{"id":"https://openalex.org/W3195133477","doi":"https://doi.org/10.1007/s10817-022-09643-1","title":"Towards Formalising Schutz\u2019 Axioms for Minkowski Spacetime in Isabelle/HOL","display_name":"Towards Formalising Schutz\u2019 Axioms for Minkowski Spacetime in Isabelle/HOL","publication_year":2022,"publication_date":"2022-10-01","ids":{"openalex":"https://openalex.org/W3195133477","doi":"https://doi.org/10.1007/s10817-022-09643-1","mag":"3195133477"},"language":"en","primary_location":{"id":"doi:10.1007/s10817-022-09643-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-022-09643-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10817-022-09643-1.pdf","source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10817-022-09643-1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005871728","display_name":"Richard Schmoetten","orcid":"https://orcid.org/0000-0003-1473-071X"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Richard Schmoetten","raw_affiliation_strings":["School of Informatics, University of Edinburgh, Edinburgh, UK","School of Informatics, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, UK"],"raw_orcid":"https://orcid.org/0000-0003-1473-071X","affiliations":[{"raw_affiliation_string":"School of Informatics, University of Edinburgh, Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Informatics, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112722525","display_name":"Jake E. Palmer","orcid":null},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Jake E. Palmer","raw_affiliation_strings":["School of Informatics, University of Edinburgh, Edinburgh, UK","School of Informatics, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Informatics, University of Edinburgh, Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Informatics, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026577518","display_name":"Jacques Fleuriot","orcid":"https://orcid.org/0000-0002-6867-9836"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Jacques D. Fleuriot","raw_affiliation_strings":["School of Informatics, University of Edinburgh, Edinburgh, UK","School of Informatics, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Informatics, University of Edinburgh, Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"School of Informatics, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, UK","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005871728","https://openalex.org/A5026577518","https://openalex.org/A5112722525"],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.05802534,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"66","issue":"4","first_page":"953","last_page":"988"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11960","display_name":"Relativity and Gravitational Theory","score":0.9803000092506409,"subfield":{"id":"https://openalex.org/subfields/3103","display_name":"Astronomy and Astrophysics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hol","display_name":"HOL","score":0.7913772463798523},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.7734470367431641},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7225480079650879},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7083388566970825},{"id":"https://openalex.org/keywords/foundations-of-geometry","display_name":"Foundations of geometry","score":0.6083565950393677},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.6061068773269653},{"id":"https://openalex.org/keywords/axiomatic-system","display_name":"Axiomatic system","score":0.4578177034854889},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4519495666027069},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4345824420452118},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"Non-Euclidean geometry","score":0.4111568331718445},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40837007761001587},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3529927134513855},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34304338693618774},{"id":"https://openalex.org/keywords/projective-geometry","display_name":"Projective geometry","score":0.10437753796577454},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10380581021308899},{"id":"https://openalex.org/keywords/differential-geometry","display_name":"Differential geometry","score":0.0881865918636322}],"concepts":[{"id":"https://openalex.org/C17435882","wikidata":"https://www.wikidata.org/wiki/Q17030435","display_name":"HOL","level":2,"score":0.7913772463798523},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.7734470367431641},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7225480079650879},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7083388566970825},{"id":"https://openalex.org/C180110497","wikidata":"https://www.wikidata.org/wiki/Q5474574","display_name":"Foundations of geometry","level":4,"score":0.6083565950393677},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.6061068773269653},{"id":"https://openalex.org/C125773388","wikidata":"https://www.wikidata.org/wiki/Q792542","display_name":"Axiomatic system","level":3,"score":0.4578177034854889},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4519495666027069},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4345824420452118},{"id":"https://openalex.org/C10784197","wikidata":"https://www.wikidata.org/wiki/Q233858","display_name":"Non-Euclidean geometry","level":3,"score":0.4111568331718445},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40837007761001587},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3529927134513855},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34304338693618774},{"id":"https://openalex.org/C185362025","wikidata":"https://www.wikidata.org/wiki/Q177409","display_name":"Projective