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@book{romanlattices2008,
location = {New York, {NY}},
title = {Lattices and Ordered Sets},
isbn = {978-0-387-78900-2 978-0-387-78901-9},
url = {http://link.springer.com/10.1007/978-0-387-78901-9},
publisher = {Springer New York},
author = {Roman, Steven},
urldate = {2021-07-28},
year = {2008},
langid = {english},
doi = {10.1007/978-0-387-78901-9},
file = {2008 - Lattices and Ordered Sets.pdf:/home/capybara/Zotero/storage/5QU8WTUR/2008 - Lattices and Ordered Sets.pdf:application/pdf},
}
@InProceedings{RRaft,
author="Bi, Yi
and You, Jia-Huai
and Feng, Zhiyong",
editor="Kontchakov, Roman
and Mugnier, Marie-Laure",
title="A Generalization of Approximation Fixpoint Theory and Application",
booktitle="Web Reasoning and Rule Systems",
year="2014",
publisher="Springer International Publishing",
address="Cham",
pages="45--59"
}
@article{gelfondstable2000,
title = {The Stable Model Semantics For Logic Programming},
volume = {2},
abstract = {We propose a new declarative semantics for logic programs with negation. Its formulation is quite simple; at the same time, it is more general than the iterated xed point semantics for stratied programs, and is applicable to some useful programs that are not stratied.},
journal = {Logic Programming},
shortjournal = {Logic Programming},
author = {Gelfond, Michael and Lifschitz, Vladimir},
date = {2000-12-14},
year = "2000",
file = {Full Text PDF:/home/gopher/Zotero/storage/LSRXUIBD/The_Stable_Model_Semantics_For_Logic_Programming.pdf:application/pdf}
}
@inproceedings{aftjust,
author = {Simon Marynissen and
Bart Bogaerts and
Marc Denecker},
editor = {Zhi{-}Hua Zhou},
title = {On the Relation Between Approximation Fixpoint Theory and Justification
Theory},
booktitle = {Proceedings of the Thirtieth International Joint Conference on Artificial
Intelligence, {IJCAI} 2021, Virtual Event / Montreal, Canada, 19-27
August 2021},
pages = {1973--1980},
publisher = {ijcai.org},
year = {2021},
url = {https://doi.org/10.24963/ijcai.2021/272},
doi = {10.24963/ijcai.2021/272},
timestamp = {Sat, 09 Apr 2022 12:47:19 +0200},
biburl = {https://dblp.org/rec/conf/ijcai/Marynissen0D21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{liuyou2021,
author = {Fangfang Liu and
Jia{-}Huai You},
title = {Alternating Fixpoint Operator for Hybrid {MKNF} Knowledge Bases as
an Approximator of {AFT}},
journal = {Theory Pract. Log. Program.},
volume = {22},
number = {2},
pages = {305--334},
year = {2022},
doi = {10.1017/S1471068421000168},
timestamp = {Wed, 27 Apr 2022 20:10:27 +0200},
biburl = {https://dblp.org/rec/journals/tplp/LiuY22.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{liuyou2019,
author = {Fangfang Liu and
Jia{-}Huai You},
editor = {Paul Fodor and
Marco Montali and
Diego Calvanese and
Dumitru Roman},
title = {Alternating Fixpoint Operator for Hybrid {MKNF} Knowledge Bases as
an Approximator of {AFT}},
booktitle = {Rules and Reasoning - Third International Joint Conference, RuleML+RR
2019, Bolzano, Italy, September 16-19, 2019, Proceedings},
series = {Lecture Notes in Computer Science},
volume = {11784},
pages = {113--127},
publisher = {Springer},
year = {2019},
url = {https://doi.org/10.1007/978-3-030-31095-0\_8},
doi = {10.1007/978-3-030-31095-0\_8},
timestamp = {Tue, 17 Sep 2019 08:40:59 +0200},
biburl = {https://dblp.org/rec/conf/ruleml/LiuY19.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{aftagg,
author = {Linde Vanbesien and
Maurice Bruynooghe and
