Abstract
This paper develops a logical theory that unifies all three standard types of argumentative attack in AI, namely rebutting, undercutting and undermining attacks. We build on default justification logic that already represents undercutting and rebutting attacks, and we add undermining attacks. Intuitively, undermining does not target default inference, as undercutting, or default conclusion, as rebutting, but rather attacks an argument’s premise as a starting point for default reasoning. In default justification logic, reasoning starts from a set of premises, which is then extended by conclusions that hold by default. We argue that modeling undermining defeaters in the view of default theories requires changing the set of premises upon receiving new information. To model changes to premises, we give a dynamic aspect to default justification logic by using the techniques from the logic of belief revision. More specifically, undermining is modeled with belief revision operations that include contracting a set of premises, that is, removing some information from it. The novel combination of default reasoning and belief revision in justification logic enriches both approaches to reasoning under uncertainty. By the end of the paper, we show some important aspects of defeasible argumentation in which our logic compares favorably to structured argumentation frameworks.
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Acknowledgements
I am grateful to Allard Tamminga, Barteld Kooi and Rineke Verbrugge for their generous advice and valuable comments on the previous versions of this manuscript. A part of the research reported here was carried out with the support of the Ammodo KNAW project Rational Dynamics and Reasoning awarded to Barteld Kooi. My current work is supported by the NWO project Empowering Human Intentions through Artificial Intelligence led by Jan Broersen. Finally, I would like to thank the audiences at “The Symposium on Logical Foundations of Computer Science” and “The 11th International Symposium on Foundations of Information and Knowledge Systems”, as well as the reviewers of this journal for many constructive suggestions that helped me to improve the manuscript.
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Pandžić, S. Structured argumentation dynamics. Ann Math Artif Intell 90, 297–337 (2022). https://doi.org/10.1007/s10472-021-09765-z
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DOI: https://doi.org/10.1007/s10472-021-09765-z