geometry","level":3,"score":0.10437753796577454},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10380581021308899},{"id":"https://openalex.org/C192939610","wikidata":"https://www.wikidata.org/wiki/Q188444","display_name":"Differential geometry","level":2,"score":0.0881865918636322},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10817-022-09643-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-022-09643-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10817-022-09643-1.pdf","source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},{"id":"pmh:oai:pure.ed.ac.uk:openaire/1b454e2b-727c-4a2f-8391-ef4efe57eaca","is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/en/publications/1b454e2b-727c-4a2f-8391-ef4efe57eaca","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Schmoetten, R, Palmer, J & Fleuriot, J 2022, 'Towards Formalising Schutz\u2019 Axioms for Minkowski Spacetime in Isabelle/HOL', Journal of Automated Reasoning, vol. 66, pp. 953-988. https://doi.org/10.1007/s10817-022-09643-1","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s10817-022-09643-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10817-022-09643-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10817-022-09643-1.pdf","source":{"id":"https://openalex.org/S99781599","display_name":"Journal of Automated Reasoning","issn_l":"0168-7433","issn":["0168-7433","1573-0670"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Automated Reasoning","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3195133477.pdf","grobid_xml":"https://content.openalex.org/works/W3195133477.grobid-xml"},"referenced_works_count":66,"referenced_works":["https://openalex.org/W14022547","https://openalex.org/W90526311","https://openalex.org/W626453988","https://openalex.org/W836255558","https://openalex.org/W963503529","https://openalex.org/W991450041","https://openalex.org/W1035810787","https://openalex.org/W1444781587","https://openalex.org/W1493718195","https://openalex.org/W1498523273","https://openalex.org/W1502264528","https://openalex.org/W1504171473","https://openalex.org/W1528908721","https://openalex.org/W1531550781","https://openalex.org/W1552678478","https://openalex.org/W1556012730","https://openalex.org/W1571434026","https://openalex.org/W1572941424","https://openalex.org/W1585420159","https://openalex.org/W1606604604","https://openalex.org/W1708936760","https://openalex.org/W1766647772","https://openalex.org/W1825294361","https://openalex.org/W1975259197","https://openalex.org/W1986121109","https://openalex.org/W1994598666","https://openalex.org/W2003552731","https://openalex.org/W2006267566","https://openalex.org/W2010959827","https://openalex.org/W2030463215","https://openalex.org/W2056474482","https://openalex.org/W2059245145","https://openalex.org/W2059324271","https://openalex.org/W2060808301","https://openalex.org/W2085972255","https://openalex.org/W2093269009","https://openalex.org/W2106895712","https://openalex.org/W2108757475","https://openalex.org/W2114758829","https://openalex.org/W2144907233","https://openalex.org/W2179792773","https://openalex.org/W2185082551","https://openalex.org/W2290832954","https://openalex.org/W2345278528","https://openalex.org/W2407069093","https://openalex.org/W2471863664","https://openalex.org/W2498310130","https://openalex.org/W2511518998","https://openalex.org/W2527478776","https://openalex.org/W2555370784","https://openalex.org/W2586568292","https://openalex.org/W2596784831","https://openalex.org/W2917377485","https://openalex.org/W2950010724","https://openalex.org/W2969487983","https://openalex.org/W2971627214","https://openalex.org/W2981616527","https://openalex.org/W3020940167","https://openalex.org/W3021747992","https://openalex.org/W3107507626","https://openalex.org/W3123808419","https://openalex.org/W3144156169","https://openalex.org/W3206346340","https://openalex.org/W4200324549","https://openalex.org/W4256124958","https://openalex.org/W6822732606"],"related_works":["https://openalex.org/W1005121375","https://openalex.org/W2152382218","https://openalex.org/W2796598708","https://openalex.org/W4240255957","https://openalex.org/W1988742612","https://openalex.org/W2515746712","https://openalex.org/W4238921260","https://openalex.org/W2595375203","https://openalex.org/W3195133477","https://openalex.org/W4200324549"],"abstract_inverted_index":{"Abstract":[0],"Special":[1],"relativity":[2],"is":[3,15,45],"a":[4,11,67],"cornerstone":[5],"of":[6,40,71,74],"modern":[7],"physical":[8],"theory.":[9],"While":[10],"standard":[12],"coordinate":[13],"model":[14],"well":[16,77],"known":[17],"and":[18],"widely":[19],"taught":[20],"today,":[21],"multiple":[22],"axiomatic":[23,51],"systems":[24],"for":[25],"SR":[26],"have":[27],"been":[28],"constructed":[29],"over":[30],"the":[31,38,58,72,90],"past":[32],"century.":[33],"This":[34],"paper":[35],"reports":[36],"on":[37],"formalisation":[39],"one":[41],"such":[42],"system,":[43],"which":[44],"closer":[46],"in":[47,69],"spirit":[48],"to":[49,53,57,81,100],"Hilbert\u2019s":[50],"approach":[52,61],"Euclidean":[54],"geometry":[55],"than":[56],"vector":[59],"space":[60],"employed":[62],"by":[63],"Minkowski.":[64],"We":[65],"present":[66],"mechanisation":[68],"Isabelle/HOL":[70],"system":[73],"axioms":[75],"as":[76,78],"theorems":[79],"relating":[80],"temporal":[82],"order.":[83],"Some":[84],"proofs":[85],"are":[86],"discussed,":[87],"particularly":[88],"where":[89],"formal":[91],"work":[92],"required":[93],"additional":[94],"steps,":[95],"alternative":[96],"approaches":[97],"or":[98],"corrections":[99],"Schutz\u2019":[101],"prose.":[102]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2025-10-10T00:00:00"}
