{"id":"https://openalex.org/W4414360418","doi":"https://doi.org/10.24963/ijcai.2025/506","title":"Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics","display_name":"Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics","publication_year":2025,"publication_date":"2025-09-01","ids":{"openalex":"https://openalex.org/W4414360418","doi":"https://doi.org/10.24963/ijcai.2025/506"},"language":"en","primary_location":{"id":"doi:10.24963/ijcai.2025/506","is_oa":false,"landing_page_url":"https://doi.org/10.24963/ijcai.2025/506","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.ou.nl/en/publications/d0730642-b8fa-4933-b506-2b6788f9e8bc","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5098691155","display_name":"Pascal Kettmann","orcid":null},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Pascal Kettmann","raw_affiliation_strings":["TU Dresden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Dresden","institution_ids":["https://openalex.org/I78650965"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047491682","display_name":"Jesse Heyninck","orcid":"https://orcid.org/0000-0002-3825-4052"},"institutions":[{"id":"https://openalex.org/I157614274","display_name":"University of Cape Town","ror":"https://ror.org/03p74gp79","country_code":"ZA","type":"education","lineage":["https://openalex.org/I157614274"]},{"id":"https://openalex.org/I8679417","display_name":"Hong Kong Metropolitan University","ror":"https://ror.org/0349bsm71","country_code":"HK","type":"education","lineage":["https://openalex.org/I8679417"]}],"countries":["HK","ZA"],"is_corresponding":false,"raw_author_name":"Jesse Heyninck","raw_affiliation_strings":["Open Universiteit","University of Cape Town"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Open Universiteit","institution_ids":["https://openalex.org/I8679417"]},{"raw_affiliation_string":"University of Cape Town","institution_ids":["https://openalex.org/I157614274"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072285823","display_name":"Hannes Stra\u00df","orcid":null},"institutions":[{"id":"https://openalex.org/I4401726909","display_name":"Center for Scalable Data Analytics and Artificial Intelligence","ror":"https://ror.org/01t4ttr56","country_code":"DE","type":"education","lineage":["https://openalex.org/I4401726909","https://openalex.org/I78650965","https://openalex.org/I926574661"]},{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hannes Strass","raw_affiliation_strings":["Center for Scalable Data Analytics and Artificial Intelligence","TU Dresden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Scalable Data Analytics and Artificial Intelligence","institution_ids":["https://openalex.org/I4401726909"]},{"raw_affiliation_string":"TU Dresden","institution_ids":["https://openalex.org/I78650965"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11893699,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4544","last_page":"4552"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9952999949455261,"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":0.9952999949455261,"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":0.9879999756813049,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.9732000231742859,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/fuzzy-logic","display_name":"Fuzzy logic","score":0.6604999899864197},{"id":"https://openalex.org/keywords/logic-programming","display_name":"Logic programming","score":0.5281000137329102},{"id":"https://openalex.org/keywords/horn-clause","display_name":"Horn clause","score":0.5231999754905701},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5134000182151794},{"id":"https://openalex.org/keywords/stable-model-semantics","display_name":"Stable model semantics","score":0.5055999755859375},{"id":"https://openalex.org/keywords/well-founded-semantics","display_name":"Well-founded semantics","score":0.48429998755455017},{"id":"https://openalex.org/keywords/classical-logic","display_name":"Classical logic","score":0.43540000915527344},{"id":"https://openalex.org/keywords/semantics","display_name":"Semantics (computer science)","score":0.42160001397132874},{"id":"https://openalex.org/keywords/scope","display_name":"Scope (computer science)","score":0.4203999936580658},{"id":"https://openalex.org/keywords/t-norm-fuzzy-logics","display_name":"T-norm fuzzy