Chapter

Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation

Volume 9060 of the series Lecture Notes in Computer Science pp 281-295

Infinite Argumentation Frameworks

On the Existence and Uniqueness of Extensions
  • Ringo BaumannAffiliated withComputer Science Institute, Leipzig University
  • , Christof SpanringAffiliated withDepartment of Computer Science, University of LiverpoolInstitute of Information Systems, Vienna University of Technology

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Abstract

Abstract properties satisfied for finite structures do not necessarily carry over to infinite structures. Two of the most basic properties are existence and uniqueness of something. In this work we study these properties for acceptable sets of arguments, so-called extensions, in the field of abstract argumentation. We review already known results, present new proofs or explain sketchy old ones in more detail. We also contribute new results and introduce as well as study the question of existence-(in)dependence between argumentation semantics.