Dominik Klein

The paper introduces a broad family of metrics applicable to finite and countably infinite strings, or, by extension, to formal structures serving as semantics for countable languages. The main focus is on applications to sets of pointed Kripke models, a semantics for modal logics. For the resulting metric spaces, the paper classifies topological properties including which metrics are topologically equivalent, providing sufficient conditions for compactness, characterizing clopen sets and isolated points, and characterizing the metrical topologies by a concept of logical convergence. We then apply the approach to maps from dynamic epistemic logic, showing that product updates with action models yield continuous maps, hence allowing for an interpretation of the iterated updates as discrete time dynamical systems.

In der Literatur finden sich zahlreiche Hinweise, dass die Versorgung mit öffentlichen Gütern in demokratischen Regierungssystemen besser funktioniert als in autokratischen Alternativen. Klassischerweise wird diese Beobachtung durch Unterschiede in den Anreizstrukturen demokratischer und autokratischer Entscheidungsverfahren erklärt (vgl. de Mesquita et al. 2005; Olson 2000). Der vorliegende Beitrag diskutiert eine weitere Erklä- rung für Unterschiede zwischen den unterschiedlichen Regierungstypen. Aufbauend auf die Debatte zur epistemischen Rechtfertigung demokrati- scher Entscheidungsverfahren (siehe Estlund 2000, Estlund und Landemo- re 2012, 2018) analysieren wir, ob demokratische Regime auch einen insti- tutionell bedingten epistemischen Vorteil haben. Wir untersuchen diese Frage mit Hilfe eines Modells, in dem Akteure vor der Aufgabe stehen, das optimale Niveau öffentlicher Gütern zu bestimmen. Es gilt für die Akteure also, den optimalen Steuersatz zu schätzen. Wir implementieren dieses Modell in eine agentenbasierte Computersimulation und analysie- ren, wie gut es Akteuren innerhalb von zwei idealtypisch verfassten, po- litischen Systemen (Demokratie und Autokratie) gelingt, diese Aufgabe zu lösen. Die resultierenden Ergebnisse erlauben uns, die epistemische Qualität von demokratischen und nicht-demokratischen, kollektiven Ent- scheidungsverfahren zu vergleichen. Wir finden erstens einen positiven Effekt der epistemischen Vielfalt großer Gruppen, die in demokratischen Entscheidungsverfahren zur Geltung kommt (für ähnliche Ergebnisse im Gebiet wissenschaftlicher Gemeinschaften siehe Zollman 2010, O'Connor und Bruner 2019). Zweitens zeigt sich überraschenderweise, dass demokra- tische Entscheidungsverfahren am besten abschneiden, wenn die Bürger auch ihre eigenen Bedürfnisse priorisieren und kommunizieren, anstatt in ihren Interaktionen mit ihren Mitbürgern lediglich das optimale Niveau des öffentlichen Nutzens aus der Sicht der Gruppe zu kommunizieren. Schließlich findet sich ein positiver Effekt von zeitlich begrenzten Deli- berationsphasen auf die epistemische Qualität kollektiver Abstimmungser- gebnisse.

We study the logic of neighbourhood models with pointwise intersection, as a means to characterize multi-modal logics. Pointwise intersection takes us from a set of neighbourhood sets Ni (one for each member i of a set G used to interpret the modality □) to a new neighbourhood set NG, which in turn allows us to interpret the operator □G Here, X is in the neighbourhood for G if and only if X equals the intersection of some Y {Yi | Yi ∈G}. We show that the notion of pointwise intersection has various applications in epistemic and doxastic logic, deontic logic, coalition logic, and evidence logic. We then establish sound and strongly complete axiomatizations for the weakest logic characterized by pointwise intersection and for a number of variants, using a new and generally applicable technique for canonical model construction.

