Nonmonotonic Reasoning, Preferential Models and Cumulative Logics

Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the eld of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, de ned in the style of Gentzen 13]. Both proof-theoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay in 10], while the latter has been advocated by Y. Shoham in 38]. Five such families are de ned and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams in 2]. The preferential model...

• Type: Journal
• Year: 2002
• Where: CORR
• Authors: Sarit Kraus, Daniel J. Lehmann, Menachem Magidor
• Keywords: CORR 2002, Education, Nonmonotonic Behavior, Nonmonotonic Consequence Relations, Nonmonotonic Reasoning