{"id":"https://openalex.org/W2294527179","doi":"https://doi.org/10.1017/s1471068415000277","title":"A denotational semantics for equilibrium logic","display_name":"A denotational semantics for equilibrium logic","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W2294527179","doi":"https://doi.org/10.1017/s1471068415000277","mag":"2294527179"},"language":"en","primary_location":{"id":"doi:10.1017/s1471068415000277","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1471068415000277","pdf_url":null,"source":{"id":"https://openalex.org/S59670734","display_name":"Theory and Practice of Logic Programming","issn_l":"1471-0684","issn":["1471-0684","1475-3081"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory and Practice of Logic Programming","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1507.06915","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066461040","display_name":"Felicidad Aguado","orcid":"https://orcid.org/0000-0002-4334-9267"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"FELICIDAD AGUADO","raw_affiliation_strings":["Department of Computer Science, University of Corunna, SPAIN (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Corunna, SPAIN (e-mail:","institution_ids":["https://openalex.org/I11019714"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028323744","display_name":"Pedro Cabalar","orcid":"https://orcid.org/0000-0001-7440-0953"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"PEDRO CABALAR","raw_affiliation_strings":["Department of Computer Science, University of Corunna, SPAIN (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Corunna, SPAIN (e-mail:","institution_ids":["https://openalex.org/I11019714"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072844178","display_name":"David Pearce","orcid":"https://orcid.org/0000-0001-7407-326X"},"institutions":[{"id":"https://openalex.org/I88060688","display_name":"Universidad Polit\u00e9cnica de Madrid","ror":"https://ror.org/03n6nwv02","country_code":"ES","type":"education","lineage":["https://openalex.org/I88060688"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"DAVID PEARCE","raw_affiliation_strings":["Universidad Polit\u00e9cnica de Madrid, SPAIN (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidad Polit\u00e9cnica de Madrid, SPAIN (e-mail:","institution_ids":["https://openalex.org/I88060688"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036317121","display_name":"Gilberto P\u00e9rez","orcid":"https://orcid.org/0000-0001-6269-6101"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"GILBERTO P\u00c9REZ","raw_affiliation_strings":["Department of Computer Science, University of Corunna, SPAIN (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Corunna, SPAIN (e-mail:","institution_ids":["https://openalex.org/I11019714"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012864207","display_name":"Concepci\u00f3n Vidal","orcid":"https://orcid.org/0000-0002-5561-6406"},"institutions":[{"id":"https://openalex.org/I11019714","display_name":"Universidade da Coru\u00f1a","ror":"https://ror.org/01qckj285","country_code":"ES","type":"education","lineage":["https://openalex.org/I11019714"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"CONCEPCI\u00d3N VIDAL","raw_affiliation_strings":["Department of Computer Science, University of Corunna, SPAIN (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Corunna, SPAIN (e-mail:","institution_ids":["https://openalex.org/I11019714"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":2.5275,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.92208107,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"15","issue":"4-5","first_page":"620","last_page":"634"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","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/T11010","display_name":"Logic, Reasoning, and Knowledge","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/T11727","display_name":"Advanced Algebra and Logic","score":0.9940999746322632,"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/T10215","display_name":"Semantic Web and Ontologies","score":0.9936000108718872,"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/denotational-semantics","display_name":"Denotational semantics","score":0.8087745904922485},{"id":"https://openalex.org/keywords/denotational-semantics-of-the-actor-model","display_name":"Denotational semantics of the Actor model","score":0.801568865776062},{"id":"https://openalex.org/keywords/normalisation-by-evaluation","display_name":"Normalisation by evaluation","score":0.7408340573310852},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.4952618181705475},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.49087220430374146},{"id":"https://openalex.org/keywords/action-semantics","display_name":"Action semantics","score":0.4487364888191223},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4432377219200134},{"id":"https://openalex.org/keywords/operational-semantics","display_name":"Operational semantics","score":0.3929445147514343},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32673993706703186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29066774249076843},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17509105801582336}],"concepts":[{"id":"https://openalex.org/C207648694","wikidata":"https://www.wikidata.org/wiki/Q1189746","display_name":"Denotational semantics","level":4,"score":0.8087745904922485},{"id":"https://openalex.org/C89448276","wikidata":"https://www.wikidata.org/wiki/Q5259284","display_name":"Denotational