An extended review of what is known about the formal behaviour of nonmonotonic inference operations, including those generated by the principal systems in the artificial intelligence literature. Directed towards computer scientists and others with some background in logic.

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

Examines the link between nonmonotonic inference relations and theory revision operations, focusing on the correspondence between abstract properties which each may satisfy.

Left freely to themselves, a group of rational individuals often fail to cooperate even when the product of social cooperation is beneficial to all. Hence, the author argues, a rule of collective decision making is clearly needed that specifies how social cooperation should be organised among contributing individuals. Suzumura gives a systematic presentation of the Arrovian impossibility theorems of social choice theory, so as to describe and enumerate the various factors that are responsible for the stability of the voluntary association (...) of free and rational individuals. Among other topics covered are an axiomatic characterisation of the concept of a rational choice, the simple majority decision rule and its extensions, the social choice implications of the concept of equity as nonenvy, the constrained majoritarian collective choice rules and the conflict between the Paretian ethics and the libertarian claims of individual rights. (shrink)