{"id":"https://openalex.org/W4366503833","doi":"https://doi.org/10.1007/978-3-031-30829-1_3","title":"Kantorovich Functors and Characteristic Logics for Behavioural Distances","display_name":"Kantorovich Functors and Characteristic Logics for Behavioural Distances","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4366503833","doi":"https://doi.org/10.1007/978-3-031-30829-1_3"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-30829-1_3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-30829-1_3","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30829-1_3.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/10.1007/978-3-031-30829-1_3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049352361","display_name":"Sergey Goncharov","orcid":"https://orcid.org/0000-0001-6924-8766"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sergey Goncharov","raw_affiliation_strings":["Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany"],"affiliations":[{"raw_affiliation_string":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028347341","display_name":"Dirk Hofmann","orcid":"https://orcid.org/0000-0002-1082-6135"},"institutions":[{"id":"https://openalex.org/I60858718","display_name":"University of Aveiro","ror":"https://ror.org/00nt41z93","country_code":"PT","type":"education","lineage":["https://openalex.org/I60858718"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Dirk Hofmann","raw_affiliation_strings":["Center for Research and Development in Mathematics and Applications, University of Aveiro, Aveiro, Portugal"],"affiliations":[{"raw_affiliation_string":"Center for Research and Development in Mathematics and Applications, University of Aveiro, Aveiro, Portugal","institution_ids":["https://openalex.org/I60858718"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004001407","display_name":"Pedro Nora","orcid":"https://orcid.org/0000-0001-8581-0675"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pedro Nora","raw_affiliation_strings":["Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany"],"affiliations":[{"raw_affiliation_string":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073765060","display_name":"Lutz Schr\u00f6der","orcid":"https://orcid.org/0000-0002-3146-5906"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Lutz Schr\u00f6der","raw_affiliation_strings":["Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany"],"affiliations":[{"raw_affiliation_string":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058881043","display_name":"P. Wild","orcid":"https://orcid.org/0000-0001-9796-9675"},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Paul Wild","raw_affiliation_strings":["Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany"],"affiliations":[{"raw_affiliation_string":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Erlangen, Germany","institution_ids":["https://openalex.org/I181369854"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5049352361"],"corresponding_institution_ids":["https://openalex.org/I181369854"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":2.6033,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.9027637,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"46","last_page":"67"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9962000250816345,"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":0.9962000250816345,"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/T10126","display_name":"Logic, programming, and type systems","score":0.983299970626831,"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":0.9739999771118164,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.8627652525901794},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6273340582847595},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5667487978935242},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.48318758606910706},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.47872304916381836},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4606130123138428},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.42551642656326294},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42365503311157227},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.42094686627388},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38923704624176025},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3275804817676544},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.26451289653778076},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26184359192848206},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07045671343803406}],"concepts":[{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.8627652525901794},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6273340582847595},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5667487978935242},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.48318758606910706},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.47872304916381836},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4606130123138428},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.42551642656326294},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42365503311157227},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.42094686627388},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38923704624176025},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3275804817676544},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.26451289653778076},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26184359192848206},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07045671343803406},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-30829-1_3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-30829-1_3","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30829-1_3.