High levels of trust have been linked to a variety of benefits including the well-functioning of markets and political institutions or the ability of societies to solve public goods problems endogenously. While there is extensive literature on the macro-level determinants of trust, the micro-level processes underlying the emergence and stability of trust are not yet sufficiently understood. We address this lacuna by means of a computer model. In this paper, conditions under which trust is likely to emerge and be sustained are identified. We focus our analysis mainly on the individual characteristics of agents: their social or geographical mobility, their attitude towards others or their general uncertainty about the environment. Contrary to predictions from previous literature, we show that immobile agents are detrimental to both, the emergence and robustness of trust. Additionally, we identify a hidden link between trusting others and being trustworthy.

Agent-based modeling has become a common and well-established tool in the social sciences and certain of the humanities. Here, we aim to provide an overview of the different modeling approaches in current use. Our discussion unfolds in two parts: we first classify different aspects of the model-building process and identify a number of characteristics shared by most agent-based models in the humanities and social sciences; then we map relevant differences between the various modeling approaches. We classify these into different dimensions including the type of target systems addressed, the intended modeling goals, and the models’ degree of abstraction. Along the way, we provide reference to related debates in contemporary philosophy of science.

We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in Van De Putte and Klein. The definition of our canonical models combines standard techniques with a so-called “puzzle piece construction”, which we first illustrate informally. After that, we apply it to the weakest classical logics with pooling modalities and investigate the technique’s potential for the axiomatization of stronger logics, obtained by imposing well-known frame conditions on the models.

The paper investigates the way norms relate to and affect agents' intentions and actions. Current work in deontic logic dealing with agency mainly falls within two different groups: a variety of frameworks which adopt a purely external approach and represent agency in terms of possible outcomes of actions, and frameworks which instead endorse an internal approach and focus exclusively on the agents' intentions. The paper argues that neither of these models alone can produce a satisfactory analysis. An integrated model which combines the internal and external approaches is therefore put forward. The model is dynamic and represents the change that accepting a goal norm triggers in an agent's intentions (especially the so-called "prior-intentions" and actions

One of the important lessons to take away from Rohit Parikh’s impressive body of work is that logicians and computer scientists have much to gain by focusing their attention on the intricacies of political campaigns. Drawing on recent work developing a theory of expressive voting, we study the dynamics of voters’ opinions during an election. In this paper, we develop a model in which the relative importance of the different issues that concern a voter may change either in response to candidates’ statements during a campaign or due to unforeseen events. We study how changes in a voter?s attention to the issues influence voting behavior under voting systems such as plurality rule and approval voting. We argue that it can be worthwhile for candidates to reshape public focus, but that doing so can be a complex and risky activity.

The emergence of economic inequality has often been linked to individual differences in mental or physical capacities. By means of an agent-based simulation this paper shows that neither of these is a necessary condition. Rather, inequality can arise from iterated interactions of fully rational agents. This bears consequences for our understanding of both inequality and rationality. In a setting of iterated bargaining games, we claim that expected utility maximizing agents perform suboptimally in comparison with other strategies. The reason for this lies in complex feedback effects between an agents’ action and the quality of beliefs used to calculate expected utility. Consequentially, we argue that the standard notion of rationality as maximizing expected utility is insufficient, even for certain standard cases of economic interaction.

Belnap-Dunn logic, sometimes also known as First Degree Entailment, is a four-valued propositional logic that complements the classical truth values of True and False with two non-classical truth values Neither and Both. The latter two are to account for the possibility of the available information being incomplete or providing contradictory evidence. In this paper, we present a probabilistic extension of BD that permits agents to have probabilistic beliefs about the truth and falsity of a proposition. We provide a sound and complete axiomatization for the framework defined and also identify policies for conditionalization and aggregation. Concretely, we introduce four-valued equivalents of Bayes’ and Jeffrey updating and also suggest mechanisms for aggregating information from different sources.

