{"id":"https://openalex.org/W3132018246","doi":"https://doi.org/10.1007/978-3-030-79876-5_11","title":"Unifying Decidable Entailments in Separation Logic with Inductive Definitions","display_name":"Unifying Decidable Entailments in Separation Logic with Inductive Definitions","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3132018246","doi":"https://doi.org/10.1007/978-3-030-79876-5_11","mag":"3132018246"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-79876-5_11","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-79876-5_11","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-79876-5_11.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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-79876-5_11.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010578735","display_name":"Mnacho Echenim","orcid":"https://orcid.org/0000-0001-5765-0758"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104430","display_name":"Laboratoire d'Informatique de Grenoble","ror":"https://ror.org/01c8rcg82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Mnacho Echenim","raw_affiliation_strings":["Univ. Grenoble Alpes, CNRS, LIG, F-38000 Grenoble France","Univ. Grenoble Alpes, CNRS, LIG, Grenoble, France#TAB#"],"raw_orcid":"https://orcid.org/0000-0001-5765-0758","affiliations":[{"raw_affiliation_string":"Univ. Grenoble Alpes, CNRS, LIG, F-38000 Grenoble France","institution_ids":["https://openalex.org/I4210104430","https://openalex.org/I1294671590","https://openalex.org/I899635006"]},{"raw_affiliation_string":"Univ. Grenoble Alpes, CNRS, LIG, Grenoble, France#TAB#","institution_ids":["https://openalex.org/I4210104430","https://openalex.org/I1294671590","https://openalex.org/I899635006"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074143130","display_name":"Radu Iosif","orcid":"https://orcid.org/0000-0003-3204-3294"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210156361","display_name":"Verimag","ror":"https://ror.org/05afmzm11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210156361","https://openalex.org/I4210159245","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Radu Iosif","raw_affiliation_strings":["Univ. Grenoble Alpes, CNRS, VERIMAG, F-38000 Grenoble France","Univ. Grenoble Alpes-CNRS Verimag, Grenoble, France"],"raw_orcid":"https://orcid.org/0000-0003-3204-3294","affiliations":[{"raw_affiliation_string":"Univ. Grenoble Alpes, CNRS, VERIMAG, F-38000 Grenoble France","institution_ids":["https://openalex.org/I4210156361","https://openalex.org/I1294671590","https://openalex.org/I899635006"]},{"raw_affiliation_string":"Univ. Grenoble Alpes-CNRS Verimag, Grenoble, France","institution_ids":["https://openalex.org/I4210156361","https://openalex.org/I899635006","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079985573","display_name":"Nicolas Peltier","orcid":"https://orcid.org/0000-0002-8943-7000"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210104430","display_name":"Laboratoire d'Informatique de Grenoble","ror":"https://ror.org/01c8rcg82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210104430","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas Peltier","raw_affiliation_strings":["Univ. Grenoble Alpes, CNRS, LIG, F-38000 Grenoble France","Univ. Grenoble Alpes, CNRS, LIG, Grenoble, France#TAB#"],"raw_orcid":"https://orcid.org/0000-0002-8943-7000","affiliations":[{"raw_affiliation_string":"Univ. Grenoble Alpes, CNRS, LIG, F-38000 Grenoble France","institution_ids":["https://openalex.org/I4210104430","https://openalex.org/I1294671590","https://openalex.org/I899635006"]},{"raw_affiliation_string":"Univ. Grenoble Alpes, CNRS, LIG, Grenoble, France#TAB#","institution_ids":["https://openalex.org/I4210104430","https://openalex.org/I1294671590","https://openalex.org/I899635006"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010578735"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210104430","https://openalex.org/I899635006"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03489327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"183","last_page":"199"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9994999766349792,"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":0.9994999766349792,"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/T10142","display_name":"Formal Methods in Verification","score":0.9941999912261963,"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/T11567","display_name":"semigroups and automata theory","score":0.9886999726295471,"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/decidability","display_name":"Decidability","score":0.9228479862213135},{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.8036553859710693},{"id":"https://openalex.org/keywords/logical-consequence","display_name":"Logical consequence","score":0.7751812934875488},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.654220461845398},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6003567576408386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5451880693435669},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5435239672660828},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.507396399974823},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.49461862444877625},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.45155560970306396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2400577962398529},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14646509289741516}],"concepts":[{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.9228479862213135},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.8036553859710693},{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.7751812934875488},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.654220461845398},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6003567576408386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5451880693435669},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5435239672660828},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.507396399974823},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.49461862444877625},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.45155560970306396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2400577962398529},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14646509289741516},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/978-3-030-79876-5_11","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-79876-5_11","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-79876-5_11.