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Unformatted text preview: An Algorithm for Stage Semantics Martin CAMINADA a a University of Luxembourg Abstract. In the current paper, we re-examine the concept of stage semantics, which is one of the oldest semantics for abstract argumentation. Using a formal treatment of its properties, we explain how the intuition behind stage semantics dif- fers from the intuition behind the admissibility based semantics that most scholars in argumentation theory are familiar with. We then provide a labelling-based algo- rithm for computing all stage extensions, based on earlier algorithms for computing all preferred, stable and semi-stable extensions. 1. Introduction The concept of stage semantics for abstract argumentation was first introduced by Verheij  and has subsequently been worked out in Verheij’s DEFLOG system [16,17], which can be regarded as a generalization of the abstract argumentation theory of Dung . Although stage semantics is one of the oldest semantics for abstract argumentation, it has so far remained relatively unknown, which might have to do with the fact that it was originally stated not in terms of the usual extensions approach, but in the form of pairs ( J,D ) where J is a set of justified arguments and D is a set of defeated arguments . Nevertheless, there exist good reasons for treating stage semantics as one of the main- stream semantics for abstract argumentation, not only because it can be expressed using a relatively simple and elegant principle, but also because it implements a fundamentally different intuition than the traditional admissibility based semantics (such as complete, grounded and preferred , ideal  or semi-stable [15,5]). Despite of the differences between stage semantics and the traditional admissibility- based semantics, it is still possible to provide an algorithm for computing all stage ex- tensions, that is very close to previously stated algorithms for computing all preferred, stable and semi-stable extensions [6,14], as is demonstrated in the current paper. 2. Stage Semantics In Verheij’s original work  stage semantics was defined in terms of pairs of sets of arguments. In the current paper, however, we will describe stage semantics in terms of the more commonly applied extensions approach. We assume familiarity with ba- sic argumentation concepts, such as that of an argumentation framework, conflict-free sets, admissible sets, complete extensions, preferred extensions, stable extensions and the grounded extension. Definitions of these can be found in . In the current paper, we only consider finite argumentation frameworks. If A is an argument then we write A + for the set of arguments attacked by A . Simi- larly, if A rgs is a set of arguments then we write A rgs + to refer to the set of arguments attacked by at least one argument in A rgs ....
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This note was uploaded on 10/23/2011 for the course ENCS ENCS5 taught by Professor Abdelsalam during the Spring '10 term at Birzeit University.
- Spring '10