{"id":"https://openalex.org/W4226322367","doi":"https://doi.org/10.1007/978-3-030-99253-8_13","title":"A first-order logic characterisation of safety and co-safety languages","display_name":"A first-order logic characterisation of safety and co-safety languages","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4226322367","doi":"https://doi.org/10.1007/978-3-030-99253-8_13"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-99253-8_13","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99253-8_13","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_13.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_13.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017426974","display_name":"Alessandro Cimatti","orcid":"https://orcid.org/0000-0002-1315-6990"},"institutions":[{"id":"https://openalex.org/I2277624104","display_name":"Fondazione Bruno Kessler","ror":"https://ror.org/01j33xk10","country_code":"IT","type":"facility","lineage":["https://openalex.org/I2277624104"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Alessandro Cimatti","raw_affiliation_strings":["Fondazione Bruno Kessler, Trento, Italy"],"affiliations":[{"raw_affiliation_string":"Fondazione Bruno Kessler, Trento, Italy","institution_ids":["https://openalex.org/I2277624104"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045151425","display_name":"Luca Geatti","orcid":"https://orcid.org/0000-0002-7125-787X"},"institutions":[{"id":"https://openalex.org/I171543936","display_name":"Free University of Bozen-Bolzano","ror":"https://ror.org/012ajp527","country_code":"IT","type":"education","lineage":["https://openalex.org/I171543936"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Luca Geatti","raw_affiliation_strings":["Free University of Bozen-Bolzano, Bolzano, Italy"],"affiliations":[{"raw_affiliation_string":"Free University of Bozen-Bolzano, Bolzano, Italy","institution_ids":["https://openalex.org/I171543936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070497827","display_name":"Nicola Gigante","orcid":"https://orcid.org/0000-0002-2254-4821"},"institutions":[{"id":"https://openalex.org/I171543936","display_name":"Free University of Bozen-Bolzano","ror":"https://ror.org/012ajp527","country_code":"IT","type":"education","lineage":["https://openalex.org/I171543936"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Nicola Gigante","raw_affiliation_strings":["Free University of Bozen-Bolzano, Bolzano, Italy"],"affiliations":[{"raw_affiliation_string":"Free University of Bozen-Bolzano, Bolzano, Italy","institution_ids":["https://openalex.org/I171543936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015702335","display_name":"Angelo Montanari","orcid":"https://orcid.org/0000-0002-4322-769X"},"institutions":[{"id":"https://openalex.org/I129043915","display_name":"University of Udine","ror":"https://ror.org/05ht0mh31","country_code":"IT","type":"education","lineage":["https://openalex.org/I129043915"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Angelo Montanari","raw_affiliation_strings":["University of Udine, Udine, Italy"],"affiliations":[{"raw_affiliation_string":"University of Udine, Udine, Italy","institution_ids":["https://openalex.org/I129043915"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018618502","display_name":"Stefano Tonetta","orcid":"https://orcid.org/0000-0001-9091-7899"},"institutions":[{"id":"https://openalex.org/I2277624104","display_name":"Fondazione Bruno Kessler","ror":"https://ror.org/01j33xk10","country_code":"IT","type":"facility","lineage":["https://openalex.org/I2277624104"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Stefano Tonetta","raw_affiliation_strings":["Fondazione Bruno Kessler, Trento, Italy"],"affiliations":[{"raw_affiliation_string":"Fondazione Bruno Kessler, Trento, Italy","institution_ids":["https://openalex.org/I2277624104"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5017426974"],"corresponding_institution_ids":["https://openalex.org/I2277624104"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":1.9919,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.85984007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"244","last_page":"263"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998000264167786,"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/T10142","display_name":"Formal Methods in Verification","score":0.9998000264167786,"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/T11549","display_name":"Synthetic Organic Chemistry Methods","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1605","display_name":"Organic Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9919999837875366,"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/algorithm","display_name":"Algorithm","score":0.6257878541946411},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4343101680278778},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4230459928512573},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39066243171691895}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6257878541946411},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4343101680278778},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4230459928512573},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39066243171691895},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-030-99253-8_13","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99253-8_13","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_13.