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"},{"id":"pmh:oai:arXiv.org:2012.14361","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.14361","pdf_url":"https://arxiv.org/pdf/2012.14361","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3132018246","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2012.14361v2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-03304653v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03304653","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"CADE 28, Jul 2021, Pittsburgh (virtual), United States. pp.183-199, &#x27E8;10.1007/978-3-030-79876-5_11&#x27E9;","raw_type":"Conference papers"},{"id":"doi:10.48550/arxiv.2012.14361","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2012.14361","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"doi:10.1007/978-3-030-79876-5_11","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-030-79876-5_11","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-030-79876-5_11.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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3132018246.pdf","grobid_xml":"https://content.openalex.org/works/W3132018246.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W122465024","https://openalex.org/W134837158","https://openalex.org/W777621473","https://openalex.org/W1581674879","https://openalex.org/W1757770995","https://openalex.org/W1910824881","https://openalex.org/W1974265510","https://openalex.org/W2061679993","https://openalex.org/W2137628566","https://openalex.org/W2930217943","https://openalex.org/W2963581951","https://openalex.org/W3016709696","https://openalex.org/W3031363853","https://openalex.org/W3032212576","https://openalex.org/W3113412086","https://openalex.org/W3183368753","https://openalex.org/W4243994983"],"related_works":["https://openalex.org/W2043790764","https://openalex.org/W1549008998","https://openalex.org/W2556763370","https://openalex.org/W1977176390","https://openalex.org/W2736516049","https://openalex.org/W1575743174","https://openalex.org/W3137580398","https://openalex.org/W148586085","https://openalex.org/W2131055468","https://openalex.org/W2286419476","https://openalex.org/W1560156525","https://openalex.org/W1837362933","https://openalex.org/W2131663704","https://openalex.org/W2013705348","https://openalex.org/W2038932611","https://openalex.org/W2053751489","https://openalex.org/W82525747","https://openalex.org/W2093865192","https://openalex.org/W2144978807","https://openalex.org/W2045354966"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"entailment":[2,78,129,198,213],"problem":[3],"$$\\upvarphi":[4,155],"\\models":[5],"\\uppsi":[6],"$$":[7,156,165],"<mml:math":[8,24,31,41,49,110,157,166,227],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>\u03c6</mml:mi><mml:mo>\u22a7</mml:mo><mml:mi>\u03c8</mml:mi></mml:mrow></mml:math>":[9],"in":[10,63,106],"Separation":[11],"Logic":[12],"[12,":[13],"15],":[14],"between":[15],"separated":[16],"conjunctions":[17],"of":[18,58,70,77,125,171,179,194,212],"equational":[19],"(":[20,35,46,154,163],"$$x":[21,27,36],"\\approx":[22,29],"y$$":[23,30],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>x</mml:mi><mml:mo>\u2248</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:math>":[25],"and":[26,44,96,118,121,160,206,218],"\\not":[28],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>x</mml:mi><mml:mo>\u2249</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:math>":[32],"),":[33],"spatial":[34],"\\mapsto":[37],"(y_1,\\ldots":[38],",y_\\upkappa":[39],")$$":[40],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>x</mml:mi><mml:mo>\u21a6</mml:mo><mml:mo>(</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>\u2026</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>y</mml:mi><mml:mi>\u03ba</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math>":[42],")":[43,51,159,168],"predicate":[45],"$$p(x_1,\\ldots":[47],",x_n)$$":[48],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>,</mml:mo><mml:mo>\u2026</mml:mo><mml:mo>,</mml:mo><mml:msub><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:math>":[50],"atoms,":[52],"interpreted":[53],"by":[54,112,144],"a":[55,122,176,221],"finite":[56],"set":[57,69],"inductive":[59,71],"rules,":[60],"is":[61],"undecidable":[62],"general.":[64],"Certain":[65],"restrictions":[66],"on":[67,88],"the":[68,113,141,146,152,161,187,192,204,209],"definitions":[72],"lead":[73],"to":[74,104,127,151,186,196],"decidable":[75,85],"classes":[76,101,211],"problems.":[79],"Currently,":[80],"there":[81],"are":[82,102],"two":[83,89],"such":[84],"classes,":[86],"based":[87],"restrictions,":[90],"called":[91,183],"establishment":[92],"[10,":[93],"13,":[94],"14]":[95],"restrictedness":[97],"[8],":[98,119],"respectively.":[99,173],"Both":[100],"shown":[103],"be":[105],"$$\\mathsf":[107,224],"{2\\text":[108,225],"{EXPTIME}}$$":[109,226],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mn>2</mml:mn><mml:mtext>EXPTIME</mml:mtext></mml:mrow></mml:math>":[111,228],"independent":[114],"proofs":[115],"from":[116],"[14]":[117],"respectively,":[120],"many-one":[123,177],"reduction":[124,178,193,202],"established":[126,188,195],"restricted":[128,142,197,217],"problems":[130,214],"has":[131],"been":[132],"given":[133],"[8].":[134],"In":[135],"this":[136,180,200],"paper,":[137],"we":[138],"strictly":[139],"generalize":[140],"class,":[143,182],"distinguishing":[145],"conditions":[147],"that":[148,208],"apply":[149],"only":[150],"left-":[153],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c6</mml:mi></mml:math>":[158],"right-":[162],"$$\\uppsi":[164],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03c8</mml:mi></mml:math>":[167],"hand":[169],"side":[170],"entailments,":[172],"We":[174],"provide":[175],"generalized":[181],"safe":[184],",":[185],"class.":[189,230],"Together":[190],"with":[191],"problems,":[199],"new":[201],"closes":[203],"loop":[205],"shows":[207],"three":[210],"(respectively":[215],"established,":[216],"safe)":[219],"form":[220],"single,":[222],"unified,":[223],"-complete":[229]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}