{"id":"https://openalex.org/W2071490614","doi":"https://doi.org/10.1080/11663081.1993.10510808","title":"Herbrand style proof procedures for modal logic","display_name":"Herbrand style proof procedures for modal logic","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W2071490614","doi":"https://doi.org/10.1080/11663081.1993.10510808","mag":"2071490614"},"language":"en","primary_location":{"id":"doi:10.1080/11663081.1993.10510808","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.1993.10510808","pdf_url":null,"source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"},"type":"article","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/A5013807767","display_name":"Marta Cialdea Mayer","orcid":"https://orcid.org/0000-0003-4692-4922"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Marta Cialdea","raw_affiliation_strings":["Dipartimento di Informatica e Sistemistica , Universit\u00e0 di Roma \u201cLa Sapienza\u201d , Via Salaria, 113, 00198 , Roma , Italy","Dipartimento di Informatica e Sistemistica , Universit\u00e0 di Roma \u201cLa Sapienza\u201d , Via Salaria 113, 00198 , Roma , Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Informatica e Sistemistica , Universit\u00e0 di Roma \u201cLa Sapienza\u201d , Via Salaria, 113, 00198 , Roma , Italy","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"Dipartimento di Informatica e Sistemistica , Universit\u00e0 di Roma \u201cLa Sapienza\u201d , Via Salaria 113, 00198 , Roma , Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013807767"],"corresponding_institution_ids":["https://openalex.org/I861853513"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.16537905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"3","issue":"2","first_page":"205","last_page":"223"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9977999925613403,"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":0.9970999956130981,"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/modal","display_name":"Modal","score":0.6862574815750122},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.6841784715652466},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6282855868339539},{"id":"https://openalex.org/keywords/unification","display_name":"Unification","score":0.6120880246162415},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5806854963302612},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5724328756332397},{"id":"https://openalex.org/keywords/normal-modal-logic","display_name":"Normal modal logic","score":0.5510894060134888},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.46648719906806946},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.4581332504749298},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.45721009373664856},{"id":"https://openalex.org/keywords/modal-operator","display_name":"Modal operator","score":0.43522393703460693},{"id":"https://openalex.org/keywords/sequent-calculus","display_name":"Sequent calculus","score":0.42728516459465027},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3979816138744354},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30574652552604675},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3030427098274231},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30145585536956787},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10809531807899475},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.10684704780578613}],"concepts":[{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.6862574815750122},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.6841784715652466},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6282855868339539},{"id":"https://openalex.org/C96146094","wikidata":"https://www.wikidata.org/wiki/Q609057","display_name":"Unification","level":2,"score":0.6120880246162415},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5806854963302612},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5724328756332397},{"id":"https://openalex.org/C114092440","wikidata":"https://www.wikidata.org/wiki/Q840226","display_name":"Normal modal logic","level":4,"score":0.5510894060134888},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.46648719906806946},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.4581332504749298},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.45721009373664856},{"id":"https://openalex.org/C78344899","wikidata":"https://www.wikidata.org/wiki/Q638442","display_name":"Modal operator","level":4,"score":0.43522393703460693},{"id":"https://openalex.org/C65880906","wikidata":"https://www.wikidata.org/wiki/Q1771121","display_name":"Sequent calculus","level":3,"score":0.42728516459465027},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3979816138744354},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30574652552604675},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3030427098274231},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30145585536956787},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10809531807899475},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.10684704780578613},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/11663081.1993.10510808","is_oa":false,"landing_page_url":"https://doi.org/10.1080/11663081.1993.10510808","pdf_url":null,"source":{"id":"https://openalex.org/S93822064","display_name":"Journal of Applied Non-Classical Logics","issn_l":"1166-3081","issn":["1166-3081","1958-5780"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Non-Classical Logics","raw_type":"journal-article"},{"id":"pmh:oai:iris.uniroma3.it:11590/144811","is_oa":false,"landing_page_url":"http://hdl.handle.net/11590/144811","pdf_url":null,"source":{"id":"https://openalex.org/S4377196120","display_name":"Iris (Roma Tre University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119003972","host_organization_name":"Roma Tre University","host_organization_lineage":["https://openalex.org/I119003972"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1509336422","https://openalex.org/W1582842241","https://openalex.org/W1589748966","https://openalex.org/W1939483552","https://openalex.org/W2022447345","https://openalex.org/W2039977878","https://openalex.org/W2099036216","https://openalex.org/W2104524304","https://openalex.org/W2121609151","https://openalex.org/W2127129973","https://openalex.org/W2163751633","https://openalex.org/W2977904728","https://openalex.org/W3039529476"],"related_works":["https://openalex.org/W4253113110","https://openalex.org/W2096191306","https://openalex.org/W2617588251","https://openalex.org/W4210342219","https://openalex.org/W2753667555","https://openalex.org/W2793924652","https://openalex.org/W2989759971","https://openalex.org/W4391818465","https://openalex.org/W1490031414","https://openalex.org/W2949019224"],"abstract_inverted_index":{"ABSTRACT":[0],"In":[1,58],"this":[2],"paper":[3],"we":[4],"state":[5],"and":[6,16,102,147],"prove":[7,140],"Herbrand's":[8],"properties":[9,34],"for":[10,24,52,81],"two":[11],"modal":[12,56,84,156],"systems,":[13],"namely":[14],"T":[15,101],"S4,":[17,103],"thus":[18],"adapting":[19],"a":[20,68,76,90,117],"previous":[21],"result":[22],"obtained":[23,86],"the":[25,36,40,45,53,60,73,96,113,120,129,133,141,151,154,164],"system":[26],"D":[27],"[CIA":[28,43],"86a]":[29],"to":[30,139],"such":[31,116],"theories.":[32],"These":[33],"allow":[35],"first":[37],"order":[38],"extension\u2014along":[39],"lines":[41],"of":[42,75,79,89,112,122,150,153,160],"91]\u2014of":[44],"resolution":[46],"method":[47],"defined":[48],"in":[49,67,115,132,158],"[ENJ":[50],"86]":[51],"corresponding":[54],"propositional":[55,110],"systems.":[57,135],"fact,":[59],"Herbrand-style":[61],"procedures":[62],"proposed":[63],"here":[64],"treat":[65],"quantifiers":[66],"uniform":[69],"way,":[70],"that":[71,119],"suggests":[72],"definition":[74],"restricted":[77],"notion":[78],"unification":[80],"quantifier":[82,123],"free":[83],"formulae":[85],"by":[87,108],"means":[88],"Skolem-like":[91],"procedure.":[92],"The":[93,136],"differences":[94],"among":[95],"three":[97],"systems":[98],"considered,":[99],"D,":[100],"are":[104,144],"taken":[105],"into":[106],"account":[107],"preliminary":[109],"transformations":[111],"formulae,":[114],"way":[118],"problem":[121],"elimination":[124,166],"can":[125],"be":[126],"treated":[127],"within":[128],"same":[130],"pattern":[131],"different":[134],"methods":[137],"employed":[138],"fundamental":[142],"theorems":[143],"purely":[145],"proof-theoretical":[146],"make":[148],"use":[149],"formalization":[152],"considered":[155],"theories":[157],"terms":[159],"sequent":[161],"calculi,":[162],"where":[163],"cut":[165],"theorem":[167],"holds.":[168]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
