V.N. Vagin, O.L. Morosin

This paper provides a brief overview of approaches to the formalization of argumentation systems.The main subject is one of these approaches - argumentation in defeasible reasoning. In contrast to classical logic, defeasible argumentation allows us to draw conclusions on the inconsistent and incomplete sets of premises. The concept of the conflict is the main point in the theory of defeasible reasoning. Moreover, the possibility of conflicts is the reason why defeasible reasoning is considered. The paper contains two types of conflict: rebutting and undercut. Defeasible reasoning allows us to find and analyze such conflicts. The purpose is to resolve these conflicts, by assigning to the conflicting arguments a certain status - \"defeated\" or \"undefeated\". The assignment of these statuses is the central problem of this theory.As well, the paper presents an overview of the auxiliary mechanismof monotonic reasoning, based on thenatural deduction theory. Without monotonic reasoning,the class of problems the reasoner could solve is much smaller. Monotonic reasoningsystem allows us to make new arguments from already existing ones. At the conclusion of the paper it is given an example of a task that is not solvable by means of classical logics.

 

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