Dominik Klein



Logics for Analyzing Games (draft)
Johan van Benthem and Dominik Klein [pdf]

Pointwise Intersection in Neighbourhood Modal Logic
Frederik Van De Putte and Dominik Klein in Advances in Modal Logic (AiML 12), College Publications, pp. 591-610 [pdf] [bib] [abstract]

    author = {Van De Putte, Frederik and Klein, Dominik },
    title  = {Pointwise Intersection in Neighbourhood Modal Logic},
    editor = {Bezhanishvili, Guram and D'Agostino, Giovanna and 
    Metcalfe, George and Studer, Thomas},
    booktitle = {{Advances in Modal Logic 12}},
    series = {{Advances in Modal Logic}},
    volume = {12},
    publisher = {College Publications},
    year = {2018},
    pages = {591-610},
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 | YiG}. 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.

Rationality in Context - On inequality and the epistemic problems of maximizing expected utility
Dominik Klein, Johannes Marx and Simon Scheller in Synthese (2018), pp. 1-18 [pdf] [doi] [bib] [abstract]

 author={Klein, Dominik and Marx, Johannes and Scheller, Simon},
 title={Rationality in context},
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.

Generalized Trust in the Mirror. An Agent-Based Model on the Dynamics of Trust.
Dominik Klein and Johannes Marx in Historical Social Research 43(1), pp. 243-258 [simulation] [pdf] [doi] [bib] [abstract]

 title = {Generalized Trust in the Mirror: An Agent-Based Model on the Dynamics of Trust},
 author = {Klein, Dominik and Marx, Johannes},
 journal = {Historical Social Research},
 number = {1},
 pages = {234--258},
 volume = {43},
 year = {2018},
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 in Social Science, History, and Philosophy: An Introduction
Dominik Klein, Johannes Marx and Kai Fischbach editorial of Historical Social Research 43(1), pp. 243-258 [pdf] [doi] [bib] [abstract]

 title = {Agent-Based Modeling in Social Science, History, and Philosophy:
 An Introduction},
 author = {Klein, Dominik and Marx, Johannes and Fischbach, Kai},
 journal = {Historical Social Research},
 number = {1},
 pages = {7-27},
 volume = {43},
 year = {2018},
  urn = {}
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.


Convergence, Continuity and Recurrence in Dynamic Epistemic Logic
Dominik Klein and Rasmus K. Rendsvig in Logic, Rationality and Interaction (LORI VII), Springer 2017, pp. 108-122 [pdf] [doi] [bib] [abstract]

    author = {Klein, Dominik and Rendsvig, Rasmus K.},
    title  = {{Convergence, Continuity and Recurrence in Dynamic Epistemic Logic}},
    editor = {Baltag, A. and Seligman, J. and Yamada, T.},
    booktitle = {{Logic, Rationality, and Interaction (LORI 2017)}},
    series = {{Lecture Notes in Computer Science}},
    volume = {10455},
    publisher = {Springer},
    year = {2017},
    pages = {108--122},
    doi = {10.1007/978-3-662-55665-8_8},
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.

Mystery and the Evidential Impact of Unexplainables
Dominik Klein and Matteo Colombo in Episteme (2017) doi:10.1017/epi.2017.13 [pdf] [doi] [bib] [abstract]

    title={Mystery and the Evidential Impact of Unexplainables}, 
    publisher={Cambridge University Press}, 
    author={Klein, Dominik and Colombo, Matteo}, 
What's the evidential impact of learning that something is a mystery? To answer this question, we first explicate the notion of a mystery in terms of unexplainability. After distinguishing different ways in which something can be unexplainable, we develop a test to evaluate the evidential impact of two distinct types of unexplainables: symmetrical and asymmetrical unexplainables. We argue that only asymmetrical unexplainables have evidential impact. We finally clarify how our explication of mysteries as unexplainables complements existing accounts of abduction and contributes to the literature on the mystery of consciousness.

Knowledge, belief, normality, and introspection
Dominik Klein, Olivier Roy and Norbert Gratzl in Synthese (2017) doi:10.1007/s11229-017-1353-8 [pdf] [doi] [bib] [abstract]

 author={Klein, Dominik and Roy, Olivier and Gratzl, Norbert},
 title={Knowledge, belief, normality, and introspection},
We study two logics of knowledge and belief stemming from the work of Stalnaker (2006), 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.

Wenn Du gehst, geh ich auch. Die Rolle von Informationskaskaden bei der Entstehung von Massenbewegungen
Dominik Klein and Johannes Marx in Politische Vierteljahresschrift 58(4) pp.560-592 [simulation] [pdf] [doi] [bib] [abstract]

 author={Klein, Dominik and Johannes Marx},
 title={Wenn Du gehst, geh ich auch. Die Rolle von Informationskaskaden
 bei der Entstehung von Massenbewegungen},
 journal={Politische Vierteljahresschrift},
This paper studies the epistemic dynamics preceding the emergence of mass movements. By means of an agent-based simulation, we study the informational processes generating those shared attitudes towards a political system that are necessary for mass movements. We show that societies of lower mobility will structurally underestimate the potential for political change. Moreover, we find systematic differences in attitudes between critics and supporters of a regime. A side-effect of the emergent informational dynamics is that system critics will, over time, develop higher estimates of the potential for change than their less discontent peers

Focusing on Campaigns
Dominik Klein and Eric Pacuit in Rohit Parikh on Logic, Language and Society, Springer (2017), pp.77-89 [pdf] [doi] [bib] [abstract]

author={Klein, Dominik and Pacuit, Eric},
editor={Ba{\c{s}}kent, Can and Moss, Lawrence S.
and Ramanujam, Ramaswamy},
title={Focusing on Campaigns},
bookTitle={Rohit Parikh on Logic, Language and Society},
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.

