In my talk I propose a three-component evaluation of arguments as an essential part of an algorithm for the argumentative dispute resolution. The idea of the algorithm stems out of Dung-style abstract argumentation approach [1] and its further developments towards creating formalisms with structured arguments, as outlined by H.Prakken and G.Vreeswijk [2]. Core obstacle for creating a formalism with structured arguments in the vein of Dung-style frameworks is the incompatibility of defeasible and indefeasible rules for arguments’ aggregation in the argumentative framework, which leads to the collapse in the formalisms, as the rationality postulates by L.Amgoud and M. Caminada demonstrate [3]. Since it is the idea of the non-monotonic arguments’ reinstating for the sake of modelling diversity of opinions in the dispute which underlies the need of merging defeasible and indefeasible rules, I propose using non-standard ordering of the truth values for modelling such diversity. The idea of the non-standard ordering of the truth-values is borrowed from the many-valued logic of Dmitry Bochvar [4] and Victor Finn [4]. It suggests that the orderings of the truth-values may vary so as to express alternating truth in justified, rebutted or indeterminate arguments, as it often happens, for instance, in legal disputes where which of the versions presented in the courtroom is true the jury will find out in the end and not at the moment of its presentation