Nonmonotonicity and the scope of reasoning
The authors begin by reviewing several apparent incongruities that have been noticed when applying to specific examples the various formalisms of nonmonotonic reasoning, notably circumscription, Reiter default logic and its variants, and autoepistemic logic. They suggest that the incongruities arise when the information at our disposal entails that there are abnormal items, whose presence tends to distort the results obtained by minimizing abnormality. The appropriate remedy, they suggest, is to regard each inference as a response to a specific problem, and restrict the scope of the data to cover only the area of that problem, within which the existence of abnormal items will rarely be entailed. In their view, ``reasoning about whole populations is more properly the domain of probability theory than of nonmonotonic logics, which seem better suited to reasoning about small numbers of cases''. With this as motivation, the authors suggest ways of integrating scope restrictions into existing formalisms, and study formal properties of the resulting ``scoped'' systems.
scientific article; zbMATH DE number 58241
scientific article