Marc Denecker},
title = {Analyzing Semantics of Aggregate Answer Set Programming Using Approximation
Fixpoint Theory},
journal = {Theory Pract. Log. Program.},
volume = {22},
number = {4},
pages = {523--537},
year = {2022},
url = {https://doi.org/10.1017/S1471068422000126},
doi = {10.1017/S1471068422000126},
timestamp = {Sat, 10 Sep 2022 20:58:45 +0200},
biburl = {https://dblp.org/rec/journals/tplp/VanbesienBD22.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{DeneckerMT04,
author = {Marc Denecker and
Victor W. Marek and
Miroslaw Truszczynski},
title = {Ultimate approximation and its application in nonmonotonic knowledge
representation systems},
journal = {Inf. Comput.},
volume = {192},
number = {1},
pages = {84--121},
year = {2004},
doi = {10.1016/j.ic.2004.02.004},
timestamp = {Fri, 12 Feb 2021 22:16:22 +0100},
biburl = {https://dblp.org/rec/journals/iandc/DeneckerMT04.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@incollection{denecker2000approximations,
title={Approximations, stable operators, well-founded fixpoints and applications in nonmonotonic reasoning},
author={Denecker, Marc and Marek, Victor and Truszczy{\'n}ski, Miros{\l}aw},
booktitle={Logic-Based Artificial Intelligence},
pages={127--144},
year={2000},
doi={10.1007/978-1-4615-1567-8_6},
publisher = {Springer},
}
@article{fittingfixpointsurvey,
author = {Melvin Fitting},
title = {Fixpoint semantics for logic programming a survey},
journal = {Theor. Comput. Sci.},
volume = {278},
number = {1-2},
pages = {25--51},
year = {2002},
url = {https://doi.org/10.1016/S0304-3975(00)00330-3},
doi = {10.1016/S0304-3975(00)00330-3},
timestamp = {Wed, 17 Feb 2021 21:58:01 +0100},
biburl = {https://dblp.org/rec/journals/tcs/Fitting02.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{Ji17,
author = {Jianmin Ji and
Fangfang Liu and
Jia{-}Huai You},
title = {Well-founded operators for normal hybrid {MKNF} knowledge bases},
journal = {Theory Pract. Log. Program.},
volume = {17},
number = {5-6},
pages = {889--905},
year = {2017},
doi = {10.1017/S1471068417000291},
timestamp = {Mon, 26 Oct 2020 08:22:48 +0100},
biburl = {https://dblp.org/rec/journals/tplp/JiLY17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{Fitting02,
author = {Melvin Fitting},
title = {Fixpoint semantics for logic programming a survey},
journal = {Theor. Comput. Sci.},
volume = {278},
number = {1-2},
pages = {25--51},
year = {2002},
doi = {10.1016/S0304-3975(00)00330-3},
timestamp = {Wed, 17 Feb 2021 21:58:01 +0100},
biburl = {https://dblp.org/rec/journals/tcs/Fitting02.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}}
@article{knorrlocal2011,
author = {Matthias Knorr and
Jos{\'{e}} J{\'{u}}lio Alferes and
Pascal Hitzler},
title = {Local closed world reasoning with description logics under the well-founded
semantics},
journal = {Artif. Intell.},
volume = {175},
number = {9-10},
pages = {1528--1554},
year = {2011},
doi = {10.1016/j.artint.2011.01.007},
timestamp = {Wed, 23 Feb 2022 14:32:41 +0100},
biburl = {https://dblp.org/rec/journals/ai/KnorrAH11.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{przymusinskistable1991,
author = {Teodor C. Przymusinski},
title = {Stable Semantics for Disjunctive Programs},
journal = {New Gener. Comput.},
volume = {9},
number = {3/4},
pages = {401--424},
year = {1991},
doi = {10.1007/BF03037171},
timestamp = {Thu, 14 May 2020 22:23:50 +0200},
biburl = {https://dblp.org/rec/journals/ngc/Przymusinski91.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{lifschitznonmonotonic1991,
