ICR
International Symposium on

Games,
Argumentation,
and Logic Programming

Luxembourg, 23-24 April 2009

Luxembourg, 23-24 April 2009

Galp |
Venue & Info | Program | Registration | Organization |

Wednesday 22nd
April

(Tourist Office, Place Guillaume II)

17:00 - 19:00

Walking tour of the city of Luxembourg

Thursday 23th April

(Salle de Conseille, Campus Kirchberg)

09:30 - 09:45

Coffee and Welcome

09:45 - 10:45

Prof. J. Dix (Technical University of Clausthal, Germany)

Extensions of ATL

10:45 - 11:15

[coffee break]

11:15 - 12:15

Dr. M. de Vos (University of Bath, UK)

From Games to Logic Programs and Back to Games

12:15 - 14:00

[lunch]

14:00 - 15:15

Dr. M. Caminada (University of Luxembourg)

Argument labellings, Games and Algorithms

15:15 - 15:30

Partizio Barbini and Yining Wu (University of Turin and University of Luxembourg)

An Implementation of Argumentation Games

15:30 - 16:00

[coffee break]

16:00 - 16:30

Serena Villata (University of Turin)

Analyzing coalitions in iterative social network design using

argumentation theory

16:30 - 16:45

[coffee break]

16:45 - 17:45

Prof. D. Gabbay (King's College London, UK)

Modal Provability Foundations for Argumentation Networks

17:45 - 18:30

[social drink]

09:30 - 09:45

Coffee

09:45 - 10:45

Dr. D. Grossi (ILLC, University of Amsterdam, The Netherlands)

Doing Argumentation Theory in Modal Logic

10:45 - 11:15

[coffee break]

11:15 - 12:15

Dr. S. Modgil (King's College London, UK)

Games for Extensions of Abstract Argumentation Frameworks

12:15 - 14:00

[lunch]

14:00 - 15:00

Prof. G. Brewka (University of Leipzig, Germany)

A Framework for Abstract Context Argumentation Systems

15:00 - 15:15

[coffee break]

15:15 - 16:15

Prof. H. Prakken (Universities of Utrecht and Groningen, The Netherlands)

Argumentation without Arguments

16:15 - 16:45

[coffee break]

16:45 - 17:45

Prof. P. M. Dung (Asian Institute of Technology, Thailand)

Argumentation, Dispute Resolution and Logic Programming: A Proof Procedure Perspective

17:45 - 18:30

[social drink]

List of talks and abstracts:

A Framework for Abstract Context Argumentation Systems

G. Brewka, University of Leipzig

We present a modular framework for distributed abstract argumentation where the argumentation context, that is information about preferences among arguments, values, validity, reasoning mode (skeptical vs. credulous) and even the chosen semantics can be explicitly represented. The framework generalizes earlier work by Modgil on meta-argumentation. A collection of abstract argument systems is connected via mediators. Each mediator integrates information coming from connected argument systems (thereby handling conflicts within this information) and determines the context used in a particular argumentation module. The framework can be used in different directions; e.g., for hierarchic argumentation as typically found in legal reasoning, or to model group argumentation processes.

This is joint work with Thomas Eiter.

An Implementation of Argumentation Games

Patrizio Barbini and Yining Wu, University of Turin and University of Luxembourg

We present a software demonstrator that, given an argumentation framework, provides the grounded, preferred, stable and semi-stable extensions. Moreover, it also allows the user to query the status of a particular argument, and is able to explain and defend its answer by entering into a discussion with the user.

Argument labellings, Games and Algorithms

Martin Caminada, University of Luxembourg

Argument labellings provide an alternative and often more flexible way of describing argumentation semantics than the traditional approach of identifying extensions. The idea is that one distinguishes not only the arguments that are accepted, but also the arguments that are rejected and the arguments that one abstains from having an explicit opinion about. It turns out that traditional concepts like grounded and preferred semantics can be expressed in quite an intuitive way, without the need for fixpoints. Moreover, the modular way in which argument labellings are defined makes them suitable for a wide range of tasks, varying from defining argumentation games, algorithms and judgement aggregation procedures.

The current presentation serves as a general introduction to formal argumentation and will also be attended by students from the University of Luxembourg.

SLIDES1 SLIDES2

Extensions of ATL

J. Dix, Technical University of Clausthal

Alternating-time temporal logic (ATL) is an interesting logic that allows to talk about what coalitions of agents can achieve. We extend ATL in two ways: (1) ATLP, which allows to express various rationality assumptions of intelligent agents and (2) ATL^c, which allows to model the actual computation of a coalition of agents.

