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This paper presents a study of the nonmonotonic consequence relation which models the skeptical reasoning formalised by constrained default logic. The nonmonotonic skeptical consequence relation is defined using the sequent calculus axiomatic system. We study the formal properties desirable for a good" nonmonotonic relation: supraclassicality, cut, cautious monotony, cumulativity, absorption, distribution.

Key words and phrases. default logics, nonmonotonic consequence relation, skeptical reasoning, sequent calculus.