author = {Vladimir Lifschitz},
editor = {John Mylopoulos and
Raymond Reiter},
title = {Nonmonotonic Databases and Epistemic Queries},
booktitle = {Proceedings of the 12th International Joint Conference on Artificial
Intelligence. Sydney, Australia, August 24-30, 1991},
pages = {381--386},
publisher = {Morgan Kaufmann},
year = {1991},
url = {http://ijcai.org/Proceedings/91-1/Papers/059.pdf},
timestamp = {Tue, 20 Aug 2019 16:18:13 +0200},
biburl = {https://dblp.org/rec/conf/ijcai/Lifschitz91.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{motikreconciling2010,
author = {Boris Motik and
Riccardo Rosati},
title = {Reconciling description logics and rules},
journal = {J. {ACM}},
volume = {57},
number = {5},
pages = {30:1--30:62},
year = {2010},
doi = {10.1145/1754399.1754403},
timestamp = {Mon, 16 Sep 2019 14:49:47 +0200},
biburl = {https://dblp.org/rec/journals/jacm/MotikR10.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{liuthreevalued2017,
author = {Fangfang Liu and
Jia{-}Huai You},
title = {Three-valued semantics for hybrid {MKNF} knowledge bases revisited},
journal = {Artif. Intell.},
volume = {252},
pages = {123--138},
year = {2017},
doi = {10.1016/j.artint.2017.08.003},
timestamp = {Thu, 28 Dec 2017 16:12:02 +0100},
biburl = {https://dblp.org/rec/journals/ai/LiuY17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{revisited,
author = {Fangfang Liu and
Jia{-}Huai You},
title = {Three-valued semantics for hybrid {MKNF} knowledge bases revisited},
journal = {Artif. Intell.},
volume = {252},
pages = {123--138},
year = {2017},
url = {https://doi.org/10.1016/j.artint.2017.08.003},
doi = {10.1016/j.artint.2017.08.003},
timestamp = {Thu, 28 Dec 2017 16:12:02 +0100},
biburl = {https://dblp.org/rec/journals/ai/LiuY17.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{tarskilatticetheoretical1955,
author = {Alfred Tarski},
title = {{A lattice-theoretical fixpoint theorem and its applications.}},
volume = {5},
journal = {Pacific Journal of Mathematics},
number = {2},
publisher = {Pacific Journal of Mathematics, A Non-profit Corporation},
pages = {285 -- 309},
doi = {10.2140/pjm.1955.5.285},
year = {1955}
}
@article{gebserconflictdriven2012,
author = {Martin Gebser and
Benjamin Kaufmann and
Torsten Schaub},
title = {Conflict-driven answer set solving: From theory to practice},
journal = {Artif. Intell.},
volume = {187},
pages = {52--89},
year = {2012},
doi = {10.1016/j.artint.2012.04.001},
timestamp = {Fri, 09 Apr 2021 18:34:15 +0200},
biburl = {https://dblp.org/rec/journals/ai/GebserKS12.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{gebseradvanced2013,
author = {Martin Gebser and
Benjamin Kaufmann and
Torsten Schaub},
editor = {Francesca Rossi},
title = {Advanced Conflict-Driven Disjunctive Answer Set Solving},
booktitle = {{IJCAI} 2013, Proceedings of the 23rd International Joint Conference
on Artificial Intelligence, Beijing, China, August 3-9, 2013},
pages = {912--918},
publisher = {{IJCAI/AAAI}},
year = {2013},
url = {http://www.aaai.org/ocs/index.php/IJCAI/IJCAI13/paper/view/6835},
timestamp = {Tue, 08 Mar 2022 17:41:53 +0100},
biburl = {https://dblp.org/rec/conf/ijcai/GebserKS13.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{killenfixpoint2021,
author = {Spencer Killen and
Jia{-}Huai You},
title = {Fixpoint Characterizations of Disjunctive Hybrid {MKNF} Knowledge
Bases},
booktitle = {Proceedings of the International Conference on Logic Programming 2021
