A gradual semantics takes a weighted argumentation framework as input and outputs a final acceptability degree for each argument, with different semantics performing the computation in different manners. In this work, we consider the problem of attack inference. That is, given a gradual semantics, a set of arguments with associated initial weights, and the final desirable acceptability degrees associated with each argument, we seek to determine whether there is a set of attacks on those arguments such that we can obtain (...) these acceptability degrees. The main contribution of our work is to demonstrate that the associated decision problem, i.e., whether a set of attacks can exist which allows the final acceptability degrees to occur for given initial weights, is NP-complete for the weighted h-categoriser and card-based semantics, and is polynomial for the weighted max-based semantics, even for the complete version of the problem (where all initial weights and final acceptability degrees are known). We then briefly discuss how this decision problem can be modified to find the attacks themselves and conclude by examining the partial problem where not all initial weights or final acceptability degrees may be known. (shrink)

In 2018, three journalists accused one of the Members of the Russian Parliament of harassment at workplace. Many influential persons of the Russian elite engaged themselves in the public discussion of the conflict. We studied that high-profiled discussion using a hybrid method merging human- and logic-oriented approaches in argumentation studies. The method develops ideas of the new dialectics, the argumentation logic and the logical-cognitive approach to argumentation, on which is based the algorithm for determining of dispute resolution by aggregating formal (...) and informal tools of analysis. We have reconstructed the discussion as two disputes about questions A and B. A: Did the MP violate the code of conduct by making statements or actions against the journalists? B: Are actions like the behavior of the MP harassment? The opinions of the discussion participants were grouped into the four points of view: A1 – the MP did not violate the code of conduct, A2 – the MP violated the code of conduct, B3 – the actions are not harassment, B4 – the actions are harassment. We mapped arguments in support or against each of them using OVA software, evaluated the arguments with the help of the critical questions, a tool proposed in the new dialectics, and determined the ultimate A + B resolution by applying of the algorithm that combines elements of gradual and labelling semantics from the argumentation logic and the classification of disputes from the dialectical approaches. The resolution was a subset of four arguments that ensured the victory of A1+B4. However, the substantial incompatibility of those arguments highlighted a deep disagreement, an unresolvable difference of opinion, between the parties about the permissibility of courtship. The deep disagreement, a bonus result yielded by the application of the hybrid method, excluded the interpretation of the determined resolution as convincing for the parties, but pointed out a way to smooth the difference of opinions by elaborating of legal, social and moral aspects of the problem of harassment at workplace. (shrink)