logics","score":0.40939998626708984}],"concepts":[{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.6604999899864197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5579000115394592},{"id":"https://openalex.org/C128838566","wikidata":"https://www.wikidata.org/wiki/Q275603","display_name":"Logic programming","level":2,"score":0.5281000137329102},{"id":"https://openalex.org/C189790780","wikidata":"https://www.wikidata.org/wiki/Q933932","display_name":"Horn clause","level":3,"score":0.5231999754905701},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5134000182151794},{"id":"https://openalex.org/C127001435","wikidata":"https://www.wikidata.org/wiki/Q7595770","display_name":"Stable model semantics","level":4,"score":0.5055999755859375},{"id":"https://openalex.org/C89497691","wikidata":"https://www.wikidata.org/wiki/Q7981058","display_name":"Well-founded semantics","level":5,"score":0.48429998755455017},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.45210000872612},{"id":"https://openalex.org/C32241873","wikidata":"https://www.wikidata.org/wiki/Q236975","display_name":"Classical logic","level":2,"score":0.43540000915527344},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.42160001397132874},{"id":"https://openalex.org/C2778012447","wikidata":"https://www.wikidata.org/wiki/Q1034415","display_name":"Scope (computer science)","level":2,"score":0.4203999936580658},{"id":"https://openalex.org/C86602344","wikidata":"https://www.wikidata.org/wiki/Q7667918","display_name":"T-norm fuzzy logics","level":5,"score":0.40939998626708984},{"id":"https://openalex.org/C169896238","wikidata":"https://www.wikidata.org/wiki/Q1644136","display_name":"Higher-order logic","level":3,"score":0.4081999957561493},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39959999918937683},{"id":"https://openalex.org/C182620335","wikidata":"https://www.wikidata.org/wiki/Q2852531","display_name":"Answer set programming","level":3,"score":0.3747999966144562},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35839998722076416},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3449999988079071},{"id":"https://openalex.org/C173125200","wikidata":"https://www.wikidata.org/wiki/Q5275729","display_name":"Modal \u03bc-calculus","level":5,"score":0.3440999984741211},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3402999937534332},{"id":"https://openalex.org/C1883856","wikidata":"https://www.wikidata.org/wiki/Q3407463","display_name":"Fuzzy number","level":4,"score":0.3310999870300293},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.3287000060081482},{"id":"https://openalex.org/C144701195","wikidata":"https://www.wikidata.org/wiki/Q10859910","display_name":"Theory","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.320499986410141},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31839999556541443},{"id":"https://openalex.org/C2777796570","wikidata":"https://www.wikidata.org/wiki/Q2351326","display_name":"Dynamic logic (digital electronics)","level":4,"score":0.3091999888420105},{"id":"https://openalex.org/C127385683","wikidata":"https://www.wikidata.org/wiki/Q1475696","display_name":"Fuzzy classification","level":4,"score":0.3066999912261963},{"id":"https://openalex.org/C19689857","wikidata":"https://www.wikidata.org/wiki/Q4055684","display_name":"Predicate logic","level":3,"score":0.2971000075340271},{"id":"https://openalex.org/C203659156","wikidata":"https://www.wikidata.org/wiki/Q6934805","display_name":"Multimodal logic","level":3,"score":0.2946000099182129},{"id":"https://openalex.org/C148671577","wikidata":"https://www.wikidata.org/wiki/Q5511133","display_name":"Fuzzy set operations","level":4,"score":0.2930000126361847},{"id":"https://openalex.org/C42011625","wikidata":"https://www.wikidata.org/wiki/Q1055058","display_name":"Fuzzy set","level":3,"score":0.2906999886035919},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2842999994754791},{"id":"https://openalex.org/C159032336","wikidata":"https://www.wikidata.org/wiki/Q2488768","display_name":"Non-monotonic logic","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C124047733","wikidata":"https://www.wikidata.org/wiki/Q5157327","display_name":"Computational logic","level":3,"score":0.2791000008583069},{"id":"https://openalex.org/C170260401","wikidata":"https://www.wikidata.org/wiki/Q5251735","display_name":"Defuzzification","level":5,"score":0.2680000066757202},{"id":"https://openalex.org/C146499914","wikidata":"https://www.wikidata.org/wiki/Q5469969","display_name":"Formal semantics (linguistics)","level":2,"score":0.25519999861717224},{"id":"https://openalex.org/C195975749","wikidata":"https://www.wikidata.org/wiki/Q1475705","display_name":"Fuzzy control system","level":3,"score":0.2549000084400177},{"id":"https://openalex.org/C2039508","wikidata":"https://www.wikidata.org/wiki/Q7239631","display_name":"Predicate functor logic","level":5,"score":0.25290000438690186},{"id":"https://openalex.org/C47884741","wikidata":"https://www.wikidata.org/wiki/Q1166618","display_name":"Mathematical logic","level":2,"score":0.2522999942302704},{"id":"https://openalex.org/C3845977","wikidata":"https://www.wikidata.org/wiki/Q4826262","display_name":"Autoepistemic logic","level":4,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.24963/ijcai.2025/506","is_oa":false,"landing_page_url":"https://doi.org/10.24963/ijcai.2025/506","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","raw_type":"proceedings-article"},{"id":"pmh:oai:research.ou.nl:publications/d0730642-b8fa-4933-b506-2b6788f9e8bc","is_oa":true,"landing_page_url":"https://research.ou.nl/en/publications/d0730642-b8fa-4933-b506-2b6788f9e8bc","pdf_url":null,"source":{"id":"https://openalex.org/S4406922485","display_name":"Open University of the Netherlands Research Portal","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kettmann, P, Heyninck, J & Strass, H 2025, Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics. in Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2025, Montreal, Canada, August 16-22, 2025. ijcai.org, pp. 4544-4552, 34th International Joint Conference on Artificial Intelligence, Montreal, Quebec, Canada, 16/08/25. https://doi.org/10.24963/ijcai.2025/506","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:research.ou.nl:publications/d0730642-b8fa-4933-b506-2b6788f9e8bc","is_oa":true,"landing_page_url":"https://research.ou.nl/en/publications/d0730642-b8fa-4933-b506-2b6788f9e8bc","pdf_url":null,"source":{"id":"https://openalex.org/S4406922485","display_name":"Open University of the Netherlands Research Portal","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Kettmann, P, Heyninck, J & Strass, H 2025, Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics. in Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2025, Montreal, Canada, August 16-22, 2025. ijcai.org, pp. 4544-4552, 34th International Joint Conference on Artificial Intelligence, Montreal, Quebec, Canada, 16/08/25. https://doi.org/10.24963/ijcai.2025/506","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2618171120","display_name":"LogicLM: Combining Logic Programs with Language Model","funder_award_id":"NGF.1609.241.010","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G4712284355","display_name":null,"funder_award_id":"57616814","funder_id":"https://openalex.org/F4320320875","funder_display_name":"Deutscher Akademischer Austauschdienst"},{"id":"https://openalex.org/G6098565189","display_name":null,"funder_award_id":"57616814","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"}],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Fuzzy":[0],"logic":[1,16,26,88,113],"programming":[2,17],"is":[3],"an":[4],"established":[5],"approach":[6],"for":[7],"reasoning":[8],"under":[9],"uncertainty.":[10],"Several":[11],"semantics":[12],"from":[13,69,109],"classical,":[14],"two-valued":[15],"have":[18],"been":[19],"generalized":[20],"to":[21,71,83,86,111],"the":[22,36,42,46,53,65,98,105,121],"case":[23],"of":[24,35,56,67,79,93,107,120],"fuzzy":[25,87,112],"programs.":[27],"In":[28],"this":[29],"paper,":[30],"we":[31,96],"show":[32],"that":[33],"two":[34],"most":[37],"prominent":[38],"classical":[39,110],"semantics,":[40,48,103],"namely":[41],"stable":[43],"model":[44],"and":[45,115],"well-founded":[47],"can":[49],"be":[50,84],"reconstructed":[51],"within":[52],"general":[54],"framework":[55],"approximation":[57],"fixpoint":[58],"theory":[59],"(AFT).":[60],"This":[61],"not":[62],"only":[63],"widens":[64],"scope":[66],"AFT":[68,81],"two-":[70],"many-valued":[72],"logics,":[73],"but":[74],"allows":[75],"a":[76],"wide":[77],"range":[78],"existing":[80,102],"results":[82],"applied":[85],"programming.":[89],"As":[90],"first":[91],"examples":[92],"such":[94],"applications,":[95],"clarify":[97],"formal":[99],"relationship":[100],"between":[101],"generalize":[104],"notion":[106],"stratification":[108],"programs,":[114],"devise":[116],"\u201cmore":[117],"precise\u201d":[118],"variants":[119],"semantics.":[122]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}