"Corrections of AIJ 2013 paper (updated January 2017)"

Corrections of:

  • S.J. Modgil & H. Prakken, A general account of argumentation with preferences. Artificial Intelligence 195 (2013): 361-397. [PDF]. (Version at AI Journal homepage).
(updated January 2017 and 2 March 2018)

In the original version as published in the AI Journal here is a counterexample to Proposition 21, which claims that the elitist last- and weakest link orderings are ``reasonable inducing''. As a consequence, there are also counterexamples to the claim (following from Propositions 19,20,21 and Theorem 15) that (c-)SAFs with an elitist last- or weakest link argument ordering satisfy indirect consistency. One such counterexample is Example 5.1 of Dung (2014). Fortunately, there is an easy repair, namely to adopt Prakken's (2010) definition of elitist orderings (Prakken 2010, p. 109, the paragraph following Corollary 6.11). (A similar solution is indicated by Dung 2014, Section 6.) This definition excludes the counterexamples.

Update January 2017: We have now put a corrected version of the AIJ paper online, in which the above-mentioned errors in the version of the paper that appears in the AIJ are corrected. The online version here includes a modified version of Section 5.1 (and proofs of results in this section in the Appendix). We are very grateful to Sjur Dyrkolbotn for further clarifying the problems with the definition of `reasonable inducing' that has now been corrected in this online version. Note that the counter-example to rationality noted in Dung (2014) is now no longer a counter-example according to this online version. Note, finally, that none of this affects the above remark that Prakken's (2010) definition of elitist orderings does not suffer from the problems.

Update 2 March 2018: We have put a new corrected version of the AIJ paper online, with some minor confusions removed.

Update 22 May 2018: An explanation of the corrections has been accepted for publication by the AI Journal.


  • P.M. Dung, An axiomatic analysis of structured argumentation for prioritised default reasoning. Proceedings of ECAI 2014, 267-272.
  • H. Prakken, An abstract framework for argumentation with structured arguments. Argument and Computation 1 (2010): 93-124. [PDF].