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:10.1007/978-3-031-30829-1_3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-30829-1_3","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-30829-1_3.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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4366503833.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1507465323","https://openalex.org/W1976268573","https://openalex.org/W2020580559","https://openalex.org/W2020879982","https://openalex.org/W2021097403","https://openalex.org/W2032916024","https://openalex.org/W2047957052","https://openalex.org/W2060917500","https://openalex.org/W2063972032","https://openalex.org/W2070034419","https://openalex.org/W2076980581","https://openalex.org/W2088189323","https://openalex.org/W2090781610","https://openalex.org/W2090847457","https://openalex.org/W2092216144","https://openalex.org/W2093436963","https://openalex.org/W2100893927","https://openalex.org/W2108446683","https://openalex.org/W2138244417","https://openalex.org/W2166510793","https://openalex.org/W2798712453","https://openalex.org/W2810752651","https://openalex.org/W2951413002","https://openalex.org/W2964568064","https://openalex.org/W2968188570","https://openalex.org/W3040048066","https://openalex.org/W3137024392","https://openalex.org/W3176847254","https://openalex.org/W3189472968","https://openalex.org/W3199486472","https://openalex.org/W4286212091","https://openalex.org/W4299417699","https://openalex.org/W4409121819","https://openalex.org/W6608154327"],"related_works":["https://openalex.org/W1912064545","https://openalex.org/W2572273616","https://openalex.org/W2650039746","https://openalex.org/W2783715148","https://openalex.org/W2150706552","https://openalex.org/W1968024712","https://openalex.org/W4226166829","https://openalex.org/W3134888030","https://openalex.org/W48537500","https://openalex.org/W4372280033"],"abstract_inverted_index":{"Abstract":[0],"Behavioural":[1],"distances":[2,51,64,144,169],"measure":[3],"the":[4,34,42,48,160,163,197],"deviation":[5],"between":[6],"states":[7],"in":[8,21,33,162],"quantitative":[9,97,138,153,213],"systems,":[10],"such":[11],"as":[12],"probabilistic":[13,60],"or":[14,83],"weighted":[15],"systems.":[16],"There":[17],"is":[18,123,193],"growing":[19],"interest":[20],"generic":[22],"approaches":[23],"to":[24,78,94],"behavioural":[25,63,143,168,199],"distances.":[26],"In":[27,174],"particular,":[28,175],"coalgebraic":[29,139],"methods":[30],"capture":[31],"variations":[32],"system":[35],"type":[36],"(nondeterministic,":[37],"probabilistic,":[38],"game-based":[39],"etc.),":[40],"and":[41,59,182],"notion":[43],"of":[44,71,80,87,96,131,167,203],"quantale":[45],"abstracts":[46],"over":[47],"actual":[49],"values":[50],"take,":[52],"thus":[53],"covering,":[54],"e.g.,":[55],"two-valued":[56],"equivalences,":[57],"(pseudo)metrics,":[58],"(pseudo)metrics.":[61],"Coalgebraic":[62],"have":[65],"been":[66],"based":[67],"either":[68],"on":[69,84,186],"liftings":[70],"$$\\textsf{Set}$$":[72,88],"<mml:math":[73,89],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[74,90],"<mml:mi>Set</mml:mi>":[75,91],"</mml:math>":[76,92],"-functors":[77,93],"categories":[79,95],"metric":[81,188],"spaces,":[82,189],"lax":[85,100,113,121,147],"extensions":[86,148],"relations.":[98],"Every":[99],"extension":[101,122],"induces":[102],"a":[103,112,128,137,212],"functor":[104,172,180,185],"lifting":[105,109],"but":[106],"not":[107],"every":[108,120,179,184],"comes":[110],"from":[111],"extension.":[114],"It":[115],"was":[116],"shown":[117],"recently":[118],"that":[119,142,178,190,196],"Kantorovich,":[124,194],"i.e.":[125],"induced":[126,145,170,198],"by":[127,146,152,171,211],"suitable":[129],"choice":[130],"monotone":[132],"predicate":[133],"liftings,":[134],"implying":[135],"via":[136],"Hennessy-Milner":[140],"theorem":[141],"can":[149,208],"be":[150,209],"characterized":[151,210],"modal":[154,214],"logics.":[155],"Here,":[156],"we":[157,176],"essentially":[158],"show":[159,177],"same":[161],"more":[164],"general":[165],"setting":[166],"liftings.":[173],"lifting,":[181],"indeed":[183],"(quantale-valued)":[187],"preserves":[191],"isometries":[192],"so":[195],"distance":[200],"(on":[201],"systems":[202],"suitably":[204],"restricted":[205],"branching":[206],"degree)":[207],"logic.":[215]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-12-24T23:09:58.560324","created_date":"2025-10-10T00:00:00"}