. The merits of set theory as a foundational tool in mathematics stimulate its use in various areas of artificial intelligence, in particular intelligent information systems. In this paper, a study of various nonstandard treatments of set theory from this perspective is offered. Applications of these alternative set theories to information or knowledge management are surveyed. Keywords: set theory, knowledge representation, information management, commonsense reasoning, nonwellfounded sets (hypersets) 1. Introduction Set theory is a branch of modern mathematics with a unique place because various other branches can be formally defined within it. For example, Book 1 of the influential works of N. Bourbaki is devoted to the theory of sets and provides the framework for the remaining volumes. Bourbaki said in 1949 (Goldblatt, 1984) 1 : "[A]ll mathematical theories may be regarded as extensions of the general theory of sets : : : [O]n these foundations I can state that I can build up t...