---
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
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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
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eprint_status: archive
eprintid: 468
fileinfo: /style/images/fileicons/application_postscript.png;/468/2/air.ps
full_text_status: public
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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
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metadata_visibility: show
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number: ~
pagerange: 279-308
pubdom: FALSE
publication: Artificial Intelligence Review
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refereed: TRUE
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relation_type: []
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reportno: ~
rev_number: 10
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source: ~
status_changed: 2007-09-12 16:28:30
subjects:
  - cog-psy
  - comp-sci-art-intel
  - ling-sem
  - phil-lang
  - phil-logic
succeeds: ~
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title: Issues in Commonsense Set Theory
type: journalp
userid: 178
volume: 8
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