Two models of unawareness: comparing the object-based and the subjective-state-space approaches

Over the past 20 years or so, a small but growing literature has emerged with the aim of modeling agents who are unaware of certain things. In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (Object-based unawareness: theory and ap...

Full description

Saved in:
Bibliographic Details
Published in:Synthese (Dordrecht) 2011-04, Vol.179 (Suppl 1), p.13-34
Main Authors: Board, Oliver J., Chung, Kim-Sau, Schipper, Burkhard C.
Format: Article
Language:English
Subjects:
Axiomatization
Economic models
Economic theory
Education
Epistemology
Explicit knowledge
Formal languages
Introspection
Logic
Logical conjunctions
Mathematical functions
Measurability
Metaphysics
Philosophy
Philosophy of Language
Philosophy of Science
Property partitioning
Space
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c381t-e5c1fc5cab47d3aa81a55e0659d4bfb02b8bbc0ea26825d38619821616d0f2543
cites cdi_FETCH-LOGICAL-c381t-e5c1fc5cab47d3aa81a55e0659d4bfb02b8bbc0ea26825d38619821616d0f2543
container_end_page 34
container_issue Suppl 1
container_start_page 13
container_title Synthese (Dordrecht)
container_volume 179
creator Board, Oliver J.
Chung, Kim-Sau
Schipper, Burkhard C.
description Over the past 20 years or so, a small but growing literature has emerged with the aim of modeling agents who are unaware of certain things. In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (Object-based unawareness: theory and applications. University of Minnesota, Mimeo, 2008) and the subjective-state-space approach of Heifetz et al. (J Econ Theory 130: 78-94,2006). In particular, we show that subjectivestate-space models (henceforth HMS structures) can be embedded within object-based models (henceforth OBU structures), demonstrating that the latter are at least as expressive. As long as certain restrictions are imposed on the form of the OBU structure, the embedding can also go the other way. A generalization of HMS structures (relaxing the partitional properties of knowledge) gives us a full converse.
doi_str_mv 10.1007/s11229-010-9850-z
format article
fullrecord <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_journals_1111793391</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>41477406</jstor_id><sourcerecordid>41477406</sourcerecordid><originalsourceid>FETCH-LOGICAL-c381t-e5c1fc5cab47d3aa81a55e0659d4bfb02b8bbc0ea26825d38619821616d0f2543</originalsourceid><addsrcrecordid>eNp9kE9LxDAQxYMouK5-AA9CwXN0JmnSxpss_oMFL-s5pGnqbtltatK6uJ_e7lbEk3OYgcd78-BHyCXCDQJktxGRMUUBgapcAN0dkQmKjFNQMj0mEwCuaJaL7JScxVgDIMoUJkQvtj7Z-NKtY-KrpG_M1gTXuBjvEus3rQmr5j3pli7xRe1sRwsTXZmYpjyIsT-oq09HY2e6YbfGusS0bfDGLl08JyeVWUd38XOn5O3xYTF7pvPXp5fZ_ZxanmNHnbBYWWFNkWYlNyZHI4QDKVSZFlUBrMiLwoIzTOZMlDyXqHKGEmUJFRMpn5Lr8e9Q_NG72Ona96EZKjUOkynOFQ4uHF02-BiDq3QbVhsTvjSC3nPUI0c9cNR7jno3ZNiYie2ehQt_Pv8TuhpDdex8-G1JMc2yFCT_Bj7TgIY</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1111793391</pqid></control><display><type>article</type><title>Two models of unawareness: comparing the object-based and the subjective-state-space approaches</title><source>JSTOR Archival Journals and Primary Sources Collection</source><source>Springer Link</source><source>ProQuest One Literature</source><source>Art, Design &amp; Architecture Collection</source><creator>Board, Oliver J. ; Chung, Kim-Sau ; Schipper, Burkhard C.</creator><creatorcontrib>Board, Oliver J. ; Chung, Kim-Sau ; Schipper, Burkhard C.</creatorcontrib><description>Over the past 20 years or so, a small but growing literature has emerged with the aim of modeling agents who are unaware of certain things. In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (Object-based unawareness: theory and applications. University of Minnesota, Mimeo, 2008) and the subjective-state-space approach of Heifetz et al. (J Econ Theory 130: 78-94,2006). In particular, we show that subjectivestate-space models (henceforth HMS structures) can be embedded within object-based models (henceforth OBU structures), demonstrating that the latter are at least as expressive. As long as certain restrictions are imposed on the form of the OBU structure, the embedding can also go the other way. A generalization of HMS structures (relaxing the partitional properties of knowledge) gives us a full converse.