid Duration Calculus

We present a logic which we call Hybrid Duration Calculus (HDC). HDC is obtained by adding the following hybrid logical machinery to the Restricted Duration Calculus (RDC): 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.

Terminating Tableaux for Dynamic Epistemic Logics

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 (both without common knowledge). 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 Brauner, Bolander, and Blackburn.

On the rationality of pluralistic ignorance

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.

A Two-Tiered Formalization of Social Influence

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.

A Hybrid Public Announcement Logic with Distributed Knowledge

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 (in the usual style of Hybrid Logic) 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.

Many-Valued Hybrid Logic

In this paper we define a many-valued semantics for hybrid logic and we give a sound and complete tableau system which is proof theoretically well-behaved, in particular, it gives rise to a decision procedure for the logic. This shows that many-valued hybrid logics is a natural enterprise and opens up the way for future applications.

Reflecting on Social Influence in Networks

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.

Logical knowledge representation of regulatory relations in biomedical pathways

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.

Truth Tracking Performance of Social Networks: How Connectivity and Clustering Can Make Groups Less Competent

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 (opinion) 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 (average degree) 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.