While ATLP can be seen as an extension to formalize several game theoretical solution concepts, ATL^c is an extension by incorporating techniques from argumentation theory.

We also consider the complexity of model checking in these extensions.

SLIDES

Argumentation, Dispute Resolution and Logic Programming: A Proof Procedure Perspective

P. M. Dung, Asian Institute of Technology

A dispute resolution procedure could be viewed as a multiagent procedure for agents to exchange their arguments. In the simplest case, it models the process in which a proponent tries to defend its arguments against attacks from an opponent. Two key desiderata for these procedures are their soundness and completeness where soundness refers to the admissibility of the winning arguments while completeness ensures that admissible arguments are also defensible wrt the procedures. These notions of soundness and completeness are closely related to the notions of sound and complete proof procedures in formal logic.

We discuss in this paper a new methodology for designing sound and complete dispute resolutions at different levels of abstraction. Starting at the level of abstract argumentation, generic parameterized classes of procedures capturing well-known procedures in the literature are developed. A key insight is that the soundness of such dispute resolution procedures depends on the choices available to the opponents while their completeness depends on the available arguments of the proponents. This insight offers a modular methodology for designing dispute procedures: The design of opponent moves determines the soundness while the design of proponent moves determines the completeness. We then present an automatic methodology for translating procedures in abstract argumentation into logical ones for defeasible systems like logic programming or assumption-based argumentation.

SLIDES

Modal Provability Foundations for Argumentation Networks

D. Gabbay, King's College London

Given an argumentation network we associate with it a modal formula representing the ‘logical content’ of the network. We show a one-to-one correspondence between all possible complete Caminada labellings of the network ( labelling arguments with 0,1 and ? ) and all possible models of the formula. Our modal logic approach is more powerful than the Caminada labeling. We can tell in more detail why a node gets value "?". We can also characterize logically all grounded extensions.

Doing Argumentation Theory in Modal Logic

D. Grossi, ILLC University of Amsterdam

We present a formalization of some fragments of abstract argumentation theory in modal logic. We show how a number of key notions in argumentation theory can obtain a natural formulation within appropriate modal languages. We start off by discussing modal formulae capturing several notions of extensions (complete, stable, grounded). This opens up the possibility to directly import results and techniques from modal logic to argumentation theory. As examples of such application we will study argumentation labellings as Kripke models, and we will present proof procedures based on semantic games (model-checking and model-construction games). Also, by resorting to the notion of bisimulation, we will address the question of when two argumentation systems can be considered to be "the same" from an argumentation theoretic standpoint.

SLIDES

Games for Extensions of Abstract Argumentation Frameworks

S. Modgil, King's College London

Dung’s abstract argumentation theory has recently been extended to accommodate arguments that attack attacks as well as arguments. In this way one can encode argumentation-based reasoning about possibly conflicting preferences between arguments; an argument attacking an attack from A to B is an argument claiming a preference for B over A. The extended theory provides a unifying framework for preference and value-based argumentation augmented to accommodate argumentation over preferences, values and value orderings. The extended theory has also been proposed as an argumentation semantics for non-monotonic logics that formalise defeasible reasoning about priorities, and as an argumentation semantics for flexible, adaptive agent defeasible reasoning. In this talk I will review the extended theory and then present argument game proof theories for evaluating the justified status of arguments in an extended framework. In these games, players not only attack their counterpart’s arguments, but also their counterpart’s attacks. The games will be illustrated with examples of argumentation over conflicting beliefs and goals.

Argumentation without Arguments

H. Prakken, University of Utrecht and University of Groningen

A well-known ambiguity in the term 'argument' is that of argument as an inferential structure and argument as a kind of dialogue. In the first sense, arguments have been studied as a way to conceptualise defeasible inference. The formal systems resulting from this research are a branch of nonmonotonic logic. In the second sense, arguments have been studied as a form of agent interaction, in which human or artificial agents aim to resolve a conflict of opinion. The formal systems resulting from this approach are part of dialogue theory.

Usually, systems for argumentation dialogues presuppose an argument-based logic. However, in this talk argumentation dialogues will be discussed without presupposing arguments as inferential structures. The motivation for this is that there are forms of inference that are not most naturally

cast in the form of arguments (e.g. abduction, statistical reasoning or coherence-based reasoning) but that can still be the subject of argumentative dialogue. Some recent formal work will be discussed which embeds non-argumentative inference in an argumentative dialogue system, and some general observations will be drawn from this discussion.

