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--- 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.' altloc: - http://www.cs.bilkent.edu.tr/~akman/jour-papers/air/air.html chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: [] creators_name: - family: Pakkan given: Mujdat honourific: '' lineage: '' - family: Akman given: Varol honourific: '' lineage: '' date: 1995 date_type: published datestamp: 1998-06-19 department: ~ dir: disk0/00/00/04/68 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 468 fileinfo: /style/images/fileicons/application_postscript.png;/468/2/air.ps full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: pub issn: ~ item_issues_comment: [] item_issues_count: 0 item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: 'ZF (Zermelo-Fraenkel) set theory, commonsense reasoning, knowledge representation, cumulative hierarchy, self-reference, nonwellfounded sets (hypersets), AFA (anti-foundation axiom), paradoxes, common knowledge.' lastmod: 2011-03-11 08:53:58 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: 279-308 pubdom: FALSE publication: Artificial Intelligence Review publisher: ~ refereed: TRUE referencetext: ~ relation_type: [] relation_uri: [] reportno: ~ rev_number: 10 series: ~ source: ~ status_changed: 2007-09-12 16:28:30 subjects: - cog-psy - comp-sci-art-intel - ling-sem - phil-lang - phil-logic succeeds: ~ suggestions: ~ sword_depositor: ~ sword_slug: ~ thesistype: ~ title: Issues in Commonsense Set Theory type: journalp userid: 178 volume: 8