Set- and Graph-theoretic Investigations in Abstract Argumentation



Spanring, C
(2017) Set- and Graph-theoretic Investigations in Abstract Argumentation. PhD thesis, University of Liverpool.

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Abstract

Abstract argumentation roots to similar parts in philosophy, linguistics and artificial intelligence. The core (syntactic) notions of argument and attack are commonly visualized via digraphs, as nodes and directed edges, respectively. Semantic evaluation functions then provide a meaning of acceptance (i.e. acceptable sets of arguments also called extensions) for any such abstract argumentation structure. In this thesis, for the very first time, we tackle the questions of acceptance and conflict from a graph- and set-theoretic point of view. We elaborate on the interspace between syntactic conflict/independence (defined by attack structure) and their semantic counterparts (defined by joint acceptance of arguments). Graph theory regards the filters and techniques we use to, respectively, categorize and describe abstract argumentation structures. Set theory regards the issues we have to deal with particularly for non-finite argument sets. For argumentation in the arbitrarily infinite case this thesis can and should be seen as reference work. For the matter of conflicts in abstract argumentation we further provide a solid base and formal framework for future research. All in all, this is a mathematicians view on abstract argumentation, deepening the field of conception and widening the angle of applicability.

Item Type: Thesis (PhD)
Divisions: Fac of Science & Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User: Symplectic Admin
Date Deposited: 13 Aug 2018 09:26
Last Modified: 09 Jan 2021 15:20
DOI: 10.17638/03014039
Supervisors:
  • Dunne, PE
  • Grossi, D
  • Woltran, S
URI: https://livrepository.liverpool.ac.uk/id/eprint/3014039