Characterizing common argumentation semantics using branch evaluations for justification systems

Thesis defence by Simon Birkenheuer

Location: APB 3027
Start: 15. August 2024 at 11:00 am
End: 15. August 2024 at 12:00 pm
Research group: Computational Logic
Research group: Logic Programming and Argumentation
Event series: Research Seminar Logic and AI
iCal

First introduced in 2015 by Denecker, Brewka and Strass, justification theory is formalism providing a new way of characterizing semantics for both logic programs and Dung style argumentation frameworks. Justification theory uses branch evaluation functions operating on a body of rules and an interpretation to define a set of justified facts. Fixpoints of the branch evaluation function on a given body of rules are called justified interpretations. Common semantics for argumentation frameworks can be obtained using these justified interpretations. In this work we characterize these semantics using branch evaluations with the goal of characterizing exactly the desired semantics with no additional conditions imposed on the justified interpretations. We present a grounded branch evaluation yielding grounded semantics for argumentation. This grounded branch evaluation coincides with the branch evaluations providing well founded and Kripke-Kleene semantics for logic programming. Furthermore we show that for admissible, preferred and stable argumentation semantics an exact characterization in the general case is not possible.