### Abstract

In an abstract argumentation framework, there are often multiple plausible ways to evaluate (or label) the status of each argument as accepted, rejected, or undecided. But often there exists a critical set of arguments whose status is sufficient to determine uniquely the status of every other argument. Once an agent has decided its position on a critical set of arguments, then essentially the entire framework has been evaluated. Likewise, once a group, e.g. a jury,

agrees on the status of a critical set of arguments, all of their different views over all other arguments are resolved. Thus, critical sets of arguments are important both for efficient evaluation by individual agents and for collective agreement by groups of such. To exploit this idea in practice, however, a number of computational questions must be considered. In particular, how much computational effort is needed to verify that a set is, indeed, a critical set or a minimal critical set. In this paper we determine exact bounds on the computational complexity of these and related questions. In addition

we provide similar analyses of issues: a concept closely related to critical set and derived in terms of (equivalence) classes of arguments related through "common" labelling behaviours.

agrees on the status of a critical set of arguments, all of their different views over all other arguments are resolved. Thus, critical sets of arguments are important both for efficient evaluation by individual agents and for collective agreement by groups of such. To exploit this idea in practice, however, a number of computational questions must be considered. In particular, how much computational effort is needed to verify that a set is, indeed, a critical set or a minimal critical set. In this paper we determine exact bounds on the computational complexity of these and related questions. In addition

we provide similar analyses of issues: a concept closely related to critical set and derived in terms of (equivalence) classes of arguments related through "common" labelling behaviours.

Original language | English |
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Title of host publication | Computational Models of Argument |

Subtitle of host publication | Proceedings of COMMA 2014 |

Editors | Simon Parsons, Nir Oren, Chris Reed, Frederico Cerutti |

Place of Publication | Amsterdam |

Publisher | IOS Press |

Pages | 173-184 |

Number of pages | 11 |

Volume | 266 |

ISBN (Electronic) | 9781614994367 |

ISBN (Print) | 9781614994350 |

DOIs | |

Publication status | Published - 2014 |

### Keywords

- argumentation frameworks
- labelling schemes
- computational complexity

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## Cite this

Booth, R., Caminada, M., Dunne, P., Podlaszewski, M., & Rahwan, I. (2014). Complexity Properties of Critical Sets of Arguments. In S. Parsons, N. Oren, C. Reed, & F. Cerutti (Eds.),

*Computational Models of Argument: Proceedings of COMMA 2014*(Vol. 266, pp. 173-184). IOS Press. https://doi.org/10.3233/978-1-61499-436-7-173