{"id":"https://openalex.org/W1869961429","doi":"https://doi.org/10.1007/bfb0012869","title":"Single axioms in the implicational propositional calculus","display_name":"Single axioms in the implicational propositional calculus","publication_year":2005,"publication_date":"2005-11-23","ids":{"openalex":"https://openalex.org/W1869961429","doi":"https://doi.org/10.1007/bfb0012869","mag":"1869961429"},"language":"en","primary_location":{"id":"doi:10.1007/bfb0012869","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0012869","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":"conference-paper","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/A5021476649","display_name":"Frank Pfenning","orcid":"https://orcid.org/0000-0002-8279-5817"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Frank Pfenning","raw_affiliation_strings":["Department of Computer Science, Carnegie Mellon University, 15213-3890, Pittsburgh, Pa","Dept. of Computer Science, Carnegie Mellon University, Pittsburgh"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Carnegie Mellon University, 15213-3890, Pittsburgh, Pa","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Dept. of Computer Science, Carnegie Mellon University, Pittsburgh","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5021476649"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.2465,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.49981398,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"710","last_page":"713"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9951000213623047,"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":0.9951000213623047,"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":0.9714000225067139,"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":0.9580000042915344,"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/propositional-variable","display_name":"Propositional variable","score":0.8677888512611389},{"id":"https://openalex.org/keywords/propositional-formula","display_name":"Propositional formula","score":0.7717485427856445},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.7414842844009399},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.721940815448761},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.6639294624328613},{"id":"https://openalex.org/keywords/well-formed-formula","display_name":"Well-formed formula","score":0.632180392742157},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.47839128971099854},{"id":"https://openalex.org/keywords/zeroth-order-logic","display_name":"Zeroth-order logic","score":0.46281683444976807},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4315350651741028},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36093151569366455},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34518760442733765},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2822504937648773},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.22828787565231323},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18141227960586548},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11527076363563538},{"id":"https://openalex.org/keywords/intermediate-logic","display_name":"Intermediate logic","score":0.0708400309085846},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.04325100779533386},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.0419444739818573},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.039121001958847046}],"concepts":[{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.8677888512611389},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.7717485427856445},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.7414842844009399},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.721940815448761},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.6639294624328613},{"id":"https://openalex.org/C191222856","wikidata":"https://www.wikidata.org/wiki/Q655328","display_name":"Well-formed formula","level":5,"score":0.632180392742157},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47839128971099854},{"id":"https://openalex.org/C110039528","wikidata":"https://www.wikidata.org/wiki/Q8069651","display_name":"Zeroth-order logic","level":4,"score":0.46281683444976807},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4315350651741028},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36093151569366455},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34518760442733765},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2822504937648773},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.22828787565231323},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18141227960586548},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11527076363563538},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.0708400309085846},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.04325100779533386},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0419444739818573},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.039121001958847046},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bfb0012869","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0012869","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.149.9581","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.9581","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.cmu.edu/afs/cs/user/fp/www/papers/cade88.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6600000262260437,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W2801726006"],"related_works":["https://openalex.org/W4251854500","https://openalex.org/W1987118140","https://openalex.org/W1975118984","https://openalex.org/W229834379","https://openalex.org/W2504237466","https://openalex.org/W2045432969","https://openalex.org/W2990043628","https://openalex.org/W2364305935","https://openalex.org/W1834198313","https://openalex.org/W1540121401"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}