In this paper we discuss Gabbay's idea of basingnonmonotonic deduction on semantic consequence inintuitionistic logic extended by a consistency operator and Turner'ssuggestion of replacing the intuitionistic base system by Kleene'sthree-valued logic. It is shown that a certain counterintuitive feature ofthese approaches can be avoided by using Nelson's constructive logic Ninstead of intuitionistic logic or Kleene's system. Moreover, in N a moregeneral notion of consistency can be defined and nonmonotonic deductioncan thus be based on a logical system satisfying the DeductionTheorem.
"Semantics-based Nonmonotonic Inference." Notre Dame J. Formal Logic 36 (1) 44 - 54, Winter 1995. https://doi.org/10.1305/ndjfl/1040308828