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Computational models of arguments grasp a rich repertoire of complex reasoning structures that are employed in various kinds of decision-making processes, e.g., in political discourse, negotiation, mediation, and legal argumentation. However, in principle, they narrow down the account of reasoning to just one type, namely to defeasible inference that draws conclusions from the premises unless there is a defeater – a piece of information that rebuts the conclusion of an argument or undercuts the premise-conclusion link. The result of this treatment is that theoretical foundations for computational approaches to argumentation generally focus on one dominant type of reasoning. In this paper, we show that the logico-methodological tradition of the Lvov–Warsaw School may serve as an important motivation for enriching theoretical foundations of computationally oriented argumentation theories. We focus on Łukasiewicz’s classification of reasoning because in our view, it is best suited for the purpose of developing computational models of argument. We also pay attention to Ajdukiewicz’s critique of the former approach, as well as his own account, as it constitutes a direction for enriching the current state of the art in the study of patterns of reasoning.