{"id":"https://openalex.org/W1486629280","doi":"https://doi.org/10.2178/jsl/1164060450","title":"Epsilon substitution method for -FIX","display_name":"Epsilon substitution method for -FIX","publication_year":2006,"publication_date":"2006-12-01","ids":{"openalex":"https://openalex.org/W1486629280","doi":"https://doi.org/10.2178/jsl/1164060450","mag":"1486629280"},"language":"en","primary_location":{"id":"doi:10.2178/jsl/1164060450","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1164060450","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110301130","display_name":"Toshiyasu Arai","orcid":null},"institutions":[{"id":"https://openalex.org/I65837984","display_name":"Kobe University","ror":"https://ror.org/03tgsfw79","country_code":"JP","type":"education","lineage":["https://openalex.org/I65837984"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Toshiyasu Arai","raw_affiliation_strings":["Graduate School of Science and Technology, Kobe University, Rokko-Dai, Nada-Ku, Kobe 657-8501, Japan, E-mail:","Graduate School of Science and Technology, Kobe University, Rokko-Dai, Nada-Ku, Kobe 657-8501, Japan, E-mail: arai@kurt.scitec.kobe-u.ac.jp"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Graduate School of Science and Technology, Kobe University, Rokko-Dai, Nada-Ku, Kobe 657-8501, Japan, E-mail:","institution_ids":["https://openalex.org/I65837984"]},{"raw_affiliation_string":"Graduate School of Science and Technology, Kobe University, Rokko-Dai, Nada-Ku, Kobe 657-8501, Japan, E-mail: arai@kurt.scitec.kobe-u.ac.jp","institution_ids":["https://openalex.org/I65837984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110301130"],"corresponding_institution_ids":["https://openalex.org/I65837984"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.04893751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"71","issue":"4","first_page":"1155","last_page":"1188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.8719000220298767,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.8719000220298767,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11178","display_name":"Receptor Mechanisms and Signaling","score":0.8533999919891357,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.7652999758720398,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ackermann-function","display_name":"Ackermann function","score":0.9723951816558838},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.9328092336654663},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41930609941482544},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36526960134506226},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11196461319923401}],"concepts":[{"id":"https://openalex.org/C33436860","wikidata":"https://www.wikidata.org/wiki/Q341835","display_name":"Ackermann function","level":3,"score":0.9723951816558838},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.9328092336654663},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41930609941482544},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36526960134506226},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11196461319923401},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.2178/jsl/1164060450","is_oa":false,"landing_page_url":"https://doi.org/10.2178/jsl/1164060450","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1164060450","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1164060450","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W13199265","https://openalex.org/W1570072295","https://openalex.org/W1576539916","https://openalex.org/W1965834052","https://openalex.org/W1985231476","https://openalex.org/W2018493916","https://openalex.org/W2035851396","https://openalex.org/W2058493504","https://openalex.org/W2061312397","https://openalex.org/W6655059164"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2076743759","https://openalex.org/W4235144492","https://openalex.org/W4388435768","https://openalex.org/W2756792282","https://openalex.org/W2756744637","https://openalex.org/W3216309640","https://openalex.org/W2759493398","https://openalex.org/W2807877113","https://openalex.org/W4254767272"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper":[3],"we":[4,18],"formulate":[5],"epsilon":[6],"substitution":[7],"method":[8],"for":[9,13],"a":[10,20],"theory":[11],"-FIX":[12],"nonmonotonic":[14],"inductive":[15],"definitions.":[16],"Then":[17],"give":[19],"termination":[21],"proof":[22],"of":[23],"the":[24],"H-processes":[25],"based":[26],"on":[27],"Ackermann":[28],"[1].":[29]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}