{"id":"https://openalex.org/W4415102304","doi":"https://doi.org/10.4204/eptcs.431.1","title":"Ground Stratification for a Logic of Definitions with Induction","display_name":"Ground Stratification for a Logic of Definitions with Induction","publication_year":2025,"publication_date":"2025-10-13","ids":{"openalex":"https://openalex.org/W4415102304","doi":"https://doi.org/10.4204/eptcs.431.1"},"language":"en","primary_location":{"id":"doi:10.4204/eptcs.431.1","is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.431.1","pdf_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?LFMTP2025.1.pdf","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?LFMTP2025.1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119965637","display_name":"Nathan Guermond","orcid":null},"institutions":[{"id":"https://openalex.org/I2800403580","display_name":"University of Minnesota System","ror":"https://ror.org/03grvy078","country_code":"US","type":"education","lineage":["https://openalex.org/I2800403580"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nathan Guermond","raw_affiliation_strings":["University of Minnesota"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Minnesota","institution_ids":["https://openalex.org/I2800403580"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080344559","display_name":"Gopalan Nadathur","orcid":"https://orcid.org/0000-0001-8456-3369"},"institutions":[{"id":"https://openalex.org/I2800403580","display_name":"University of Minnesota System","ror":"https://ror.org/03grvy078","country_code":"US","type":"education","lineage":["https://openalex.org/I2800403580"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gopalan Nadathur","raw_affiliation_strings":["University of Minnesota"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Minnesota","institution_ids":["https://openalex.org/I2800403580"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27167014,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"431","issue":null,"first_page":"1","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9484000205993652,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9484000205993652,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9180999994277954,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/stratification","display_name":"Stratification (seeds)","score":0.6794999837875366},{"id":"https://openalex.org/keywords/soundness","display_name":"Soundness","score":0.6011999845504761},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.573199987411499},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.49709999561309814},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.4156999886035919},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3321000039577484},{"id":"https://openalex.org/keywords/atomic-sentence","display_name":"Atomic sentence","score":0.31049999594688416},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.3012999892234802}],"concepts":[{"id":"https://openalex.org/C192943249","wikidata":"https://www.wikidata.org/wiki/Q1893382","display_name":"Stratification (seeds)","level":5,"score":0.6794999837875366},{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.6011999845504761},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.573199987411499},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.49709999561309814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46389999985694885},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.439300000667572},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43380001187324524},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.4156999886035919},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33660000562667847},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C34849589","wikidata":"https://www.wikidata.org/wiki/Q4345785","display_name":"Atomic sentence","level":3,"score":0.31049999594688416},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.3012999892234802},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3003999888896942},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C168993435","wikidata":"https://www.wikidata.org/wiki/Q6501125","display_name":"Ground","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.29179999232292175},{"id":"https://openalex.org/C4777664","wikidata":"https://www.wikidata.org/wiki/Q1536492","display_name":"Linear temporal logic","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2581999897956848},{"id":"https://openalex.org/C173856430","wikidata":"https://www.wikidata.org/wiki/Q3257964","display_name":"Separation logic","level":2,"score":0.257999986410141}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.4204/eptcs.431.1","is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.431.1","pdf_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?LFMTP2025.1.pdf","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2510.12297","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2510.12297","pdf_url":"https://arxiv.org/pdf/2510.12297","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.4204/eptcs.431.1","is_oa":true,"landing_page_url":"https://doi.org/10.4204/eptcs.431.1","pdf_url":"https://eptcs.web.cse.unsw.edu.au/paper.cgi?LFMTP2025.1.pdf","source":{"id":"https://openalex.org/S4210216316","display_name":"Electronic Proceedings in Theoretical Computer Science","issn_l":"2075-2180","issn":["2075-2180"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310318029","host_organization_name":"Open Publishing Association","host_organization_lineage":["https://openalex.org/P4310318029"],"host_organization_lineage_names":["Open Publishing Association"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Electronic Proceedings in Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415102304.pdf","grobid_xml":"https://content.openalex.org/works/W4415102304.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"logic":[1,30,84,191],"underlying":[2,192],"the":[3,25,29,83,125,132,166,189],"Abella":[4],"proof":[5],"assistant":[6],"includes":[7,31,196],"mechanisms":[8],"for":[9,42,153,186,208],"interpreting":[10],"atomic":[11],"predicates":[12],"through":[13],"fixed":[14],"point":[15],"definitions":[16,37,155,187],"that":[17,38,48,85,93,109,147,215],"can":[18,63,95],"additionally":[19,195],"be":[20,64,96,139],"treated":[21],"inductively":[22],"or":[23],"co-inductively.However,":[24],"original":[26],"formulation":[27],"of":[28,82,211],"a":[32,50,68,80,177,182,201],"strict":[33],"stratification":[34,137,149],"condition":[35],"on":[36],"is":[39,122],"too":[40],"restrictive":[41],"some":[43],"applications":[44],"such":[45,100],"as":[46,73,205],"those":[47],"use":[49,121],"logical":[51,168],"relations":[52,169],"based":[53],"approach":[54],"to":[55,72,79,98,124,150,157,180,204],"semantic":[56],"equivalence.Tiu":[57],"has":[58],"shown":[59],"how":[60],"this":[61,118,151],"restriction":[62],"eased":[65],"by":[66,106,218],"utilizing":[67],"weaker":[69],"notion":[70],"referred":[71,203],"ground":[74,136],"stratification.Tiu's":[75],"results":[76,103,174],"were":[77],"limited":[78],"version":[81],"does":[86],"not":[87],"treat":[88],"inductive":[89,154],"definitions.We":[90],"show":[91,146],"here":[92],"they":[94],"extended":[97],"cover":[99],"definitions.While":[101],"our":[102],"are":[104,170,175,216],"obtained":[105],"using":[107],"techniques":[108],"have":[110],"been":[111],"previously":[112],"deployed":[113],"in":[114,117,128,172,213],"related":[115],"ways":[116],"context,":[119],"their":[120],"sensitive":[123],"particular":[126,159],"way":[127,167],"which":[129,194],"we":[130,145,161],"generalize":[131],"logic.In":[133],"particular,":[134],"although":[135],"may":[138],"used":[140,171],"with":[141,165],"arbitrary":[142],"fixed-point":[143],"definitions,":[144],"weakening":[148],"form":[152,185],"leads":[156],"inconsistency.The":[158],"generalization":[160],"describe":[162],"accords":[163],"well":[164],"practice.Our":[173],"also":[176],"intermediate":[178],"step":[179],"building":[181],"more":[183],"flexible":[184],"into":[188],"full":[190],"Abella,":[193],"co-induction,":[197],"generic":[198,219],"quantification,":[199],"and":[200],"mechanism":[202],"nominal":[206],"abstraction":[207],"analyzing":[209],"occurrences":[210],"objects":[212],"terms":[214],"governed":[217],"quantifiers.":[220]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-13T00:00:00"}