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A gradual semantics takes a weighted argumentation framework as input andoutputs a final acceptability degree for each argument, with differentsemantics performing the computation in different manners. In this work, weconsider the problem of attack inference. That is, given a gradual semantics, aset of arguments with associated initial weights, and the final desirableacceptability degrees associated with each argument, we seek to determinewhether there is a set of attacks on those arguments such that we can obtainthese acceptability degrees. The main contribution of our work is todemonstrate that the associated decision problem, i.e., whether a set ofattacks can exist which allows the final acceptability degrees to occur forgiven initial weights, is NP-complete for the weighted h-categoriser andcardinality-based semantics, and is polynomial for the weighted max-basedsemantics, even for the complete version of the problem (where all initialweights and final acceptability degrees are known). We then briefly discuss howthis decision problem can be modified to find the attacks themselves andconclude by examining the partial problem where not all initial weights orfinal acceptability degrees may be known.

Inferring Attack Relations for Gradual Semantics