{"id":"https://openalex.org/W2002128996","doi":"https://doi.org/10.5220/0005073700370052","title":"An Order Hyperresolution Calculus for G\u00f6del Logic with Truth Constants","display_name":"An Order Hyperresolution Calculus for G\u00f6del Logic with Truth Constants","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2002128996","doi":"https://doi.org/10.5220/0005073700370052","mag":"2002128996"},"language":"en","primary_location":{"id":"doi:10.5220/0005073700370052","is_oa":false,"landing_page_url":"https://doi.org/10.5220/0005073700370052","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the International Conference on Fuzzy Computation Theory and Applications","raw_type":"proceedings-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/A5083703034","display_name":"Du\u0161an Guller","orcid":"https://orcid.org/0000-0002-6854-240X"},"institutions":[{"id":"https://openalex.org/I4210153803","display_name":"Trencianska Univerzita Alexandra Dubceka V Trencine","ror":"https://ror.org/04v8db398","country_code":"SK","type":"education","lineage":["https://openalex.org/I4210153803"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"Du\u0161an Guller","raw_affiliation_strings":["Alexander Dub\u010dek University of Tren\u010d\u00edn, Slovak Republic"],"affiliations":[{"raw_affiliation_string":"Alexander Dub\u010dek University of Tren\u010d\u00edn, Slovak Republic","institution_ids":["https://openalex.org/I4210153803"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5083703034"],"corresponding_institution_ids":["https://openalex.org/I4210153803"],"apc_list":null,"apc_paid":null,"fwci":0.7122,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.70506036,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"37","last_page":"52"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9986000061035156,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9986000061035156,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9966999888420105,"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":0.9829000234603882,"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/mathematics","display_name":"Mathematics","score":0.6660264730453491},{"id":"https://openalex.org/keywords/countable-set","display_name":"Countable set","score":0.6566945910453796},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.6555838584899902},{"id":"https://openalex.org/keywords/infimum-and-supremum","display_name":"Infimum and supremum","score":0.6070056557655334},{"id":"https://openalex.org/keywords/first-order-logic","display_name":"First-order logic","score":0.5134116411209106},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.4802411198616028},{"id":"https://openalex.org/keywords/truth-value","display_name":"Truth value","score":0.4598802328109741},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4571118652820587},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45633429288864136},{"id":"https://openalex.org/keywords/second-order-logic","display_name":"Second-order logic","score":0.44824865460395813},{"id":"https://openalex.org/keywords/truth-function","display_name":"Truth function","score":0.4348345994949341},{"id":"https://openalex.org/keywords/higher-order-logic","display_name":"Higher-order logic","score":0.37518587708473206},{"id":"https://openalex.org/keywords/propositional-calculus","display_name":"Propositional calculus","score":0.1927388310432434},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16782337427139282},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09366539120674133},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09122982621192932},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.09018811583518982}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6660264730453491},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.6566945910453796},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.6555838584899902},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.6070056557655334},{"id":"https://openalex.org/C100481476","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"First-order logic","level":2,"score":0.5134116411209106},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.4802411198616028},{"id":"https://openalex.org/C46274116","wikidata":"https://www.wikidata.org/wiki/Q185521","display_name":"Truth value","level":2,"score":0.4598802328109741},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4571118652820587},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45633429288864136},{"id":"https://openalex.org/C144791301","wikidata":"https://www.wikidata.org/wiki/Q1548746","display_name":"Second-order logic","level":4,"score":0.44824865460395813},{"id":"https://openalex.org/C37754750","wikidata":"https://www.wikidata.org/wiki/Q913874","display_name":"Truth function","level":3,"score":0.4348345994949341},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.37518587708473206},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.1927388310432434},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16782337427139282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09366539120674133},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09122982621192932},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.09018811583518982},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.5220/0005073700370052","is_oa":false,"landing_page_url":"https://doi.org/10.5220/0005073700370052","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the International Conference on Fuzzy Computation Theory and Applications","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.5400000214576721,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2116215193","https://openalex.org/W4387318785","https://openalex.org/W2142816242","https://openalex.org/W4229335084","https://openalex.org/W316780827","https://openalex.org/W1981373951","https://openalex.org/W1580672106","https://openalex.org/W4388397425","https://openalex.org/W3101683417","https://openalex.org/W1855588255"],"abstract_inverted_index":{"We":[0,23,38,115],"have":[1],"generalised":[2],"the":[3,8,13,28,40,86,118,123,126,133,170],"well-known":[4],"hyperresolution":[5,29,144],"principle":[6],"to":[7,65],"first-order":[9,41,127],"G\u00a8odel":[10,42,128],"logic":[11,43,129],"for":[12,31,150,159],"general\r\n\r\ncase.":[14],"This":[15],"paper":[16],"is":[17,58,79,93,130,146],"a":[18,25,45,63,80,94,151],"continuation":[19],"of":[20,27,47,62,73,85,125,163],"our":[21],"work.":[22],"propose":[24],"modification":[26],"calculus\r\n\r\nsuitable":[30],"automated":[32],"deduction":[33],"with":[34],"explicit":[35],"partial":[36],"truth.":[37],"expand":[39],"by":[44,105,132,140],"countable\r\n\r\nset":[46],"intermediate":[48],"truth":[49,136,166],"constants":[50,137,167],"\u00af":[51],"c,":[52],"c":[53],"2":[54],"(0;1).":[55],"Our":[56],"approach":[57],"based":[59],"on":[60,112],"translation":[61],"formula":[64],"an\r\n\r\nequivalent":[66],"satisfiable":[67],"finite":[68,81],"order":[69,74,77,83,111,153],"clausal":[70,154],"theory,":[71],"consisting":[72],"clauses.":[75],"An":[76],"clause":[78],"set\r\n\r\nof":[82],"literals":[84],"form":[87],"e1":[88],"\u25c7":[89,92],"e2":[90],"where":[91,122],"connective":[95],"either":[96],"\u2256":[97,100],"or":[98],"\u227a.":[99],"and":[101,107,161],"\u227a":[102],"are":[103,138],"interpreted":[104,139],"the\r\n\r\nequality":[106],"standard":[108,134],"strict":[109],"linear":[110],"[0;1],":[113],"respectively.":[114],"shall":[116],"investigate":[117],"so-called":[119],"canonical\r\n\r\nstandard":[120],"completeness,":[121],"semantics":[124],"given":[131],"G-algebra\r\n\r\nand":[135],"themselves.":[141],"The":[142],"modified":[143],"calculus":[145],"refutation":[147],"sound\r\n\r\nand":[148],"complete":[149],"countable":[152],"theory":[155],"under":[156],"certain":[157],"condition":[158],"suprema":[160],"infima":[162],"sets":[164],"of\r\n\r\nthe":[165],"occurring":[168],"in":[169],"theory.":[171]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}