Intuitonistic Basis for Non-Monotonic Logic

McDermott and Doyle [4] suggested a system, denoted by ⊢, of non-monotonic logic. This notion was intended to formalise non-monotonic reasoning as involved in real situations and in artificial intelligence. McDermott and Doyle also list in their paper several difficulties and problems in their approach. Their semantics seems to be inadequate and there are several counterintuitive results obtained in their system.