Analyzing coalitions in iterative social network design using argumentation theory

Serena Villata, University of Turin

We present a model for iterative design introducing four viewpoints, the refinement relations between them, and the analysis methods we use to analyze cooperation based on emerging coalitions. At the most abstract level, which we call the coalition view, coalitions are abstract entities that may dominate or attack other coalitions. During iterative design these abstract entities are refined with agents and their dependencies constituting the coalitions (dependence view), the powers of sets of agents to see to goals (power view) and finally the beliefs, plans, tasks and goals of agents (agent view). We adapt existing coalition argumentation theory to reason about the coalitions defined in the coalition view. We introduce the coalition argument, the stability argument preferring a coalition over the others and the attack relations between them.

Our theory of argumentation is based on the following three steps:

1. Extend the set of arguments with auxiliary arguments;

2. Calculate the extensions of the extended theory using one of Dung's semantics;

3. For each extension of the extended theory, filter out the auxiliary arguments;

the resulting sets of arguments are the extensions of the theory.

This argumentation theory allows to model the attacks among potential coalitions and to decide if a coalition is really formed thanks to an higher order attack of the stability argument.This is joint work with Guido Boella and Leon van der Torre.

SLIDES

From Games to Logic Programs and Back to Games

M. de Vos, University of Bath

Answer set programming (ASP) provides an intuitive and powerful programming paradigm for

declarative problem solving and knowledge representation. Problems are represented as AnsProlog programs, logic programs under the answer set semantics, such that the answer sets corresponds to the solutions of the modelled problem.

In the first part of this presentation, we discuss how strategic games and extensive games can be modelled using ASP in such a way that their equilibria match the answer sets of the programs that model these games. To model player's reasoning we extend our model to logic programming agent systems, where each agent embodies the reasoning of a game player, such that the equilibria of the game correspond with the semantics agreed upon by the agents.

Denotational semantics for programming languages provide mathematical tools for analysing the programs. In the second part of this presentation we present a new denotational semantics for answer set programs using an interaction model based on logic games. For our games, we are using arenas, which have a very general and versatile interaction structure. We show that this model is correct in that a winning strategy of the game denotes an execution of the program, and that it is sound with respect to the answer set semantics.

SLIDES

This symposium is held under the auspices of:

(Tourist Office, Place Guillaume II)

17:00 - 19:00

Walking tour of the city of Luxembourg

Thursday 23th April

(Salle de Conseille, Campus Kirchberg)

09:30 - 09:45

Coffee and Welcome

09:45 - 10:45

Prof. J. Dix (Technical University of Clausthal, Germany)

Extensions of ATL

10:45 - 11:15

[coffee break]

11:15 - 12:15

Dr. M. de Vos (University of Bath, UK)

From Games to Logic Programs and Back to Games

12:15 - 14:00

[lunch]

14:00 - 15:15

Dr. M. Caminada (University of Luxembourg)

Argument labellings, Games and Algorithms

15:15 - 15:30

Partizio Barbini and Yining Wu (University of Turin and University of Luxembourg)

An Implementation of Argumentation Games

15:30 - 16:00

[coffee break]

16:00 - 16:30

Serena Villata (University of Turin)

Analyzing coalitions in iterative social network design using

argumentation theory

16:30 - 16:45

[coffee break]

16:45 - 17:45

Prof. D. Gabbay (King's College London, UK)

Modal Provability Foundations for Argumentation Networks

17:45 - 18:30

[social drink]

Friday 24th April

(Salle Paul Feidert, Campus Kirchberg)

(Salle Paul Feidert, Campus Kirchberg)

09:30 - 09:45

Coffee

09:45 - 10:45

Dr. D. Grossi (ILLC, University of Amsterdam, The Netherlands)

Doing Argumentation Theory in Modal Logic

10:45 - 11:15

[coffee break]

11:15 - 12:15

Dr. S. Modgil (King's College London, UK)

Games for Extensions of Abstract Argumentation Frameworks

12:15 - 14:00

[lunch]

14:00 - 15:00

Prof. G. Brewka (University of Leipzig, Germany)

A Framework for Abstract Context Argumentation Systems

15:00 - 15:15

[coffee break]

15:15 - 16:15

Prof. H. Prakken (Universities of Utrecht and Groningen, The Netherlands)

Argumentation without Arguments

16:15 - 16:45

[coffee break]

16:45 - 17:45

Prof. P. M. Dung (Asian Institute of Technology, Thailand)

Argumentation, Dispute Resolution and Logic Programming: A Proof Procedure Perspective