</description><identifier>ISSN: 0039-7857</identifier><identifier>EISSN: 1573-0964</identifier><identifier>DOI: 10.1007/s11229-010-9850-z</identifier><language>eng</language><publisher>Dordrecht: Springer</publisher><subject>Axiomatization ; Economic models ; Economic theory ; Education ; Epistemology ; Explicit knowledge ; Formal languages ; Introspection ; Logic ; Logical conjunctions ; Mathematical functions ; Measurability ; Metaphysics ; Philosophy ; Philosophy of Language ; Philosophy of Science ; Property partitioning ; Space</subject><ispartof>Synthese (Dordrecht), 2011-04, Vol.179 (Suppl 1), p.13-34</ispartof><rights>2011 Springer</rights><rights>The Author(s) 2010</rights><rights>Springer Science+Business Media B.V. 2011</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c381t-e5c1fc5cab47d3aa81a55e0659d4bfb02b8bbc0ea26825d38619821616d0f2543</citedby><cites>FETCH-LOGICAL-c381t-e5c1fc5cab47d3aa81a55e0659d4bfb02b8bbc0ea26825d38619821616d0f2543</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/1111793391/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/1111793391?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,776,780,12840,27901,27902,34752,44176,58213,58446,62634,62635,62650,73939,74471</link.rule.ids></links><search><creatorcontrib>Board, Oliver J.</creatorcontrib><creatorcontrib>Chung, Kim-Sau</creatorcontrib><creatorcontrib>Schipper, Burkhard C.</creatorcontrib><title>Two models of unawareness: comparing the object-based and the subjective-state-space approaches</title><title>Synthese (Dordrecht)</title><addtitle>Synthese</addtitle><description>Over the past 20 years or so, a small but growing literature has emerged with the aim of modeling agents who are unaware of certain things. In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (Object-based unawareness: theory and applications. University of Minnesota, Mimeo, 2008) and the subjective-state-space approach of Heifetz et al. (J Econ Theory 130: 78-94,2006). In particular, we show that subjectivestate-space models (henceforth HMS structures) can be embedded within object-based models (henceforth OBU structures), demonstrating that the latter are at least as expressive. As long as certain restrictions are imposed on the form of the OBU structure, the embedding can also go the other way. A generalization of HMS structures (relaxing the partitional properties of knowledge) gives us a full converse.</description><subject>Axiomatization</subject><subject>Economic models</subject><subject>Economic theory</subject><subject>Education</subject><subject>Epistemology</subject><subject>Explicit knowledge</subject><subject>Formal languages</subject><subject>Introspection</subject><subject>Logic</subject><subject>Logical conjunctions</subject><subject>Mathematical functions</subject><subject>Measurability</subject><subject>Metaphysics</subject><subject>Philosophy</subject><subject>Philosophy of Language</subject><subject>Philosophy of Science</subject><subject>Property partitioning</subject><subject>Space</subject><issn>0039-7857</issn><issn>1573-0964</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>AIMQZ</sourceid><sourceid>K50</sourceid><sourceid>M1D</sourceid><recordid>eNp9kE9LxDAQxYMouK5-AA9CwXN0JmnSxpss_oMFL-s5pGnqbtltatK6uJ_e7lbEk3OYgcd78-BHyCXCDQJktxGRMUUBgapcAN0dkQmKjFNQMj0mEwCuaJaL7JScxVgDIMoUJkQvtj7Z-NKtY-KrpG_M1gTXuBjvEus3rQmr5j3pli7xRe1sRwsTXZmYpjyIsT-oq09HY2e6YbfGusS0bfDGLl08JyeVWUd38XOn5O3xYTF7pvPXp5fZ_ZxanmNHnbBYWWFNkWYlNyZHI4QDKVSZFlUBrMiLwoIzTOZMlDyXqHKGEmUJFRMpn5Lr8e9Q_NG72Ona96EZKjUOkynOFQ4uHF02-BiDq3QbVhsTvjSC3nPUI0c9cNR7jno3ZNiYie2ehQt_Pv8TuhpDdex8-G1JMc2yFCT_Bj7TgIY</recordid><startdate>20110401</startdate><enddate>20110401</enddate><creator>Board, Oliver J.</creator><creator>Chung, Kim-Sau</creator><creator>Schipper, Burkhard C.</creator><general>Springer</general><general>Springer Netherlands</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7XB</scope><scope>8FK</scope><scope>8G5</scope><scope>AABKS</scope><scope>ABSDQ</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AIMQZ</scope><scope>AVQMV</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GB0</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>K50</scope><scope>LIQON</scope><scope>M1D</scope><scope>M2O</scope><scope>MBDVC</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>Q9U</scope></search><sort><creationdate>20110401</creationdate><title>Two models of unawareness: comparing the object-based and the subjective-state-space approaches</title><author>Board, Oliver J. ; Chung, Kim-Sau ; Schipper, Burkhard C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c381t-e5c1fc5cab47d3aa81a55e0659d4bfb02b8bbc0ea26825d38619821616d0f2543</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Axiomatization</topic><topic>Economic models</topic><topic>Economic theory</topic><topic>Education</topic><topic>Epistemology</topic><topic>Explicit knowledge</topic><topic>Formal languages</topic><topic>Introspection</topic><topic>Logic</topic><topic>Logical conjunctions</topic><topic>Mathematical functions</topic><topic>Measurability</topic><topic>Metaphysics</topic><topic>Philosophy</topic><topic>Philosophy of Language</topic><topic>Philosophy of Science</topic><topic>Property partitioning</topic><topic>Space</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Board, Oliver J.