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-99253-8_13","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-99253-8_13","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_13.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"score":0.47999998927116394,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4226322367.pdf","grobid_xml":"https://content.openalex.org/works/W4226322367.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W813383233","https://openalex.org/W1491593738","https://openalex.org/W1540883472","https://openalex.org/W1577761978","https://openalex.org/W1979919662","https://openalex.org/W2023808162","https://openalex.org/W2063322197","https://openalex.org/W2090731055","https://openalex.org/W2131064738","https://openalex.org/W2138856440","https://openalex.org/W2147348835","https://openalex.org/W2157319504","https://openalex.org/W2963056188","https://openalex.org/W3098140864","https://openalex.org/W6606406588"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W2350741829"],"abstract_inverted_index":{"Abstract":[0],"Linear":[1],"Temporal":[2],"Logic":[3],"(":[4,64],"$$\\mathsf":[5,51,65,125,132,146,164,194,212,228,249,267,281,312,339,348,381],"{LTL}$$":[6,52,126,165,250,313,340],"<mml:math":[7,53,68,127,137,151,166,197,216,232,251,272,286,314,341,353,386],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[8,54,69,128,138,152,167,198,217,233,252,273,287,315,342,354,387],"<mml:mi>LTL</mml:mi>":[9,55,129,142,156,168,253,277,291,316,343,358,391],"</mml:math>":[10,56,80,130,144,158,169,209,223,239,254,279,293,317,344,360,393],")":[11,81,159],"is":[12,35,46,160,345],"one":[13,62],"of":[14,27,29,44,61,116,163,193,306,309,320,375,380],"the":[15,58,105,114,248,307,372,376],"most":[16],"popular":[17],"temporal":[18,175],"logics,":[19],"that":[20,50,179,262,297,333],"comes":[21],"into":[22],"play":[23,108],"in":[24,112,318,338,347],"a":[25,90,97,109,161,191,295,303,327,364],"variety":[26],"branches":[28],"computer":[30],"science.":[31],"Its":[32],"widespread":[33],"use":[34],"also":[36],"due":[37],"to":[38,94,104,247],"its":[39,226],"strong":[40],"foundational":[41],"properties.":[42],"One":[43],"them":[45],"Kamp\u2019s":[47,299],"theorem,":[48,300],"showing":[49],"and":[57,86,121,225,280,301,330,397],"first-order":[59,321],"theory":[60],"successor":[63],"{S1S}[\\mathsf":[66,195],"{FO}]$$":[67,196],"<mml:mrow>":[70,71,139,153,199,200,218,234,274,288,355,388],"<mml:mi>S</mml:mi>":[72,74,201,203],"<mml:mn>1</mml:mn>":[73,202],"</mml:mrow>":[75,79,143,157,204,208,222,238,278,292,359,392],"<mml:mo>[</mml:mo>":[76,205],"<mml:mi>FO</mml:mi>":[77,206,221,237],"<mml:mo>]</mml:mo>":[78,207],"are":[82,177,242],"expressively":[83,243],"equivalent.":[84],"Safety":[85],"co-safety":[87],"languages,":[88],"where":[89,170],"finite":[91,396],"prefix":[92],"suffices":[93],"establish":[95],"whether":[96],"word":[98],"does":[99,102],"not":[100],"or":[101],"belong":[103],"language,":[106],"respectively,":[107],"crucial":[110],"role":[111],"lowering":[113],"complexity":[115],"problems":[117],"like":[118],"model":[119],"checking":[120],"reactive":[122],"synthesis":[123],"for":[124],".":[131],"{Safety\\text":[133,213,268,349,382],"{-}":[134,148,214,230,269,283,350,383],"\\mathsf":[135,149,270,284,351,384],"{LTL}}$$":[136,150,271,285,352,385],"<mml:mi>Safety</mml:mi>":[140,219,275,356,389],"<mml:mo>-</mml:mo>":[141,155,220,236,276,290,357,390],"(resp.,":[145,173,182],"{coSafety\\text":[147,229,282],"<mml:mi>coSafety</mml:mi>":[154,235,289],"fragment":[162,192],"only":[171],"universal":[172],"existential)":[174],"modalities":[176],"allowed,":[178],"recognises":[180],"safety":[181,256,335],"co-safety)":[183],"languages":[184],"only.":[185],"In":[186,258,323],"this":[187],"paper,":[188],"we":[189,260,366],"introduce":[190],",":[210,224,240,294],"called":[211],"FO}$$":[215,231],"dual":[227],"which":[241],"complete":[244],"with":[245],"regards":[246],"-definable":[255],"languages.":[257,322],"particular,":[259],"prove":[261],"they":[263],"respectively":[264],"characterise":[265],"exactly":[266],"result":[296],"joins":[298],"provides":[302],"clearer":[304],"view":[305],"charactisations":[308],"(fragments":[310],"of)":[311],"terms":[319],"addition,":[324],"it":[325],"gives":[326],"direct,":[328],"compact,":[329],"self-contained":[331],"proof":[332],"any":[334],"language":[336],"definable":[337,346],"as":[361],"well.":[362],"As":[363],"by-product,":[365],"obtain":[367],"some":[368],"interesting":[369],"results":[370],"on":[371],"expressive":[373],"power":[374],"weak":[377],"tomorrow":[378],"operator":[379],"interpreted":[394],"over":[395],"infinite":[398],"traces.":[399]},"counts_by_year":[{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