17:45 - 18:30

[social drink]

List of talks and abstracts:

A Framework for Abstract Context Argumentation Systems

G. Brewka, University of Leipzig

We present a modular framework for distributed abstract argumentation where the argumentation context, that is information about preferences among arguments, values, validity, reasoning mode (skeptical vs. credulous) and even the chosen semantics can be explicitly represented. The framework generalizes earlier work by Modgil on meta-argumentation. A collection of abstract argument systems is connected via mediators. Each mediator integrates information coming from connected argument systems (thereby handling conflicts within this information) and determines the context used in a particular argumentation module. The framework can be used in different directions; e.g., for hierarchic argumentation as typically found in legal reasoning, or to model group argumentation processes.

This is joint work with Thomas Eiter.

An Implementation of Argumentation Games

Patrizio Barbini and Yining Wu, University of Turin and University of Luxembourg

We present a software demonstrator that, given an argumentation framework, provides the grounded, preferred, stable and semi-stable extensions. Moreover, it also allows the user to query the status of a particular argument, and is able to explain and defend its answer by entering into a discussion with the user.

Argument labellings, Games and Algorithms

Martin Caminada, University of Luxembourg

Argument labellings provide an alternative and often more flexible way of describing argumentation semantics than the traditional approach of identifying extensions. The idea is that one distinguishes not only the arguments that are accepted, but also the arguments that are rejected and the arguments that one abstains from having an explicit opinion about. It turns out that traditional concepts like grounded and preferred semantics can be expressed in quite an intuitive way, without the need for fixpoints. Moreover, the modular way in which argument labellings are defined makes them suitable for a wide range of tasks, varying from defining argumentation games, algorithms and judgement aggregation procedures.

The current presentation serves as a general introduction to formal argumentation and will also be attended by students from the University of Luxembourg.

SLIDES1 SLIDES2

Extensions of ATL

J. Dix, Technical University of Clausthal

Alternating-time temporal logic (ATL) is an interesting logic that allows to talk about what coalitions of agents can achieve. We extend ATL in two ways: (1) ATLP, which allows to express various rationality assumptions of intelligent agents and (2) ATL^c, which allows to model the actual computation of a coalition of agents.

While ATLP can be seen as an extension to formalize several game theoretical solution concepts, ATL^c is an extension by incorporating techniques from argumentation theory.

We also consider the complexity of model checking in these extensions.

SLIDES

Argumentation, Dispute Resolution and Logic Programming: A Proof Procedure Perspective

P. M. Dung, Asian Institute of Technology

A dispute resolution procedure could be viewed as a multiagent procedure for agents to exchange their arguments. In the simplest case, it models the process in which a proponent tries to defend its arguments against attacks from an opponent. Two key desiderata for these procedures are their soundness and completeness where soundness refers to the admissibility of the winning arguments while completeness ensures that admissible arguments are also defensible wrt the procedures. These notions of soundness and completeness are closely related to the notions of sound and complete proof procedures in formal logic.

We discuss in this paper a new methodology for designing sound and complete dispute resolutions at different levels of abstraction. Starting at the level of abstract argumentation, generic parameterized classes of procedures capturing well-known procedures in the literature are developed. A key insight is that the soundness of such dispute resolution procedures depends on the choices available to the opponents while their completeness depends on the available arguments of the proponents. This insight offers a modular methodology for designing dispute procedures: The design of opponent moves determines the soundness while the design of proponent moves determines the completeness. We then present an automatic methodology for translating procedures in abstract argumentation into logical ones for defeasible systems like logic programming or assumption-based argumentation.

SLIDES

Modal Provability Foundations for Argumentation Networks

D. Gabbay, King's College London

Given an argumentation network we associate with it a modal formula representing the ‘logical content’ of the network. We show a one-to-one correspondence between all possible complete Caminada labellings of the network ( labelling arguments with 0,1 and ? ) and all possible models of the formula. Our modal logic approach is more powerful than the Caminada labeling. We can tell in more detail why a node gets value "?". We can also characterize logically all grounded extensions.

Doing Argumentation Theory in Modal Logic

D. Grossi, ILLC University of Amsterdam

We present a formalization of some fragments of abstract argumentation theory in modal logic. We show how a number of key notions in argumentation theory can obtain a natural formulation within appropriate modal languages. We start off by discussing modal formulae capturing several notions of extensions (complete, stable, grounded). This opens up the possibility to directly import results and techniques from modal logic to argumentation theory. As examples of such application we will study argumentation labellings as Kripke models, and we will present proof procedures based on semantic games (model-checking and model-construction games). Also, by resorting to the notion of bisimulation, we will address the question of when two argumentation systems can be considered to be "the same" from an argumentation theoretic standpoint.