</creatorcontrib><creatorcontrib>Chung, Kim-Sau</creatorcontrib><creatorcontrib>Schipper, Burkhard C.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Philosophy Collection</collection><collection>Philosophy Database</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest One Literature</collection><collection>Arts Premium Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>DELNET Social Sciences &amp; Humanities Collection</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Art, Design &amp; Architecture Collection</collection><collection>One Literature (ProQuest)</collection><collection>Arts &amp; Humanities Database</collection><collection>ProQuest Research Library</collection><collection>Research Library (Corporate)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>ProQuest Central Basic</collection><jtitle>Synthese (Dordrecht)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Board, Oliver J.</au><au>Chung, Kim-Sau</au><au>Schipper, Burkhard C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two models of unawareness: comparing the object-based and the subjective-state-space approaches</atitle><jtitle>Synthese (Dordrecht)</jtitle><stitle>Synthese</stitle><date>2011-04-01</date><risdate>2011</risdate><volume>179</volume><issue>Suppl 1</issue><spage>13</spage><epage>34</epage><pages>13-34</pages><issn>0039-7857</issn><eissn>1573-0964</eissn><abstract>Over the past 20 years or so, a small but growing literature has emerged with the aim of modeling agents who are unaware of certain things. In this paper we compare two different approaches to modeling unawareness: the object-based approach of Board and Chung (Object-based unawareness: theory and applications. University of Minnesota, Mimeo, 2008) and the subjective-state-space approach of Heifetz et al. (J Econ Theory 130: 78-94,2006). In particular, we show that subjectivestate-space models (henceforth HMS structures) can be embedded within object-based models (henceforth OBU structures), demonstrating that the latter are at least as expressive. As long as certain restrictions are imposed on the form of the OBU structure, the embedding can also go the other way. A generalization of HMS structures (relaxing the partitional properties of knowledge) gives us a full converse.</abstract><cop>Dordrecht</cop><pub>Springer</pub><doi>10.1007/s11229-010-9850-z</doi><tpages>22</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0039-7857
ispartof Synthese (Dordrecht), 2011-04, Vol.179 (Suppl 1), p.13-34
issn 0039-7857
1573-0964
language eng
recordid cdi_proquest_journals_1111793391
source JSTOR Archival Journals and Primary Sources Collection; Springer Link; ProQuest One Literature; Art, Design & Architecture Collection
subjects Axiomatization
Economic models
Economic theory
Education
Epistemology
Explicit knowledge
Formal languages
Introspection
Logic
Logical conjunctions
Mathematical functions
Measurability
Metaphysics
Philosophy
Philosophy of Language
Philosophy of Science
Property partitioning
Space
title Two models of unawareness: comparing the object-based and the subjective-state-space approaches
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-02T02%3A56%3A57IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Two%20models%20of%20unawareness:%20comparing%20the%20object-based%20and%20the%20subjective-state-space%20approaches&rft.jtitle=Synthese%20(Dordrecht)&rft.au=Board,%20Oliver%20J.&rft.date=2011-04-01&rft.volume=179&rft.issue=Suppl%201&rft.spage=13&rft.epage=34&rft.pages=13-34&rft.issn=0039-7857&rft.eissn=1573-0964&rft_id=info:doi/10.1007/s11229-010-9850-z&rft_dat=%3Cjstor_proqu%3E41477406%3C/jstor_proqu%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c381t-e5c1fc5cab47d3aa81a55e0659d4bfb02b8bbc0ea26825d38619821616d0f2543%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1111793391&rft_id=info:pmid/&rft_jstor_id=41477406&rfr_iscdi=true