Extension Removal in Abstract Argumentation – An Axiomatic Approach


  • Ringo Baumann University of Leipzig
  • Gerhard Brewka University of Leipzig




This paper continues the rather recent line of research on the dynamics of non-monotonic formalisms. In particular, we consider semantic changes in Dung’s abstract argumentation formalism. One of the most studied problems in this context is the so-called enforcing problem which is concerned with manipulating argumentation frameworks (AFs) such that a certain desired set of arguments becomes an extension. Here we study the inverse problem, namely the extension removal problem: is it possible – and if so how – to modify a given argumentation framework in such a way that certain undesired extensions are no longer generated? Analogously to the well known AGM paradigm we develop an axiomatic approach to the removal problem, i.e. a certain set of axioms will determine suitable manipulations. Although contraction (that is, the elimination of a particular belief) is conceptually quite different from extension removal, there are surprisingly deep connections between the two: it turns out that postulates for removal can be directly obtained as reformulations of the AGM contraction postulates. We prove a series of formal results including conditional and unconditional existence and semantical uniqueness of removal operators as well as various impossibility results – and show possible ways out.




How to Cite

Baumann, R., & Brewka, G. (2019). Extension Removal in Abstract Argumentation – An Axiomatic Approach. Proceedings of the AAAI Conference on Artificial Intelligence, 33(01), 2670-2677. https://doi.org/10.1609/aaai.v33i01.33012670



AAAI Technical Track: Knowledge Representation and Reasoning