{"id":"https://openalex.org/W3045221647","doi":"https://doi.org/10.3390/axioms9030084","title":"Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic","display_name":"Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic","publication_year":2020,"publication_date":"2020-07-21","ids":{"openalex":"https://openalex.org/W3045221647","doi":"https://doi.org/10.3390/axioms9030084","mag":"3045221647"},"language":"en","primary_location":{"id":"doi:10.3390/axioms9030084","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms9030084","pdf_url":"https://www.mdpi.com/2075-1680/9/3/84/pdf?version=1595578054","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/9/3/84/pdf?version=1595578054","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060976799","display_name":"Sopo Pkhakadze","orcid":"https://orcid.org/0000-0003-2247-8147"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Sopo Pkhakadze","raw_affiliation_strings":["Knowledge-Based System Group, Institut f\u00fcr Logic and Computation, Technische Universit\u00e4t Wien, Favoritenstra\u00dfe 9-11, 1040 Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0003-2247-8147","affiliations":[{"raw_affiliation_string":"Knowledge-Based System Group, Institut f\u00fcr Logic and Computation, Technische Universit\u00e4t Wien, Favoritenstra\u00dfe 9-11, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073662063","display_name":"Hans Tompits","orcid":"https://orcid.org/0000-0001-5673-2460"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Hans Tompits","raw_affiliation_strings":["Knowledge-Based System Group, Institut f\u00fcr Logic and Computation, Technische Universit\u00e4t Wien, Favoritenstra\u00dfe 9-11, 1040 Vienna, Austria"],"raw_orcid":"https://orcid.org/0000-0001-5673-2460","affiliations":[{"raw_affiliation_string":"Knowledge-Based System Group, Institut f\u00fcr Logic and Computation, Technische Universit\u00e4t Wien, Favoritenstra\u00dfe 9-11, 1040 Vienna, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073662063"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.136,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55248727,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"9","issue":"3","first_page":"84","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":1.0,"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":1.0,"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":0.9984999895095825,"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":0.9955000281333923,"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/default-logic","display_name":"Default logic","score":0.8775618076324463},{"id":"https://openalex.org/keywords/non-monotonic-logic","display_name":"Non-monotonic logic","score":0.8584338426589966},{"id":"https://openalex.org/keywords/sequent","display_name":"Sequent","score":0.6399434804916382},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5107924938201904},{"id":"https://openalex.org/keywords/proof-calculus","display_name":"Proof calculus","score":0.5074769854545593},{"id":"https://openalex.org/keywords/predicate-logic","display_name":"Predicate logic","score":0.5021665096282959},{"id":"https://openalex.org/keywords/circumscription","display_name":"Circumscription","score":0.4815147817134857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4567810297012329},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4410393238067627},{"id":"https://openalex.org/keywords/rule-of-inference","display_name":"Rule of inference","score":0.43548816442489624},{"id":"https://openalex.org/keywords/default","display_name":"Default","score":0.4260086119174957},{"id":"https://openalex.org/keywords/autoepistemic-logic","display_name":"Autoepistemic logic","score":0.4011683166027069},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38919442892074585},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3141440451145172},{"id":"https://openalex.org/keywords/multimodal-logic","display_name":"Multimodal logic","score":0.26690855622291565},{"id":"https://openalex.org/keywords/linear-logic","display_name":"Linear logic","score":0.2662574052810669},{"id":"https://openalex.org/keywords/description-logic","display_name":"Description logic","score":0.26389920711517334},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2545672655105591}],"concepts":[{"id":"https://openalex.org/C160236029","wikidata":"https://www.wikidata.org/wiki/Q842421","display_name":"Default logic","level":5,"score":0.8775618076324463},{"id":"https://openalex.org/C159032336","wikidata":"https://www.wikidata.org/wiki/Q2488768","display_name":"Non-monotonic logic","level":2,"score":0.8584338426589966},{"id":"https://openalex.org/C89421646","wikidata":"https://www.wikidata.org/wiki/Q843632","display_name":"Sequent","level":2,"score":0.6399434804916382},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5107924938201904},{"id":"https://openalex.org/C6489637","wikidata":"https://www.wikidata.org/wiki/Q7250002","display_name":"Proof calculus","level":3,"score":0.5074769854545593},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.5021665096282959},{"id":"https://openalex.org/C62360110","wikidata":"https://www.wikidata.org/wiki/Q96777007","display_name":"Circumscription","level":2,"score":0.4815147817134857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4567810297012329},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4410393238067627},{"id":"https://openalex.org/C3746660","wikidata":"https://www.wikidata.org/wiki/Q1068763","display_name":"Rule of inference","level":2,"score":0.43548816442489624},{"id":"https://openalex.org/C69637215","wikidata":"https://www.wikidata.org/wiki/Q702362","display_name":"Default","level":2,"score":0.4260086119174957},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.4011683166027069},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38919442892074585},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3141440451145172},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.26690855622291565},{"id":"https://openalex.org/C28077239","wikidata":"https://www.wikidata.org/wiki/Q841728","display_name":"Linear