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Mathieu Beirlaen: Reasoning by Cases in Formal Argumentation

Lecture by Mathieu Beirlaen (Bochum), organized by the Department of Theoretical Philosophy / Grolog

Given a premise ‘P or Q’, an argument for R on the basis of P, and an argument for R on the basis of Q, the reasoning by cases inference scheme allows us to conclude that R. If each of P and Q classically entail R, then the inference to R given ‘P or Q’ is deductively valid. In cases where the argument from P to R and the argument from Q to R hold only tentatively, the conclusion R may be derivable tentatively as well. We are interested here in this more tentative, defeasible variant of the reasoning by cases scheme, the formalization of which is well-known to cause trouble in many rule-based systems of non-monotonic logic, such as default logic [1].

We study and formalize the scheme of reasoning by cases within structured argumentation frameworks. More specifically, we extend the ASPIC+ framework for structured argumentation [2] so as to allow for the construction of arguments applying the reasoning by cases scheme, called rbc-arguments. In the rbc-argument from ‘P or Q’ to R from the previous paragraph, we refer to the argument for R on the basis of P (respectively Q) as a hypothetical argument on the basis of P (respectively Q). We extend the definition of argumentative attack so as to include rbc-arguments as well as hypothetical arguments relative to a knowledge base. We show how our framework differs from other approaches in non-monotonic logic for dealing with disjunctive information, such as disjunctive default theory [3] or approaches based on the OR-rule [4,5], which allows to derive a defeasible rule ‘If (P or Q) then R’, given two defeasible rules ‘If P then R’ and ‘If Q then R’.

[1] N. Roos. Reasoning by cases in default logic. Artificial Intelligence 99(1):165-183, 1998.
[2] S. Modgil and H. Prakken. The ASPIC+ framework for structured argumentation: a tutorial. Argument & Computation 1(5):31-62, 2014.
[3] M. Gelfond, V. Lifschitz, H. Przymusinska, and M. Truszczynski. Disjunctive defaults. Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning (KR): 230-237, 1991.
[4] D. Makinson and L. van der Torre. Input/Output logics. Journal of Philosophical Logic 29:383-408, 2000.

[5] S. Kraus, D. Lehmann, and M. Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44:167-207, 1990.

When and where?
Thursday 2 February 2017, 15:15-17:00
Room Alpha, Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52
Last modified:09 January 2017 4.54 p.m.