{"id":"https://openalex.org/W4414589094","doi":"https://doi.org/10.1007/978-3-032-04167-8_19","title":"A Finite Abstraction of\u00a0Real-Valued Functions for\u00a0Complete Reasoning About Influence","display_name":"A Finite Abstraction of\u00a0Real-Valued Functions for\u00a0Complete Reasoning About Influence","publication_year":2025,"publication_date":"2025-09-14","ids":{"openalex":"https://openalex.org/W4414589094","doi":"https://doi.org/10.1007/978-3-032-04167-8_19"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-032-04167-8_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-04167-8_19","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-04167-8_19.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/10.1007/978-3-032-04167-8_19.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119757212","display_name":"S\u00f6ren M\u00f6ller","orcid":null},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"S\u00f6ren M\u00f6ller","raw_affiliation_strings":["Theoretical Computer Science/Formal Methods, University of Kassel, Kassel, Germany"],"raw_orcid":"https://orcid.org/0009-0007-8942-7279","affiliations":[{"raw_affiliation_string":"Theoretical Computer Science/Formal Methods, University of Kassel, Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065538455","display_name":"Florian Bruse","orcid":"https://orcid.org/0000-0001-6800-7135"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florian Bruse","raw_affiliation_strings":["TUM School of Computation, Information and Technology, Technical University of Munich, Munich, Germany"],"raw_orcid":"https://orcid.org/0000-0001-6800-7135","affiliations":[{"raw_affiliation_string":"TUM School of Computation, Information and Technology, Technical University of Munich, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087768042","display_name":"Martin Lange","orcid":"https://orcid.org/0000-0002-1621-0972"},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Lange","raw_affiliation_strings":["Theoretical Computer Science/Formal Methods, University of Kassel, Kassel, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1621-0972","affiliations":[{"raw_affiliation_string":"Theoretical Computer Science/Formal Methods, University of Kassel, Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5119757212"],"corresponding_institution_ids":["https://openalex.org/I106157433"],"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":0.41182808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"346","last_page":"363"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9887999892234802,"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":0.9887999892234802,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9775999784469604,"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":0.9731000065803528,"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/completeness","display_name":"Completeness (order theory)","score":0.6047000288963318},{"id":"https://openalex.org/keywords/uncountable-set","display_name":"Uncountable set","score":0.5922999978065491},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5572999715805054},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.551800012588501},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5200999975204468},{"id":"https://openalex.org/keywords/automated-reasoning","display_name":"Automated reasoning","score":0.46309998631477356},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45739999413490295},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.4018000066280365},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.37619999051094055},{"id":"https://openalex.org/keywords/logical-equivalence","display_name":"Logical equivalence","score":0.37040001153945923}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7153000235557556},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.6047000288963318},{"id":"https://openalex.org/C142399903","wikidata":"https://www.wikidata.org/wiki/Q1128796","display_name":"Uncountable set","level":3,"score":0.5922999978065491},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5572999715805054},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.551800012588501},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5200999975204468},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5077999830245972},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.46309998631477356},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45739999413490295},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.4018000066280365},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.37619999051094055},{"id":"https://openalex.org/C70846408","wikidata":"https://www.wikidata.org/wiki/Q220433","display_name":"Logical equivalence","level":3,"score":0.37040001153945923},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36329999566078186},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.35100001096725464},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.3490999937057495},{"id":"https://openalex.org/C204707403","wikidata":"https://www.wikidata.org/wiki/Q1152398","display_name":"Canonical form","level":2,"score":0.3474999964237213},{"id":"https://openalex.org/C89288958","wikidata":"https://www.wikidata.org/wiki/Q7301504","display_name":"Reasoning system","level":2,"score":0.32850000262260437},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3257000148296356},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.30399999022483826},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.29989999532699585},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2906999886035919},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2870999872684479},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C62073222","wikidata":"https://www.wikidata.org/wiki/Q1572108","display_name":"Natural deduction","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C2318724","wikidata":"https://www.wikidata.org/wiki/Q852732","display_name":"Proof theory","level":3,"score":0.27880001068115234},{"id":"https://openalex.org/C203265346","wikidata":"https://www.wikidata.org/wiki/Q11387554","display_name":"Proof assistant","level":3,"score":0.2777999937534332},{"id":"https://openalex.org/C97364631","wikidata":"https://www.wikidata.org/wiki/Q484284","display_name":"Deductive reasoning","level":2,"score":0.27720001339912415},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2768999934196472},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.2741999924182892},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.2720000147819519},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C195324797","wikidata":"https://www.wikidata.org/wiki/Q33742","display_name":"Natural language","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C81721847","wikidata":"https://www.wikidata.org/wiki/Q163468","display_name":"Prolog","level":2,"score":0.26080000400543213}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-032-04167-8_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-04167-8_19","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-04167-8_19.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:10.1007/978-3-032-04167-8_19","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-032-04167-8_19","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-032-04167-8_19.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":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4414589094.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1514247755","https://openalex.org/W1521372188","https://openalex.org/W1608522276","https://openalex.org/W1976836655","https://openalex.org/W2081100183","https://openalex.org/W2135388829","https://openalex.org/W2147340401","https://openalex.org/W2154363390","https://openalex.org/W2757443477","https://openalex.org/W3016306176","https://openalex.org/W3061663726","https://openalex.org/W3210476636","https://openalex.org/W4233253115","https://openalex.org/W4239007999","https://openalex.org/W4386350841","https://openalex.org/W6947822005"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,108],"consider":[2],"the":[3,13,22,80,86,115,129],"reasoning":[4,30,55,116],"problem":[5],"of":[6,15,39,82,85,89,92,105,128,146],"logical":[7],"consequence":[8],"between":[9],"simple":[10,50],"statements":[11,33],"about":[12],"behaviour":[14],"continuous":[16],"functions":[17],"on":[18],"certain":[19],"intervals,":[20],"representing":[21],"way":[23],"that":[24,110],"variables":[25],"influence":[26],"each":[27],"other.":[28],"Automated":[29],"for":[31,53,70,114],"such":[32],"has":[34,134],"applications":[35],"in":[36,42,79],"formal":[37],"modelling":[38],"classroom":[40],"experiments":[41],"natural":[43],"sciences.":[44],"A":[45],"previous":[46],"attempt,":[47],"employing":[48],"a":[49,98],"proof":[51],"system":[52],"this":[54,111],"task,":[56],"is":[57,112],"known":[58],"to":[59,64,67],"be":[60,65],"incomplete":[61],"and":[62,141],"unlikely":[63],"extendable":[66],"obtain":[68],"completeness":[69,123],"arbitrary":[71],"experiments.":[72],"Here":[73],"we":[74],"develop":[75],"an":[76,83,143],"algebraic":[77],"approach":[78,121],"form":[81],"abstraction":[84],"uncountable":[87],"space":[88],"finite":[90],"collections":[91],"continuous,":[93],"real-valued":[94],"functions,":[95],"connected":[96],"by":[97],"composition":[99],"principle,":[100],"into":[101],"finitely":[102],"many":[103],"representatives":[104],"equivalence":[106],"classes.":[107],"show":[109],"sufficient":[113],"task":[117],"at":[118],"hand.":[119],"The":[120],"achieves":[122],"under":[124],"very":[125],"reasonable":[126],"restrictions":[127],"involved":[130],"statements,":[131],"extending":[132],"what":[133],"previously":[135],"been":[136],"achieved":[137],"using":[138],"proof-theoretic":[139],"means,":[140],"yields":[142],"upper":[144],"bound":[145],"coNP.":[147]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
