{"id":"https://openalex.org/W1575418955","doi":"https://doi.org/10.1007/978-3-642-13824-9_1","title":"Entailment Multipliers: An Algebraic Characterization of Validity for Classical and Modal Logics","display_name":"Entailment Multipliers: An Algebraic Characterization of Validity for Classical and Modal Logics","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1575418955","doi":"https://doi.org/10.1007/978-3-642-13824-9_1","mag":"1575418955"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-13824-9_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-13824-9_1","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024395125","display_name":"Marcelo Finger","orcid":"https://orcid.org/0000-0002-1391-1175"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]},{"id":"https://openalex.org/I4210092357","display_name":"Institute of Mathematics and Computer Science","ror":"https://ror.org/00fy4at53","country_code":"MD","type":"facility","lineage":["https://openalex.org/I112090838","https://openalex.org/I4210092357"]}],"countries":["BR","MD"],"is_corresponding":false,"raw_author_name":"Marcelo Finger","raw_affiliation_strings":["Department of Computer Science, Institute of Mathematics and Statistics, University of Sao Paulo,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Institute of Mathematics and Statistics, University of Sao Paulo,","institution_ids":["https://openalex.org/I4210092357","https://openalex.org/I17974374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057859482","display_name":"Mauricio S. C. Hernandes","orcid":null},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]},{"id":"https://openalex.org/I4210092357","display_name":"Institute of Mathematics and Computer Science","ror":"https://ror.org/00fy4at53","country_code":"MD","type":"facility","lineage":["https://openalex.org/I112090838","https://openalex.org/I4210092357"]}],"countries":["BR","MD"],"is_corresponding":false,"raw_author_name":"Mauricio S. C. Hernandes","raw_affiliation_strings":["Department of Computer Science, Institute of Mathematics and Statistics, University of Sao Paulo,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Institute of Mathematics and Statistics, University of Sao Paulo,","institution_ids":["https://openalex.org/I4210092357","https://openalex.org/I17974374"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.285,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56542198,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"18"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9987999796867371,"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":0.9979000091552734,"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/logical-consequence","display_name":"Logical consequence","score":0.7946760654449463},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5805130004882812},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.5783279538154602},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.534112274646759},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4834659695625305},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.4746951460838318},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4519391655921936},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4324095547199249},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.392880380153656},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3366572856903076},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31080162525177},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.25055232644081116},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17463231086730957}],"concepts":[{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.7946760654449463},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5805130004882812},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.5783279538154602},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.534112274646759},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4834659695625305},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.4746951460838318},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4519391655921936},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4324095547199249},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.392880380153656},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3366572856903076},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31080162525177},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.25055232644081116},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17463231086730957},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-13824-9_1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-13824-9_1","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W166015792","https://openalex.org/W1016912189","https://openalex.org/W1596067335","https://openalex.org/W1968655942","https://openalex.org/W1991138028","https://openalex.org/W2011039300","https://openalex.org/W2037434830","https://openalex.org/W2063416709","https://openalex.org/W2156265441","https://openalex.org/W2163846023","https://openalex.org/W2323554188","https://openalex.org/W2609942030","https://openalex.org/W2610670723","https://openalex.org/W2908436493","https://openalex.org/W4211144022","https://openalex.org/W4241764762","https://openalex.org/W4242309855","https://openalex.org/W4244913272","https://openalex.org/W4285719527","https://openalex.org/W4388397150"],"related_works":["https://openalex.org/W2487444950","https://openalex.org/W2250460949","https://openalex.org/W2055243143","https://openalex.org/W2811486295","https://openalex.org/W2071098659","https://openalex.org/W12963412","https://openalex.org/W2980673234","https://openalex.org/W4388313856","https://openalex.org/W2784994561","https://openalex.org/W1969574412"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
