{"id":"https://openalex.org/W1549066371","doi":"https://doi.org/10.1007/bfb0012821","title":"Elements of Z-module reasoning","display_name":"Elements of Z-module reasoning","publication_year":2005,"publication_date":"2005-11-23","ids":{"openalex":"https://openalex.org/W1549066371","doi":"https://doi.org/10.1007/bfb0012821","mag":"1549066371"},"language":"en","primary_location":{"id":"doi:10.1007/bfb0012821","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0012821","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/A5110240649","display_name":"Tie Cheng Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210156228","display_name":"Kestrel Institute","ror":"https://ror.org/04deyvw92","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210156228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tie Cheng Wang","raw_affiliation_strings":["Kestrel Institute, 1801 Page Mill Road, 94304, Palo Alto, CA","Kestrel Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Kestrel Institute, 1801 Page Mill Road, 94304, Palo Alto, CA","institution_ids":["https://openalex.org/I4210156228"]},{"raw_affiliation_string":"Kestrel Institute","institution_ids":["https://openalex.org/I4210156228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110240649"],"corresponding_institution_ids":["https://openalex.org/I4210156228"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.08139391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"21","last_page":"40"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998999834060669,"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/T10126","display_name":"Logic, programming, and type systems","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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9987000226974487,"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":0.9973999857902527,"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/soundness","display_name":"Soundness","score":0.7802313566207886},{"id":"https://openalex.org/keywords/automated-theorem-proving","display_name":"Automated theorem proving","score":0.6290654540061951},{"id":"https://openalex.org/keywords/automated-reasoning","display_name":"Automated reasoning","score":0.5901765823364258},{"id":"https://openalex.org/keywords/axiom","display_name":"Axiom","score":0.5538248419761658},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5240048170089722},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.4908340573310852},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48718327283859253},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.4774613678455353},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4452989101409912},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44000160694122314},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4199448227882385},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41896387934684753},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3997917175292969},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39184993505477905},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.3231356143951416},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.20545372366905212}],"concepts":[{"id":"https://openalex.org/C39920170","wikidata":"https://www.wikidata.org/wiki/Q693083","display_name":"Soundness","level":2,"score":0.7802313566207886},{"id":"https://openalex.org/C206880738","wikidata":"https://www.wikidata.org/wiki/Q431667","display_name":"Automated theorem proving","level":2,"score":0.6290654540061951},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.5901765823364258},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.5538248419761658},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5240048170089722},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.4908340573310852},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48718327283859253},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.4774613678455353},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4452989101409912},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44000160694122314},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4199448227882385},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41896387934684753},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3997917175292969},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39184993505477905},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3231356143951416},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20545372366905212},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bfb0012821","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bfb0012821","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":15,"referenced_works":["https://openalex.org/W150491715","https://openalex.org/W959963806","https://openalex.org/W1538534850","https://openalex.org/W1973465924","https://openalex.org/W1975303053","https://openalex.org/W2016316314","https://openalex.org/W2023139438","https://openalex.org/W2032703874","https://openalex.org/W2033288425","https://openalex.org/W2069663616","https://openalex.org/W2092133382","https://openalex.org/W2093918239","https://openalex.org/W2913781829","https://openalex.org/W4255937913","https://openalex.org/W6632099168"],"related_works":["https://openalex.org/W13634261","https://openalex.org/W4250462479","https://openalex.org/W3163509751","https://openalex.org/W958050847","https://openalex.org/W2396405675","https://openalex.org/W175051304","https://openalex.org/W4402823833","https://openalex.org/W1549730417","https://openalex.org/W1548499332","https://openalex.org/W1994524667"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
