creators_name: Pakkan, Mujdat creators_name: Akman, Varol type: journalp datestamp: 1998-06-19 lastmod: 2011-03-11 08:53:58 metadata_visibility: show title: Issues in Commonsense Set Theory ispublished: pub subjects: cog-psy subjects: comp-sci-art-intel subjects: ling-sem subjects: phil-lang subjects: phil-logic full_text_status: public keywords: ZF (Zermelo-Fraenkel) set theory, commonsense reasoning, knowledge representation, cumulative hierarchy, self-reference, nonwellfounded sets (hypersets), AFA (anti-foundation axiom), paradoxes, common knowledge. abstract: The success of set theory as a foundation for mathematics inspires its use in artificial intelligence, particularly in commonsense reasoning. In this survey, we briefly review classical set theory from an AI perspective, and then consider alternative set theories. Desirable properties of a possible commonsense set theory are investigated, treating different aspects like cumulative hierarchy, self-reference, cardinality, etc. Assorted examples from the ground-breaking research on the subject are also given. date: 1995 date_type: published publication: Artificial Intelligence Review volume: 8 pagerange: 279-308 refereed: TRUE citation: Pakkan, Mujdat and Akman, Varol (1995) Issues in Commonsense Set Theory. [Journal (Paginated)] document_url: http://cogprints.org/468/2/air.ps