Metrics for Formal Structures, with an Application to Kripke Models and their Dynamics (Preprint)
Dominik Klein and Rasmus K. Rendsvig in Preprint: Arxiv:1704.00977 [pdf] [bib] [abstract]

    author = {{Klein}, Dominik. and {Rendsvig}, Rasmus K.},
    title = "{Metrics for Formal Structures, with an Application to Kripke Models
      and their Dynamics}",
    journal = {ArXiv e-prints},
    eprint = {1704.00977},
    year = 2017,
    month = apr,
This paper introduces and investigates a family of metrics on sets of structures for formal languages, with a special focus on their application to sets of pointed Kripke models and modal logic, and, in extension, to dynamic epistemic logic. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or semantic structures. We first study the topological properties of the resulting metric spaces. A key result provides sufficient conditions for spaces having the Stone property, i.e., being compact, totally disconnected and Hausdorff. Second, we turn to mappings, where it is shown that a widely used type of model transformations, product updates, give rise to continuous maps in the induced topology.

Turing Completeness of Finite Epistemic Programs (Preprint)
Dominik Klein and Rasmus K. Rendsvig in Preprint: Arxiv:1706.06845 [pdf] [bib] [abstract]

  author    = {Klein, Dominik and
               Rendsvig, Rasmus K.},
  title     = {Turing Completeness of Finite, Epistemic Programs},
  journal = {ArXiv e-prints},
  year      = {2017},
  url       = {},
  eprint    = {1706.06845},
In this note, we present the proof of Lemma 1.1 of [8], namely that the class of epistemic programs [1] is Turing complete. Following preliminary definitions in Section 1 , Section 2 states and proves the theorem.


Modelling Individual Expertise in Group Judgements
Dominik Klein and Jan Sprenger in Economics and Philosophy 31(1), pp.3-25 [pdf] [doi] [bib] [abstract]

    title={Modelling Individual Expertise in Group Judgements},
    journal={Economics and Philosophy},
    publisher={Cambridge University Press},
    author={Klein, Dominik and Sprenger, Jan},
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.

Social Interaction - a Formal Exploration
Dominik Klein, PhD Thesis Tilburg 2015 [pdf] [bib]

  title={Social Interaction -- a Formal Exploration},
  author={Klein, Dominik},
  school={TiLPS Tilburg},

Introspection, Normality and Agglomeration
Dominik Klein, Norbert Gratzl and Olivier Roy in Logic, Rationality and Interaction (LORI VI), Springer 2015, pp. 195-206 [pdf] [doi] [bib] [abstract]

 author={Klein, Dominik and Gratzl, Norbert and Roy, Olivier},
 editor={van der Hoek, Wiebe and Holliday, Wesley H. and Wang, Wen-fang},
 title={Introspection, Normality and Agglomeration},
 booktitle={Logic, Rationality, and Interaction},
This paper explores a non-normal logic of beliefs for boundedly rational agents. The logic we study stems from the epistemic-doxastic system developed by Stalnaker. In that system, if knowledge is not positively introspective then beliefs are not closed under conjunction. They are, however, required to be pairwise consistent, a requirement that has been called agglomerativity elsewhere. While bounded agglomerativity requirements, i.e., joint consistency for every n-tuple of beliefs up to a fixed n, are expressible in that logic, unbounded agglomerativity is not. We study an extension of this logic of beliefs with such an unbounded agglomerativity operator, provide a sound and complete axiomatization for it, show that it has a sequent calculus that enjoys the admissibility of cut, that it has the finite model property, and that it is decidable.

Logic and Ethics: An Integrated Model for Norms, Intentions and Actions
Alessandra Marra and Dominik Klein in Logic, Rationality and Interaction (LORI VI), Springer 2015, pp. 268-281 [pdf] [doi] [bib] [abstract]

 author={Marra, Alessandra and Klein, Dominik},
 editor={van der Hoek, Wiebe and Holliday, Wesley H. and Wang, Wen-fang},
 title={Logic and Ethics: An Integrated Model for Norms, Intentions and Actions},
 booktitle={Logic, Rationality, and Interaction},
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 agent’s 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.


Changing Types: Information Dynamics on Type Spaces
Dominik Klein and Eric Pacuit in Studia Logica, 102(2) pp. 297-319. [pdf] [doi] [bib] [abstract]

 author={Klein, Dominik and Pacuit, Eric},
 title={Changing Types: Information Dynamics for Qualitative Type Spaces},
 journal={Studia Logica},
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).

The Dynamics of Trust - Emergence and Destruction
Dominik Klein and Johannes Marx in Proceedings of the 17th International Workshop on Trust in Agent Societies pp. 68-77. [pdf] [bib] [abstract]

 author={Klein, Dominik and Marx, Johannes},
 editor={Cohen, Robin and Falcone, Rino and Norman, Timothy},
 title={The Dynamics of Trust - Emergence and Destruction},
 booktitle={Proceedings of the 17th International Workshop on Trust in Agent Societies},
We study the emergence and evolution of trust in larger societies. We focus on the thin notion of trust, that is the trust needed for interacting with hitherto unknown individuals encountered for just a single interaction. Our model builds upon well established theoretical knowledge of the determinants of trust. These works identify parameters such as the existence of networks, the level of mobility or the percent- age of trust-abusing agents in a society. While the influence of each of these factors individually is well-established by empirical work, a precise account of the interplay of these factors is lacking. To bridge this gap, we devise a multi agent computer simulation that allows a fine grained analysis of the dynamic processes governing the emergence of trust and its dependencies upon these parameters. We model agents using a bayesian learning framework about the value of trust, taking both individual and social information into account.