Note on Short-comings in CumulA
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Abstract:
Abstract. In this brief note, we point out two problems with the argumentation framework CumulA, introduced in [2, Chapter 5]. We believe that these are important to be aware of, if one considers building on this framework. 1 CumulA CumulA is presented in [2], where it is given a thorough treatment with lots of examples. Here we only introduce the parts that are essential to understand our point. We do not follow the notation used in [2] to the letter, partly due to space concerns, and partly to render the connection with the popular framework presented in [1] more clear. CumulA builds an argumentation framework starting with some language L, which we take to be implicit wherever this leads to no confusion. The set of arguments of L is the smallest set A satisfying: – L ⊆ A, – if A1,...,An ∈ A and s ∈ L, then {{A1,..., An}} → s ∈ A, and – if {A1} → s,...,{An} → s ∈ A, then {A1,..., An} → s ∈ A. Given an argument A, the conclusion [c(A)], premises [p(A)], initials [i(A)], and narrowings [n(A)] of A are defined as follows:
