ConArg: Argumentation with Constraints?;??;? ? ?

Abstract

ConArg [3,4]4 is a tool based on Constraint Programming that is able to model and solve di erent problems related to (Abstract) Argumentation Frameworks (AFs) [6]. For the implementation we adopted JaCoP, which is a Java library that provides the user with a Finite Domain Constraint Programming paradigm [7]. Through its graphic interface, it is possible to select the extensions (e.g., admissible) the user wants to find, and to browse the obtained solutions. Constraint Programming (CP) [7] is a powerful paradigm for solving combinatorial search problems, which exploits a wide range of techniques from artificial intelligence and operations research. The basic idea in constraint programming is that the user states the constraints and a general purpose constraint solver is used to solve them. Constraints are just relations, and a Constraint Satisfaction Problem (CSP) [7] states which relations should hold among the variables. ConArg [3,4] is able to find all Dung's classical extensions [6] (i.e., conflictfree, admissible, complete, stable, grounded and preferred extensions) by defining the properties of these extensions through constraints, and solving the related CSP. To show the feasibility of such solution, in [3,4] we test the tool on di erent randomly generated small-world networks (i.e., Barabasi and Kleinberg ones) and we report the performance of the search in time. Since the total number of these extensions may explode for large sets of arguments (particularly in case of conflict-free extensions, i.e., the less constrained ones), it is important to use techniques to tackle this inherent complexity, as CP-based ones. Moreover, ConArg can solve di erent classical hard-problems that concern weighted AFs (where attacks are associated with a “strength” value), as the ones related to weighted grounded extensions presented in [5]. For example, given a weighted argument system, a set of arguments S Args and an inconsistency budget (i.e., the tolerated sum of the considered strength values), to find if is minimal w.r.t. S represents a co-NP-complete problem [5]. ? This work was carried out during the tenure of the ERCIM “Alain Bensoussan” Fellowship Programme, which is supported by the Marie Curie Co-funding of Regional, National and International Programmes (COFUND) of the European Commission. ?? Research partially supported by MIUR PRIN 20089M932N project: “Innovative and multi-disciplinary approaches for constraint and preference reasoning”. ? ? ? AT2012, 15-16 October 2012, Dubrovnik, Croatia. Copyright held by the author(s). 4 https://sites.google.com/site/santinifrancesco/tools/ConArg.zip

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Recently ConArg has been extended to encompass and solve some other semantics, as the stage, semi-stable and ideal extensions [ 6 ]. In addition, we enhanced the tool with the implementation of the extensions developed in [ 1,2 ].

In [ 1 ] we extend the Dung AFs in order to deal with coalitions of arguments. The initial set of arguments is partitioned into subsets. Each subset represents a di erent “line of thought” and can be considered as a coalition of arguments. All the found coalitions inherit the same semantics, e.g., all the coalitions in the same partition are, for instance, admissible. Therefore, in [ 1 ] we extend Dung’s semantics from extensions to partitions of arguments, whose number, in general, can be combinatorial.

In [ 2 ] we revisit the concept of Value-based AFs [ 6 ] with the goal to unify many of the proposals into the same semiring-based framework, as long as the considered system of weights can be represented with a semiring structure. We suggest semirings as a mean to parametrically represent attack-weights of di erent Value-based AFs. For instance, a value may represent a “fuzziness”, a “cost” or a probability score for a given attack. The novel idea is to provide a common quantitative framework, where it is possible to represent and compute weighted extensions. The defined Value-based AF is mapped into a semiringbased Soft Constraint Satisfaction Problem (SCSP) [ 7 ], and then solved [ 2 ].

In the future we plan to further extend ConArg along di erent lines. For example, we would like to introduce other extensions, as the CF2 or the Prudent semantics [ 6 ]. Moreover, we want to develop ad-hoc heuristics to be used during the search, in order to improve the performance. Eventually, we want to test ConArg over large real small-world (i.e., social) networks, and to retrieve some statistical data for the di erent classical extensions (e.g., their average size).

References

1. Bistarelli , S. , Campli , P. , Santini , F. : Finding partitions of arguments with dung's properties via scsps . In: ACM Symposium on Applied Computing (SAC) . pp. 913 - 919 . ACM ( 2011 )

2. Bistarelli , S. , Santini , F. : A common computational framework for semiring-based argumentation systems . In: European Conference on Artificial Intelligence (ECAI10) ( 2010 )

3. Bistarelli , S. , Santini , F. : Conarg: A constraint-based computational framework for argumentation systems . In: 23rd International Conference on Tools with Artificial Intelligence , ICTAI 2011 . pp. 605 - 612 . IEEE ( 2011 )

4. Bistarelli , S. , Santini , F. : Modeling and solving afs with a constraint-based tool: Conarg . In: Theory and Applications of Formal Argumentation - First International Workshop, TAFA 2011. Lecture Notes in Computer Science , vol. 7132 , pp. 99 - 116 . Springer ( 2012 )

5. Dunne , P.E. , Hunter , A. , McBurney , P. , Parsons , S. , Wooldridge , M. : Weighted argument systems: Basic definitions, algorithms, and complexity results . Artif. Intell . 175 ( 2 ), 457 - 486 ( 2011 )

6. Rahwan , I. , Simari , G.R. : Argumentation in Artificial Intelligence . Springer Publishing Company, Incorporated, 1st edn. ( 2009 )

7. Rossi , F., van Beek , P. , Walsh , T. : Handbook of Constraint Programming (Foundations of Artificial Intelligence) . Elsevier Science Inc., New York, NY, USA ( 2006 )