SLIDES

Games for Extensions of Abstract Argumentation Frameworks

S. Modgil, King's College London

Dung’s abstract argumentation theory has recently been extended to accommodate arguments that attack attacks as well as arguments. In this way one can encode argumentation-based reasoning about possibly conflicting preferences between arguments; an argument attacking an attack from A to B is an argument claiming a preference for B over A. The extended theory provides a unifying framework for preference and value-based argumentation augmented to accommodate argumentation over preferences, values and value orderings. The extended theory has also been proposed as an argumentation semantics for non-monotonic logics that formalise defeasible reasoning about priorities, and as an argumentation semantics for flexible, adaptive agent defeasible reasoning. In this talk I will review the extended theory and then present argument game proof theories for evaluating the justified status of arguments in an extended framework. In these games, players not only attack their counterpart’s arguments, but also their counterpart’s attacks. The games will be illustrated with examples of argumentation over conflicting beliefs and goals.

Argumentation without Arguments

H. Prakken, University of Utrecht and University of Groningen

A well-known ambiguity in the term 'argument' is that of argument as an inferential structure and argument as a kind of dialogue. In the first sense, arguments have been studied as a way to conceptualise defeasible inference. The formal systems resulting from this research are a branch of nonmonotonic logic. In the second sense, arguments have been studied as a form of agent interaction, in which human or artificial agents aim to resolve a conflict of opinion. The formal systems resulting from this approach are part of dialogue theory.

Usually, systems for argumentation dialogues presuppose an argument-based logic. However, in this talk argumentation dialogues will be discussed without presupposing arguments as inferential structures. The motivation for this is that there are forms of inference that are not most naturally

cast in the form of arguments (e.g. abduction, statistical reasoning or coherence-based reasoning) but that can still be the subject of argumentative dialogue. Some recent formal work will be discussed which embeds non-argumentative inference in an argumentative dialogue system, and some general observations will be drawn from this discussion.

Analyzing coalitions in iterative social network design using argumentation theory

Serena Villata, University of Turin

We present a model for iterative design introducing four viewpoints, the refinement relations between them, and the analysis methods we use to analyze cooperation based on emerging coalitions. At the most abstract level, which we call the coalition view, coalitions are abstract entities that may dominate or attack other coalitions. During iterative design these abstract entities are refined with agents and their dependencies constituting the coalitions (dependence view), the powers of sets of agents to see to goals (power view) and finally the beliefs, plans, tasks and goals of agents (agent view). We adapt existing coalition argumentation theory to reason about the coalitions defined in the coalition view. We introduce the coalition argument, the stability argument preferring a coalition over the others and the attack relations between them.

Our theory of argumentation is based on the following three steps:

1. Extend the set of arguments with auxiliary arguments;

2. Calculate the extensions of the extended theory using one of Dung's semantics;

3. For each extension of the extended theory, filter out the auxiliary arguments;

the resulting sets of arguments are the extensions of the theory.

This argumentation theory allows to model the attacks among potential coalitions and to decide if a coalition is really formed thanks to an higher order attack of the stability argument.This is joint work with Guido Boella and Leon van der Torre.

SLIDES

From Games to Logic Programs and Back to Games

M. de Vos, University of Bath

Answer set programming (ASP) provides an intuitive and powerful programming paradigm for

declarative problem solving and knowledge representation. Problems are represented as AnsProlog programs, logic programs under the answer set semantics, such that the answer sets corresponds to the solutions of the modelled problem.

In the first part of this presentation, we discuss how strategic games and extensive games can be modelled using ASP in such a way that their equilibria match the answer sets of the programs that model these games. To model player's reasoning we extend our model to logic programming agent systems, where each agent embodies the reasoning of a game player, such that the equilibria of the game correspond with the semantics agreed upon by the agents.

Denotational semantics for programming languages provide mathematical tools for analysing the programs. In the second part of this presentation we present a new denotational semantics for answer set programs using an interaction model based on logic games. For our games, we are using arenas, which have a very general and versatile interaction structure. We show that this model is correct in that a winning strategy of the game denotes an execution of the program, and that it is sound with respect to the answer set semantics.

SLIDES

This symposium is held under the auspices of:

(ICR)
Individual and Collective Reasoning Group University of Luxembourg |

Benelux Association for Artificial Intelligence |