In this mathematical research paper, the authors present an algebraic method for nonmonotonic proof systems, in the style of D. Gabbay [1]. More precisely, they study logical systems in which a nonmonotonic consequence relation is combined with the usual deduction.

Such systems may be interpreted in special algebraic systems, the main theorem of the paper being a theorem of completeness. But how can such algebraic systems be obtained? The authors describe a procedure for building them from posets; this is their second contribution.

In the remaining paragraphs, the authors survey extensions to more elaborate logics: cumulative systems (with an implication) and preferential systems (with an implication and a disjunction).

The paper is rather technical, as the matter is, and is of a theoretical nature (there is no application, but this was not the goal).