Lena Kurzen

Learning and teaching as a game: a sabotage approach

In formal approaches to inductive learning, the ability to learn is understood as the ability to single out a correct hypothesis from a range of possibilities. Although most of the existing research focuses on the characteristics of the learner, in many paradigms the significance of the teachers abilities and strategies is in fact undeniable. Motivated by this observation, this paper highlights the interactive nature of learning by showing its relation with games. We show how learning can be seen as a sabotage-type game between Teacher and Learner, and we present different variants based on the level of cooperativeness and the actions available to the players, characterizing the existence of winning strategies by formulas of Sabotage Modal Logic and analyzing their complexity. We also give a two-way conceptual account of how to further combine games and learning: we propose to use game theory to analyze the grammar inference approach, and moreover, we indicate that existing inductive inference games can be analyzed using learning theory tools. Our work aims at unifying game-theoretical and logical approach to formal learning theory.

Exploring the tractability border in epistemic tasks

We analyse the computational complexity of comparing informational structures. Intuitively, we study the complexity of deciding queries such as the following: Is Alice’s epistemic information strictly coarser than Bob’s? Do Alice and Bob have the same knowledge about each other’s knowledge? Is it possible to manipulate Alice in a way that she will have the same beliefs as Bob? The results show that these problems lie on both sides of the border between tractability (P) and intractability (NP-hard). In particular, we investigate the impact of assuming information structures to be partition-based (rather than arbitrary relational structures) on the complexity of various problems. We focus on the tractability of concrete epistemic tasks and not on epistemic logics describing them.

Modal Logics for Preferences and Cooperation: Expressivity and Complexity

This paper studies expressivity and complexity of normal modal logics for reasoning about cooperation and preferences. We identify a class of local and global notions relevant for reasoning about cooperation of agents that have preferences. Many of these notions correspond to game- and social choice-theoretical concepts. We specify the expressive power required to express these notions by determining whether they are invariant under certain relevant operations on different classes of Kripke models and frames. A large class of known extended modal languages is specified and we show how the chosen notions can be expressed in fragments of this class. To determine how demanding reasoning about cooperation is in terms of computational complexity, we use known complexity results for extended modal logics and obtain for each local notion an upper bound on the complexity of modal logics expressing it.

Reasoning about cooperation, actions and preferences

In this paper, a logic for reasoning about coalitional power is developed which explicitly represents agents’ preferences and the actions by which the agents can achieve certain results. A complete axiomatization is given and its satisfiability problem is shown to be decidable and EXPTIME-hard.

Getting together: a unified perspective on modal logics for coalitional interaction

Cooperation of agents is a major issue in fields such as computer science, economics and philosophy. The conditions under which coalitions are formed occur in various situations involving multiple agents.