Workshops co-located with the 37th International Conference on Logic
Programming {(ICLP} 2021), Porto, Portugal (virtual), September 20th-21st,
2021},
series = {{CEUR} Workshop Proceedings},
volume = {2970},
publisher = {CEUR-WS.org},
year = {2021},
url = {http://ceur-ws.org/Vol-2970/aspocppaper3.pdf},
timestamp = {Thu, 28 Oct 2021 14:11:18 +0200},
biburl = {https://dblp.org/rec/conf/iclp/KillenY21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{killen2022,
author = {Spencer Killen and
Jia{-}Huai You},
editor = {Yuliya Lierler and
Jos{\'{e}} F. Morales and
Carmine Dodaro and
Ver{\'{o}}nica Dahl and
Martin Gebser and
Tuncay Tekle},
title = {A Fixpoint Characterization of Three-Valued Disjunctive Hybrid {MKNF}
Knowledge Bases},
booktitle = {Proceedings 38th International Conference on Logic Programming, {ICLP}
2022 Technical Communications / Doctoral Consortium, Haifa, Israel,
31st July 2022 - 6th August 2022},
series = {{EPTCS}},
volume = {364},
pages = {51--64},
year = {2022},
url = {https://doi.org/10.4204/EPTCS.364.6},
doi = {10.4204/EPTCS.364.6},
timestamp = {Sat, 15 Oct 2022 11:57:01 +0200},
biburl = {https://dblp.org/rec/journals/corr/abs-2208-03087.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{killenunfounded,
author = {Spencer Killen and
Jia{-}Huai You},
editor = {Meghyn Bienvenu and
Gerhard Lakemeyer and
Esra Erdem},
title = {Unfounded Sets for Disjunctive Hybrid {MKNF} Knowledge Bases},
booktitle = {Proceedings of the 18th International Conference on Principles of
Knowledge Representation and Reasoning, {KR} 2021, Online event, November
3-12, 2021},
pages = {432--441},
year = {2021},
doi = {10.24963/kr.2021/41},
timestamp = {Wed, 03 Nov 2021 12:47:32 +0100},
biburl = {https://dblp.org/rec/conf/kr/KillenY21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{heyninckapproximation2021,
author = {Jesse Heyninck and
Ofer Arieli},
editor = {Meghyn Bienvenu and
Gerhard Lakemeyer and
Esra Erdem},
title = {Approximation Fixpoint Theory for Non-Deterministic Operators and
Its Application in Disjunctive Logic Programming},
booktitle = {Proceedings of the 18th International Conference on Principles of
Knowledge Representation and Reasoning, {KR} 2021, Online event, November
3-12, 2021},
pages = {334--344},
year = {2021},
doi = {10.24963/kr.2021/32},
timestamp = {Wed, 03 Nov 2021 12:47:32 +0100},
biburl = {https://dblp.org/rec/conf/kr/HeyninckA21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{kaminskiefficient2015,
author = {Tobias Kaminski and
Matthias Knorr and
Jo{\~{a}}o Leite},
editor = {Qiang Yang and
Michael J. Wooldridge},
title = {Efficient Paraconsistent Reasoning with Ontologies and Rules},
booktitle = {Proceedings of the Twenty-Fourth International Joint Conference on
Artificial Intelligence, {IJCAI} 2015, Buenos Aires, Argentina, July
25-31, 2015},
pages = {3098--3105},
publisher = {{AAAI} Press},
year = {2015},
url = {http://ijcai.org/Abstract/15/437},
timestamp = {Wed, 23 Feb 2022 14:32:42 +0100},
biburl = {https://dblp.org/rec/conf/ijcai/KaminskiKL15.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{headcycleisNP,
author = {Rachel Ben{-}Eliyahu and
Rina Dechter},
title = {Propositional Semantics for Disjunctive Logic Programs},
journal = {Ann. Math. Artif. Intell.},
volume = {12},
number = {1-2},
pages = {53--87},
year = {1994},
doi = {10.1007/BF01530761},
timestamp = {Sun, 28 May 2017 13:20:59 +0200},
biburl = {https://dblp.org/rec/journals/amai/Ben-EliyahuD94.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}