5 research outputs found
Argumentation Frameworks as Constraint Satisfaction Problems
This paper studies how to encode the problem of computing the extensions of an argumentation framework (under a given semantics) as a constraint satisfaction problem (CSP). Such encoding is of great importance since it makes it possible to use the very efficient solvers (developed by the CSP community) for computing the extensions. We focus on three families of frameworks: Dungās abstract framework, its constrained version and preference-based argumentation frameworks
A QBF-based Formalization of Abstract Argumentation Semantics
Supported by the National Research Fund, Luxembourg (LAAMI project) and by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant ref. EP/J012084/1 (SAsSY project).Peer reviewedPostprin
Theory of Semi-Instantiation in Abstract Argumentation
We study instantiated abstract argumentation frames of the form ,
where is an abstract argumentation frame and where the arguments of
are instantiated by as well formed formulas of a well known logic,
for example as Boolean formulas or as predicate logic formulas or as modal
logic formulas. We use the method of conceptual analysis to derive the
properties of our proposed system. We seek to define the notion of complete
extensions for such systems and provide algorithms for finding such extensions.
We further develop a theory of instantiation in the abstract, using the
framework of Boolean attack formations and of conjunctive and disjunctive
attacks. We discuss applications and compare critically with the existing
related literature
Argumentation frameworks as Constraint Satisfaction Problems
International audienceArgumentation is a promising approach for defeasible reasoning. It consists of justifying each plausible conclusion by arguments. Since the available information may be inconsistent, a conclusion and its negation may both be justified. The arguments are thus said to be conflicting. The main issue is how to evaluate the arguments. Several semantics were proposed for that purpose. The most important ones are: stable, preferred, complete, grounded and admissible. A semantics is a set of criteria that should be satisfied by a set of arguments, called extension, in order to be acceptable. Different decision problems related to these semantics were defined (like whether an argumentation framework has a stable extension). It was also shown that most of these problems are intractable. Consequently, developing algorithms for these problems is not trivial and thus the implementation of argumentation systems not obvious. Recently, some solutions to this problem were found. The idea is to use a reduction method where a given problem is translated in another one like SAT or ASP. This paper follows this line of research. It studies how to encode the problem of computing the extensions of an argumentation framework (under each of the previous semantics) as a constraint satisfaction problem (CSP). Such encoding is of great importance since it makes it possible to use the very efficient solvers (developed by the CSP community) for computing the extensions. Our encodings take advantage of existing reductions to SAT problems in the case of Dungās abstract framework. Among the various ways of translating a SAT problem into a CSP one, we propose the most appropriate one in the argumentation context. We also provide encodings in case two other families of argumentation frameworks: the constrained version of Dungās abstract framework and preference-based argumentation framework