%0 Journal Article %1 Baumann2019-xu %A Baumann, Ringo %A Brewka, Gerhard %D 2019 %I Association for the Advancement of Artificial Intelligence (AAAI) %J Proc. Conf. AAAI Artif. Intell. %K %N 01 %P 2670--2677 %T Extension removal in abstract argumentation -- an axiomatic approach %V 33 %X 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.

@article{Baumann2019-xu, abstract = {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.}, added-at = {2024-09-10T11:56:37.000+0200}, author = {Baumann, Ringo and Brewka, Gerhard}, biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/2c6c8029f4064b9dacd09d654360e7082/scadsfct}, interhash = {efa6d129d6f7defaecf73a9e050a6b3c}, intrahash = {c6c8029f4064b9dacd09d654360e7082}, journal = {Proc. Conf. AAAI Artif. Intell.}, keywords = {}, month = jul, number = 01, pages = {2670--2677}, publisher = {Association for the Advancement of Artificial Intelligence (AAAI)}, timestamp = {2024-09-10T15:15:57.000+0200}, title = {Extension removal in abstract argumentation -- an axiomatic approach}, volume = 33, year = 2019 }