Dung's work "On the Acceptability of Arguments and its Fundamental Role in Non-monotonic Reasoning, Logic Programming and N-persons games" (Artificial Intelligence, 1995) has provided argumentation theory with the necessary mathematical abstractions for it to reach scientific maturity, and become an independent research area within the field of non-monotonic reasoning. However, while Dung's formal semantics have soon become part of the basic techniques of argumentation theorists, his argument-based analysis of N-persons games and logic programming has received considerably less attention.

The symposium brings together leading researchers working at the interface of the three disciplines of game theory, logic and argumentation, in order to foster the interaction between these research fields along the lines already presented in Dung's seminal work. A report of the symposium (to appear on The Reasoner) can be found here below:




"The GALP symposium held by the Individual and Collective Reasoning Group (ICS) of the University of Luxembourg on 23th-24th April 2009 has brought together, for two days, a number of distinguished researchers who are contributing and have contributed to interdisciplinary research at the interface of the disciplines of games, argumentation and logic (with particular focus on logic programming). The aim of the symposium was to foster the interaction between the aforementioned research areas along the lines already present in the seminal contribution of Dung ("On the Acceptability of Arguments and Its Fundamental Role in Non-Monotonic Reasoning,  Logic Programming, and N-Persons Games", Artificial Intelligence 1995). While this contribution has laid the foundations of argumentation theory as a mathematical discipline, sparkling a rich and lively research area within Artificial Intelligence, its interaction with Game Theory and Logic Programming has been relatively neglected. The symposium has filled this gap by highlighting a number of recent scientific developments as well as stimulating future research directions.

The talks presented can be grouped according to four focus points: talks concerning argumentation theory in general; and talks focusing on the three overlapping areas of games and logic (programming), games and argumentation, argumentation and logic.

Argumentation. Dr. Martin Caminada (University of Luxembourg) has provided a thorough introduction to argumentation theory presenting novel results concerning, in particular, algorithmic aspects of argumentation theory and dialogue games. The implementation of the algorithms introduced by Dr. Caminada has then been presented in a comprehensive demo by Patrizio Barbini (Universities of Turin and Luxembourg) and Yining Wu (University of Luxembourg). Finally, Prof. Gerhard Brewka (University of Leipzig) has proposed a multi-agent framework for argumentation generalizing Dung's setting to cover the interaction of different argumentative contexts.

Games and Logic. The contribution of Prof. Juergen Dix (Technical University of Clausthal) concerned the use of logic as a formal language for talking about games. It illustrated a number of systematic extensions of ATL---focusing in particular on their complexity---able to capture several game-theoretic concepts, from the typical "power-view" of games based on effectivity functions, to the full-fledged characterization of equilibrium concepts such as the Nash equilibrium. Along a similar line, Dr. Marina de Vos (University of Bath) has shown how Answer Set Programming can be successively used to encode games and, consequently, compute their Nash equilibria. Then, somehow closing the circle, she has shown how the solutions of answer set programs can be seen as the product of playing winning strategies in appropriately designed logic games.

Argumentation and Games.  This was definitely the richest section in the symposium. Its talks focused on two main aspects: 1) the game-theoretic proof theory of argumentation based on the so-called dialogue or discussion games; 2) the application of argumentation theory to strategic situations in rational interaction, such as dispute resolution.
In the first group, Dr. Sanjay Modgil (King's College London) has introduced dialogue games for an extension of argumentation frameworks incorporating, besides the standard attack relation between arguments, an attack relation from arguments to attack relations. Prof. Henry Prakken (Universities of Utrecht and Groningen) emphasized the procedural and goal-driven aspects of dialogue games, besides their logical and argumentation-theoretic nature, which still await a full-fledged formal analysis.
As to the second group, Serena Villata has proposed an argumentation-theoretic approach to study the dynamics of coalition-formation in multi-agent systems. Finally, professor P. M. Dung (Asian Institute of Technology) has introduced a novel argumentation-theoretic perspective to dispute resolution based on a form of mechanism design for dialogue games. According to this perspective dialogue games are viewed as procedures for dispute resolution where all arguments defensible via the procedure are also admissible (soundness) and, vice versa, all admissible arguments are defensible via the procedure (completeness).

Argumentation and Logic.  The symposium hosted two talks which bridged argumentation theory with modal logic. The first one, by Prof. Dov Gabbay (King's College London) applied Provability Logic to characterize the content of an argumentation framework as a modal formula whose models naturally correspond to the possible complete extensions of the framework. The second one, by Dr. Davide Grossi (University of Amsterdam) has systematically investigated the simple idea of viewing Dung's argumentation frameworks as Kripke models. The talk has shown how such perspective opens up the possibility of importing techniques (e.g., calculi, evaluation games) and results (e.g., complexity of model-checking) from modal logic to argumentation theory.

All in all, the symposium has beautifully shown how rich the overlaps are between game theory, argumentation theory and logic, and how promising future research lines can be in further investigating such overlaps. For the abstract of the talks, as well as the slides, see the program page."

Davide Grossi
Institute of Logic, Language and Computation
University of Amsterdam