{"id":"https://openalex.org/W2078440864","doi":"https://doi.org/10.2478/v10037-011-0026-1","title":"Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms","display_name":"Definition of First Order Language with Arbitrary Alphabet. Syntax of Terms, Atomic Formulas and their Subterms","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2078440864","doi":"https://doi.org/10.2478/v10037-011-0026-1","mag":"2078440864"},"language":"en","primary_location":{"id":"doi:10.2478/v10037-011-0026-1","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0026-1","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-011-0026-1","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://sciendo.com/pdf/10.2478/v10037-011-0026-1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013198849","display_name":"Marco B. Caminati","orcid":"https://orcid.org/0000-0002-4529-5442"},"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":"Marco Caminati","raw_affiliation_strings":["Mathematics Department \"G.Castelnuovo\" Sapienza University of Rome Piazzale Aldo Moro 5, 00185 Roma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department \"G.Castelnuovo\" Sapienza University of Rome Piazzale Aldo Moro 5, 00185 Roma, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013198849"],"corresponding_institution_ids":["https://openalex.org/I861853513"],"apc_list":null,"apc_paid":null,"fwci":1.1917,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79375424,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9958000183105469,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9865999817848206,"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/alphabet","display_name":"Alphabet","score":0.6713948249816895},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.6244033575057983},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5550146102905273},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.527695894241333},{"id":"https://openalex.org/keywords/syntax","display_name":"Syntax","score":0.5054116249084473},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.45422935485839844},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4057609736919403},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38837718963623047},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.2997511625289917},{"id":"https://openalex.org/keywords/natural-language-processing","display_name":"Natural language processing","score":0.18029701709747314},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15193399786949158}],"concepts":[{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6713948249816895},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.6244033575057983},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5550146102905273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.527695894241333},{"id":"https://openalex.org/C60048249","wikidata":"https://www.wikidata.org/wiki/Q37437","display_name":"Syntax","level":2,"score":0.5054116249084473},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.45422935485839844},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4057609736919403},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38837718963623047},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.2997511625289917},{"id":"https://openalex.org/C204321447","wikidata":"https://www.wikidata.org/wiki/Q30642","display_name":"Natural language processing","level":1,"score":0.18029701709747314},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15193399786949158},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2478/v10037-011-0026-1","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0026-1","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-011-0026-1","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3613","is_oa":true,"landing_page_url":"http://hdl.handle.net/11320/3613","pdf_url":"https://repozytorium.uwb.edu.pl/jspui/bitstream/11320/3613/1/v10037-011-0026-1.pdf","source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:c5b1ce50d9004733adb96ac70ae62497","is_oa":false,"landing_page_url":"https://doaj.org/article/c5b1ce50d9004733adb96ac70ae62497","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 19, Iss 3, Pp 169-178 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.2478/v10037-011-0026-1","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0026-1","pdf_url":"https://sciendo.com/pdf/10.2478/v10037-011-0026-1","source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.44999998807907104,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2078440864.pdf","grobid_xml":"https://content.openalex.org/works/W2078440864.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W22141270","https://openalex.org/W180239714","https://openalex.org/W260340778","https://openalex.org/W1574512757","https://openalex.org/W1974420731","https://openalex.org/W2035381591","https://openalex.org/W2105559527","https://openalex.org/W2150348213","https://openalex.org/W2153830101","https://openalex.org/W2163641194","https://openalex.org/W2296232473","https://openalex.org/W2304533832","https://openalex.org/W4285719527","https://openalex.org/W4300622081"],"related_works":["https://openalex.org/W2074481494","https://openalex.org/W2808006995","https://openalex.org/W4250156143","https://openalex.org/W4247156967","https://openalex.org/W4388713123","https://openalex.org/W3194438104","https://openalex.org/W582626623","https://openalex.org/W4240940369","https://openalex.org/W4298850403","https://openalex.org/W2808496111"],"abstract_inverted_index":{"Definition":[0],"of":[1,9,16,19,40,47,71,118,123,125,164,171],"First":[2],"Order":[3],"Language":[4],"with":[5,102,179],"Arbitrary":[6],"Alphabet.":[7],"Syntax":[8],"Terms,":[10],"Atomic":[11],"Formulas":[12],"and":[13,49,78,120,153,161],"their":[14,112],"SubtermsSecond":[15],"a":[17,37,45,50,65,100,103,126,188],"series":[18],"articles":[20],"laying":[21],"down":[22],"the":[23,53,69,72,83,106,134,150,154,162,198],"bases":[24],"for":[25,52,60,138],"classical":[26],"first":[27],"order":[28],"model":[29],"theory.":[30],"A":[31],"language":[32,66,127],"is":[33,67,76,88,114,145,167,174,187,193],"defined":[34],"basically":[35],"as":[36,131],"tuple":[38,62],"made":[39],"an":[41],"integer-valued":[42],"function":[43],"(adicity),":[44],"symbol":[46,51],"equality":[48],"NOR":[54],"logical":[55],"connective.":[56],"The":[57,169],"only":[58],"requests":[59],"this":[61,144],"to":[63,111,176,181,195],"be":[64,93,177],"that":[68,79,185],"value":[70],"adicity":[73,113],"in":[74,86,159],"=":[75],"-2":[77],"its":[80],"preimage":[81],"(i.e.":[82],"variables":[84],"set)":[85],"0":[87],"infinite.":[89],"Existential":[90],"quantification":[91],"will":[92],"rendered":[94],"(see":[95,137],"[11])":[96],"by":[97,148],"mere":[98],"prefixing":[99],"formula":[101],"letter.":[104],"Then":[105],"hierarchy":[107],"among":[108],"symbols":[109,124],"according":[110],"introduced,":[115],"taking":[116],"advantage":[117],"attributes":[119],"clusters.The":[121],"strings":[122],"are":[128],"depth-recursively":[129],"classified":[130],"terms":[132,173],"using":[133],"standard":[135],"approach":[136],"example":[139],"[16],":[140],"definition":[141],"1.1.2);":[142],"technically,":[143],"done":[146],"here":[147],"deploying":[149],"\u2018-multiCat'":[151],"functor":[152],"\u2018unambiguous\u2019":[155],"attribute":[156],"previously":[157],"introduced":[158],"[10],":[160],"set":[163,170],"atomic":[165],"formulas":[166],"introduced.":[168],"all":[172],"shown":[175],"unambiguous":[178],"respect":[180],"concatenation;":[182],"we":[183],"say":[184],"it":[186],"prefix":[189],"set.":[190],"This":[191],"fact":[192],"exploited":[194],"uniquely":[196],"define":[197],"subterms":[199]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2016-06-24T00:00:00"}