semantics of the Actor model","level":5,"score":0.801568865776062},{"id":"https://openalex.org/C87365073","wikidata":"https://www.wikidata.org/wiki/Q7051843","display_name":"Normalisation by evaluation","level":5,"score":0.7408340573310852},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.4952618181705475},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.49087220430374146},{"id":"https://openalex.org/C150607116","wikidata":"https://www.wikidata.org/wiki/Q4677421","display_name":"Action semantics","level":5,"score":0.4487364888191223},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4432377219200134},{"id":"https://openalex.org/C156325763","wikidata":"https://www.wikidata.org/wiki/Q1930895","display_name":"Operational semantics","level":3,"score":0.3929445147514343},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32673993706703186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29066774249076843},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17509105801582336}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s1471068415000277","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s1471068415000277","pdf_url":null,"source":{"id":"https://openalex.org/S59670734","display_name":"Theory and Practice of Logic Programming","issn_l":"1471-0684","issn":["1471-0684","1475-3081"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory and Practice of Logic Programming","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1507.06915","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.06915","pdf_url":"https://arxiv.org/pdf/1507.06915","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1507.06915","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.06915","pdf_url":"https://arxiv.org/pdf/1507.06915","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W150743059","https://openalex.org/W578063101","https://openalex.org/W1582030611","https://openalex.org/W1582978375","https://openalex.org/W1592150968","https://openalex.org/W1598263475","https://openalex.org/W1601726121","https://openalex.org/W1627528933","https://openalex.org/W1639901403","https://openalex.org/W1672891595","https://openalex.org/W1770842667","https://openalex.org/W1800801472","https://openalex.org/W1843148560","https://openalex.org/W1985058553","https://openalex.org/W1985274317","https://openalex.org/W1985387287","https://openalex.org/W1989634318","https://openalex.org/W2015640848","https://openalex.org/W2027980228","https://openalex.org/W2091138122","https://openalex.org/W2102960254","https://openalex.org/W2152131859","https://openalex.org/W2166791089","https://openalex.org/W2167765443","https://openalex.org/W2178463746","https://openalex.org/W2401444989","https://openalex.org/W2608239929","https://openalex.org/W2914398864","https://openalex.org/W3098246338","https://openalex.org/W3152800724","https://openalex.org/W4298168953","https://openalex.org/W6686124083"],"related_works":["https://openalex.org/W2348616540","https://openalex.org/W3036972880","https://openalex.org/W1968765218","https://openalex.org/W1929699059","https://openalex.org/W2604895854","https://openalex.org/W2072493788","https://openalex.org/W2154982982","https://openalex.org/W2066556632","https://openalex.org/W1869423547","https://openalex.org/W2092481413"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,127],"paper":[3],"we":[4,63,81],"provide":[5,64,130,180],"an":[6,53,194],"alternative":[7],"semantics":[8,104,128],"for":[9,68,88,134,174],"Equilibrium":[10],"Logic":[11],"and":[12,52,120,143,192],"its":[13],"monotonic":[14],"basis,":[15],"the":[16,27,38,46,77,98,102,109,141,159,189],"logic":[17],"of":[18,40,42,70,76,79,97,111,114,162,170,183,188,196],"Here-and-There":[19],"(also":[20],"known":[21],"as":[22],"G\u00f6del'sG3logic)":[23],"that":[24,32,36,43,90,137,153,200],"relies":[25],"on":[26],"idea":[28],"ofdenotationof":[29],"a":[30,34,49,115,118,146,181,197],"formula,":[31],"is,":[33],"function":[35],"collects":[37],"set":[39,110,122],"models":[41,59,113,161,169],"formula.":[44],"Using":[45],"three-valued":[47],"logicG3as":[48],"starting":[50],"point":[51],"ordering":[54],"relation":[55],"(for":[56],"which":[57],"equilibrium/stable":[58],"are":[60,138,166],"minimal":[61],"elements)":[62],"several":[65,131],"elementary":[66],"operations":[67],"sets":[69],"interpretations.":[71],"By":[72],"analysing":[73],"structural":[74],"properties":[75],"denotation":[78],"formulas,":[80],"show":[82],"some":[83,205],"expressiveness":[84],"results":[85],"forG3such":[86],"as,":[87],"instance,":[89],"conjunction":[91],"is":[92],"not":[93],"expressible":[94],"in":[95,140,186,204],"terms":[96,187],"other":[99],"connectives.":[100],"Moreover,":[101],"denotational":[103,190],"allows":[105],"us":[106],"to":[107,129],"capture":[108],"equilibrium":[112,160,168],"formula":[116],"with":[117],"simple":[119],"compact":[121],"expression.":[123],"We":[124,151,178],"also":[125,167,179],"use":[126],"formal":[132],"definitions":[133],"entailment":[135,185],"relations":[136],"usual":[139],"literature,":[142],"further":[144],"introduce":[145],"new":[147],"one":[148],"calledstrong":[149],"entailment.":[150],"say":[152],"\u03b1":[154,163],"strongly":[155],"entails":[156],"\u03b2":[157,171],"when":[158],"\u2227":[164,172],"\u03b3":[165,173],"any":[175],"context":[176],"\u03b3.":[177],"characterisation":[182],"strong":[184],"semantics,":[191],"give":[193],"example":[195],"sufficient":[198],"condition":[199],"can":[201],"be":[202],"applied":[203],"cases.":[206]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