Group judgements are often – implicitly or explicitly – influenced by their members’ individual expertise. However, given that expertise is seldom recognized fully and that some distortions may occur (bias, correlation, etc.), it is not clear that differential weighting is an epistemically advantageous strategy with respect to straight averaging. Our paper characterizes a wide set of conditions under which differential weighting outperforms straight averaging and embeds the results into the multidisciplinary group decision-making literature.

Analyzing situations where information is partial, incomplete or contradictory has created a demand for quantitative belief measures that are weaker than classic probability theory. In this paper, we compare two frameworks that have been proposed for this task, Dempster-Shafer theory and non-standard probability theory based on Belnap-Dunn logic. We show the two frameworks to assume orthogonal perspectives on informational shortcomings, but also provide a partial correspondence result. Lastly, we also compare various dynamical rules of the two frameworks, all seen as generalizations of classic Bayes’ conditioning.

We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation underlying both models of belief, showing that neither is strong enough to support a probabilistic interpretation, nor an interpretation in terms of certainty or the “mental component” of knowledge.

We study two logics of knowledge and belief stemming from the work of Stalnaker, omitting positive introspection for knowledge. The two systems are equivalent with positive introspection, but not without. We show that while the logic of beliefs remains unaffected by omitting introspection for knowledge in one system, it brings significant changes to the other. The resulting logic of belief is non-normal, and its complete axiomatization uses an infinite hierarchy of coherence constraints. We conclude by returning to the philosophical interpretation underlying both models of belief, showing that neither is strong enough to support a probabilistic interpretation, nor an interpretation in terms of certainty or the “mental component” of knowledge.

Many different approaches to describing the players’ knowledge and beliefs can be found in the literature on the epistemic foundations of game theory. We focus here on non-probabilistic approaches. The two most prominent are the so-called Kripkeor Aumann- structures and knowledge structures (non-probabilistic variants of Harsanyi type spaces). Much of the recent work on Kripke structures has focused on dynamic extensions and simple ways of incorporating these. We argue that many of these ideas can be applied to knowledge structures as well. Our main result characterizes precisely when one type can be transformed into another type by a specific type of information update. Our work in this paper suggest that it would be interesting to pursue a theory of “information dynamics” for knowledge structures (and eventually Harsanyi type spaces)

This paper focuses on the Enkratic principle of rationality, according to which rationality requires that if an agent sincerely and with conviction believes she ought to X, then X-ing is a goal in her plan. We analyze the logical structure of Enkrasia and its implications for deontic logic. To do so, we elaborate on the distinction between basic and derived oughts, and provide a multi-modal neighborhood logic with three characteristic operators: a non-normal operator for basic oughts, a non-normal operator for goals in plans, and a normal operator for derived oughts. We prove two completeness theorems for the resulting logic, and provide a dynamic extension of the logic by means of product updates. We illustrate how this setting informs deontic logic by considering issues related to the filtering of inconsistent oughts, the restricted validity of deontic closure, and the stability of oughts and goals under dynamics.

How should the information that a proposition p is a mystery impact your credence in p? To answer this question, we first provide a taxonomy of mysteries; then, we develop a test to distinguish two types of mysteries. When faced with mysteries of the first type, rational epistemic agents should lower their credence in p upon learning that p is a mystery. The same information should not impact agents’ credence in p, when they face mysteries of the second type. Our account of mystery complements existing explications of abduction. We illustrate its significance by examining the mystery of consciousness.

The paper analyzes dynamic epistemic logic from a topological perspective. The main contribution consists of a framework in which dynamic epistemic logic satisfies the requirements for being a topological dynamical system thus interfacing discrete dynamic logics with continuous mappings of dynamical systems. The setting is based on a notion of logical convergence, demonstratively equivalent with convergence in Stone topology. Presented is a flexible, parametrized family of metrics inducing the latter, used as an analytical aid. We show maps induced by action model transformations continuous with respect to the Stone topology and present results on the recurrent behavior of said maps.