In this paper we discuss Gabbay's idea of basing
nonmonotonic deduction on semantic consequence in
intuitionistic logic extended by a consistency operator and Turner's
suggestion of replacing the intuitionistic base system by Kleene's
three-valued logic. It is shown that a certain counterintuitive feature of
these approaches can be avoided by using Nelson's constructive logic N
instead of intuitionistic logic or Kleene's system. Moreover, in N a more
general notion of consistency can be defined and nonmonotonic deduction
can thus be based on a logical system satisfying the Deduction
Theorem.