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This paper is devoted to a new algebraic modelling approach to distributed problem-solving in multi-agent systems (MAS), which is featured by a unified framework for describing and treating social behaviors, social dynamics and social intelligence. A conceptual architecture of algebraic modelling is presented. The algebraic modelling of typical social behaviors, social situation and social dynamics is discussed in the context of distributed problemsolving in MAS. The comparison and simulation on distributed task allocations and resource assignments in MAS show more advantages of the algebraic approach than other conventional methods.