In this paper, the specific features of cognitive conflicts and methods for
their resolution are considered. The basic problems of decision support in
cognitive conflicts are emphasized: situation and structural analysis of c
onflict situations, design of behavioural models under the conditions choic
e, argumentation of decisions made, and acquisition and formalization Of Su
bjective knowledge. The basic methods of formalization and solving the prob
lems posed that employ the methodology of reconstruction Of subjective repr
esentations, the analysis of conceptual cognitive models, and formal argume
ntation facilities joined within the framework of quasi-axiomatic argumenta
tion theory are considered. This paper presents a survey of the subject in
question.