{"id":"https://openalex.org/W7204207151","doi":"https://doi.org/10.5281/zenodo.22102208","title":"Extensionality and Positive Introspection without Monotonicity or Conjunctive Closure: A Rosser Provability Construction","display_name":"Extensionality and Positive Introspection without Monotonicity or Conjunctive Closure: A Rosser Provability Construction","publication_year":2026,"publication_date":"2026-08-25","ids":{"openalex":"https://openalex.org/W7204207151","doi":"https://doi.org/10.5281/zenodo.22102208"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.22102208","doi":"https://doi.org/10.5281/zenodo.22102208","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22102208","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.22102208","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148148998","display_name":"Lu\u00eds Salvador Marques da Silva Reis Borges","orcid":"https://orcid.org/0009-0003-1624-2469","observed_orcids":["https://orcid.org/0009-0003-1624-2469"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Borges, Lu\u00eds Salvador Marques da Silva Reis","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0003-1624-2469","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5148148998"],"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.7250999808311462,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.7250999808311462,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.0989999994635582,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.06710000336170197,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/provability-logic","display_name":"provability logic","score":0.7039999961853027},{"id":"https://openalex.org/keywords/extensionality","display_name":"extensionality","score":0.6809999942779541},{"id":"https://openalex.org/keywords/monotonicity","display_name":"monotonicity","score":0.7889999747276306},{"id":"https://openalex.org/keywords/non-normal-modal-logics","display_name":"non-normal modal logics","score":0.8550000190734863},{"id":"https://openalex.org/keywords/neighborhood-semantics","display_name":"neighborhood semantics","score":0.8870000243186951},{"id":"https://openalex.org/keywords/biconditional","display_name":"biconditional","score":0.7070000171661377},{"id":"https://openalex.org/keywords/arithmetical-completeness","display_name":"arithmetical completeness","score":0.6489999890327454}],"concepts":[{"id":"https://openalex.org/C150355047","wikidata":"https://www.wikidata.org/wiki/Q965432","display_name":"Extensionality","level":2,"score":0.8108999729156494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7958999872207642},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5002999901771545},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4986000061035156},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4848000109195709},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.4794999957084656},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.476500004529953},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4632999897003174},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C180937797","wikidata":"https://www.wikidata.org/wiki/Q200787","display_name":"G\u00f6del's incompleteness theorems","level":3,"score":0.43380001187324524},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.424699991941452},{"id":"https://openalex.org/C97489613","wikidata":"https://www.wikidata.org/wiki/Q842755","display_name":"Peano axioms","level":2,"score":0.41290000081062317},{"id":"https://openalex.org/C178421362","wikidata":"https://www.wikidata.org/wiki/Q176786","display_name":"Intuitionistic logic","level":3,"score":0.4009000062942505},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.3718000054359436},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3635999858379364},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.3490999937057495},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3483000099658966},{"id":"https://openalex.org/C153107464","wikidata":"https://www.wikidata.org/wiki/Q10879018","display_name":"Intuitionism","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.32670000195503235},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.320499986410141},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.3010999858379364},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.29670000076293945},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C137155000","wikidata":"https://www.wikidata.org/wiki/Q468422","display_name":"Law of excluded middle","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.26429998874664307},{"id":"https://openalex.org/C203702658","wikidata":"https://www.wikidata.org/wiki/Q1073063","display_name":"Recursively enumerable language","level":2,"score":0.26350000500679016},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.25859999656677246},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25110000371932983},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.25060001015663147},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.22102208","doi":"https://doi.org/10.5281/zenodo.22102208","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22102208","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.22102209","doi":"https://doi.org/10.5281/zenodo.22102209","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22102209","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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:10.5281/zenodo.22102208","doi":"https://doi.org/10.5281/zenodo.22102208","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22102208","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Let":[0],"T":[1,68],"be":[2,121],"a":[3,14,70],"consistent":[4],"primitive-recursively":[5],"axiomatized":[6],"extension":[7],"of":[8,114,141,145],"Peano":[9],"Arithmetic":[10],"(PA).":[11],"We":[12],"construct":[13],"genuine":[15,71],"\u03a3\u2081":[16],"Rosser":[17,72,90],"provability":[18,159],"predicate":[19,57,73],"satisfying":[20],"extensionality":[21],"under":[22],"T-provable":[23],"equivalence":[24,119],"(E),":[25],"positive":[26],"introspection":[27],"(D3),":[28],"and":[29,61],"provable":[30,118],"local":[31],"consistency":[32],"(P).":[33],"In":[34],"fact,":[35],"PA":[36],"itself":[37],"proves":[38],"that":[39,156],"0":[40],"=":[41],"1":[42],"is":[43,105,154,161],"not":[44],"Rosser-provable":[45],"with":[46,74],"respect":[47],"to":[48,106,120,133],"the":[49,53,56,88,134,157],"constructed":[50],"predicate.":[51],"At":[52],"same":[54],"time,":[55],"fails":[58],"monotonicity":[59],"(M)":[60],"conjunctive":[62],"closure":[63],"(C).":[64],"Thus":[65],"every":[66],"such":[67],"admits":[69],"signature":[75],"E":[76],"+":[77,79,81,83],"D3":[78],"P":[80],"\u00acM":[82],"\u00acC.":[84],"The":[85,127],"construction":[86],"adapts":[87],"finite-frame":[89],"machinery":[91],"used":[92],"in":[93,138],"arithmetical":[94],"completeness":[95],"proofs":[96],"for":[97],"non-normal":[98,146],"modal":[99,147],"logics.":[100],"Its":[101],"main":[102],"structural":[103],"modification":[104],"replace":[107],"bounded":[108],"implication":[109],"paths":[110,113],"by":[111],"directed":[112],"literal":[115],"biconditionals,":[116],"allowing":[117],"transported":[122],"without":[123],"recovering":[124],"full":[125],"monotonicity.":[126],"result":[128],"gives":[129],"an":[130],"affirmative":[131],"answer":[132],"second":[135],"existence":[136],"question":[137],"Problem":[139],"5.2":[140],"Kogure's":[142],"\u201cProvability":[143],"interpretation":[144],"logics":[148],"having":[149],"neighborhood":[150],"semantics\u201d.":[151],"No":[152],"claim":[153],"made":[155],"resulting":[158],"logic":[160],"exactly":[162],"ENP4.":[163]},"counts_by_year":[],"updated_date":"2026-10-07T09:51:55.459714","created_date":"2026-08-26T00:00:00"}