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 .
We study and formalize the scheme of reasoning by cases within structured argumentation frameworks. More specifically, we extend the ASPIC+ framework for structured argumentation  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  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’.REFERENCES
 S. Kraus, D. Lehmann, and M. Magidor. Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence 44:167-207, 1990.
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