{"id":"https://openalex.org/W7160525521","doi":"https://doi.org/10.48550/arxiv.2605.04689","title":"Continuations and Completeness in Proof-theoretic Semantics","display_name":"Continuations and Completeness in Proof-theoretic Semantics","publication_year":2026,"publication_date":"2026-05-06","ids":{"openalex":"https://openalex.org/W7160525521","doi":"https://doi.org/10.48550/arxiv.2605.04689"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.04689","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04689","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.04689","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135540742","display_name":"Tao Gu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gu, Tao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135558859","display_name":"David Pym","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pym, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086646386","display_name":"Eike Ritter","orcid":"https://orcid.org/0009-0005-2100-8866"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ritter, Eike","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135612572","display_name":"Edmund Robinson","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robinson, Edmund","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.7699999809265137,"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"}},"topics":[{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.7699999809265137,"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"}},{"id":"https://openalex.org/T10258","display_name":"Philosophy and Theoretical Science","score":0.09740000218153,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.05979999899864197,"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/completeness","display_name":"Completeness (order theory)","score":0.7052000164985657},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.5241000056266785},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.44850000739097595},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4133000075817108},{"id":"https://openalex.org/keywords/proof-theoretic-semantics","display_name":"Proof-theoretic semantics","score":0.40220001339912415},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39660000801086426},{"id":"https://openalex.org/keywords/proof-theory","display_name":"Proof theory","score":0.39640000462532043},{"id":"https://openalex.org/keywords/propositional-variable","display_name":"Propositional variable","score":0.3944000005722046},{"id":"https://openalex.org/keywords/g\u00f6dels-completeness-theorem","display_name":"G\u00f6del's completeness theorem","score":0.392300009727478},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.38119998574256897}],"concepts":[{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.7052000164985657},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5241000056266785},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4927999973297119},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.44850000739097595},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C61151141","wikidata":"https://www.wikidata.org/wiki/Q7249983","display_name":"Proof-theoretic semantics","level":5,"score":0.40220001339912415},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39660000801086426},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.39640000462532043},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.3944000005722046},{"id":"https://openalex.org/C200116569","wikidata":"https://www.wikidata.org/wiki/Q902052","display_name":"G\u00f6del's completeness theorem","level":2,"score":0.392300009727478},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.3797999918460846},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3732999861240387},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.37049999833106995},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.3549000024795532},{"id":"https://openalex.org/C89497691","wikidata":"https://www.wikidata.org/wiki/Q7981058","display_name":"Well-founded semantics","level":5,"score":0.34130001068115234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3276999890804291},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.3240000009536743},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.313400000333786},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.3093000054359436},{"id":"https://openalex.org/C146499914","wikidata":"https://www.wikidata.org/wiki/Q5469969","display_name":"Formal semantics (linguistics)","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C156325763","wikidata":"https://www.wikidata.org/wiki/Q1930895","display_name":"Operational semantics","level":3,"score":0.2863999903202057},{"id":"https://openalex.org/C135790938","wikidata":"https://www.wikidata.org/wiki/Q242028","display_name":"Lambda calculus","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C191222856","wikidata":"https://www.wikidata.org/wiki/Q655328","display_name":"Well-formed formula","level":5,"score":0.2815999984741211},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.28029999136924744},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C93682546","wikidata":"https://www.wikidata.org/wiki/Q1056428","display_name":"Type theory","level":3,"score":0.2605000138282776},{"id":"https://openalex.org/C25016198","wikidata":"https://www.wikidata.org/wiki/Q781833","display_name":"Temporal logic","level":2,"score":0.25699999928474426},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C102315432","wikidata":"https://www.wikidata.org/wiki/Q649732","display_name":"Formal system","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.25450000166893005}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.04689","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04689","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.04689","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04689","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"is":[1,15,34,53,79],"a":[2,17,40],"short":[3],"paper":[4],"about":[5,16,118],"the":[6,20,28,44,65,88,94,119,132],"relationship":[7,18,74,120],"between":[8,19,75,121],"logic":[9,26],"and":[10,39,64,68,77,99,124],"computation.":[11],"More":[12],"specifically,":[13],"it":[14],"completeness":[21,76,89],"proof":[22,86],"for":[23],"intuitionistic":[24],"propositional":[25],"within":[27],"form":[29],"of":[30,46,59,71,84,87,97,112,134],"proof-theoretic":[31,135],"semantics":[32,38],"that":[33],"known":[35],"as":[36,91],"base-extension":[37],"fundamental":[41],"idea":[42],"from":[43,93],"theory":[45],"computation":[47],"called":[48],"continuation-passing":[49],"semantics.":[50,101,136],"The":[51,73],"latter":[52],"explained":[54],"herein":[55],"both":[56],"in":[57,61,69],"terms":[58,70],"reduction":[60],"natural":[62],"deduction":[63],"lambda":[66],"calculus":[67],"proof-search.":[72],"continuations":[78,113],"explored":[80],"through":[81],"an":[82],"analysis":[83,103],"Sandqvist's":[85],"theorem":[90],"seen":[92,106],"mathematical":[95],"perspective":[96],"Kripke's":[98],"Heyting's":[100],"Our":[102],"can":[104],"be":[105],"to":[107],"reveal":[108],"how":[109],"syntactic":[110],"representations":[111],"embody":[114],"intensional":[115],"semantical":[116],"intuitions":[117,127],"their":[122],"meaning":[123],"use.":[125],"These":[126],"are":[128],"made":[129],"precise":[130],"using":[131],"tools":[133]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-08T00:00:00"}