logic","level":2,"score":0.2662574052810669},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.26389920711517334},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2545672655105591},{"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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms9030084","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms9030084","pdf_url":"https://www.mdpi.com/2075-1680/9/3/84/pdf?version=1595578054","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:243d1e9f7f42445eada69f5c46b62024","is_oa":true,"landing_page_url":"https://doaj.org/article/243d1e9f7f42445eada69f5c46b62024","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 9, Iss 3, p 84 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/9/3/84/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms9030084","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 9; Issue 3; Pages: 84","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms9030084","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms9030084","pdf_url":"https://www.mdpi.com/2075-1680/9/3/84/pdf?version=1595578054","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4699999988079071}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3045221647.pdf","grobid_xml":"https://content.openalex.org/works/W3045221647.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W3296631","https://openalex.org/W12673449","https://openalex.org/W44518539","https://openalex.org/W82724731","https://openalex.org/W185205532","https://openalex.org/W1492502874","https://openalex.org/W1533523731","https://openalex.org/W1566498025","https://openalex.org/W1573063610","https://openalex.org/W1586926492","https://openalex.org/W1668477564","https://openalex.org/W1802022415","https://openalex.org/W1966552757","https://openalex.org/W1992852948","https://openalex.org/W1997929764","https://openalex.org/W2000863621","https://openalex.org/W2013153283","https://openalex.org/W2016171120","https://openalex.org/W2016237468","https://openalex.org/W2017977375","https://openalex.org/W2019738341","https://openalex.org/W2027047567","https://openalex.org/W2027980228","https://openalex.org/W2039977878","https://openalex.org/W2074656184","https://openalex.org/W2076698873","https://openalex.org/W2078926321","https://openalex.org/W2082253949","https://openalex.org/W2085956853","https://openalex.org/W2101932158","https://openalex.org/W2146658047","https://openalex.org/W2149153440","https://openalex.org/W2155322595","https://openalex.org/W2175268987","https://openalex.org/W2188982370","https://openalex.org/W2914398864","https://openalex.org/W2945259913","https://openalex.org/W2989366559","https://openalex.org/W3020913839","https://openalex.org/W4229938980","https://openalex.org/W4249259371","https://openalex.org/W4251401320","https://openalex.org/W6607905022","https://openalex.org/W6750961868","https://openalex.org/W6977246978","https://openalex.org/W7045584002"],"related_works":["https://openalex.org/W2044503422","https://openalex.org/W610916638","https://openalex.org/W2008106366","https://openalex.org/W2009976639","https://openalex.org/W1526931790","https://openalex.org/W290319452","https://openalex.org/W2087561262","https://openalex.org/W62879400","https://openalex.org/W2005957522","https://openalex.org/W1545424768"],"abstract_inverted_index":{"Default":[0],"logic":[1,101,126,130,135],"is":[2,47,178,187],"one":[3,96],"of":[4,22,90,124,146,160,174,181,192,208,224,229],"the":[5,20,29,32,65,95,107,132,137,179,200,206,226],"basic":[6],"formalisms":[7],"for":[8,77,87,98,110,171,218],"nonmonotonic":[9,45,58,209],"reasoning,":[10],"a":[11,73,144,184,193,215],"well-established":[12],"area":[13],"from":[14],"logic-based":[15],"artificial":[16],"intelligence":[17],"dealing":[18,71],"with":[19,72],"representation":[21],"rational":[23],"conclusions,":[24],"which":[25,54,177,213],"are":[26,55],"characterised":[27],"by":[28,142,211],"feature":[30],"that":[31],"inference":[33,52],"process":[34],"may":[35],"require":[36],"to":[37,50,103,115,155],"retract":[38],"prior":[39],"conclusions":[40],"given":[41,185,194],"additional":[42],"premisses.":[43],"This":[44],"aspect":[46],"in":[48,64,148,189,205],"contrast":[49],"valid":[51],"relations,":[53],"monotonic.":[56],"Although":[57],"reasoning":[59,170,210],"has":[60],"been":[61,153],"extensively":[62],"studied":[63],"literature,":[66],"only":[67],"few":[68],"works":[69],"exist":[70],"proper":[74],"proof":[75],"theory":[76],"specific":[78],"logics.":[79],"In":[80],"this":[81],"paper,":[82],"we":[83,166],"introduce":[84,167],"sequent-type":[85],"calculi":[86,165],"two":[88],"variants":[89],"default":[91,100,112,125,162,175,195],"logic,":[92,113,176],"viz.,":[93],"on":[94,106],"hand,":[97,109],"three-valued":[99,129],"due":[102,114],"Radzikowska,":[104],"and":[105,119,136],"other":[108],"disjunctive":[111],"Gelfond,":[116],"Lifschitz,":[117],"Przymusinska,":[118],"Truszczy\u0144ski.":[120],"The":[121,164],"first":[122,203],"variant":[123,139],"employs":[127,214],"\u0141ukasiewicz\u2019s":[128],"as":[131],"underlying":[133],"base":[134],"second":[138],"generalises":[140],"defaults":[141],"allowing":[143],"selection":[145],"consequents":[147],"defaults.":[149,230],"Both":[150],"versions":[151,173],"have":[152],"introduced":[154,204],"address":[156],"certain":[157],"representational":[158],"shortcomings":[159],"standard":[161],"logic.":[163],"axiomatise":[168],"brave":[169],"these":[172],"task":[180],"determining":[182],"whether":[183],"formula":[186],"contained":[188],"some":[190],"extension":[191],"theory.":[196],"Our":[197],"approach":[198],"follows":[199],"sequent":[201],"method":[202],"context":[207],"Bonatti,":[212],"rejection":[216],"calculus":[217],"axiomatising":[219],"invalid":[220],"formulas,":[221],"taking":[222],"care":[223],"expressing":[225],"consistency":[227],"condition":[228]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2020-07-29T00:00:00"}