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@inproceedings{loop_formulas,
author = {Joohyung Lee and
Vladimir Lifschitz},
editor = {Catuscia Palamidessi},
title = {Loop Formulas for Disjunctive Logic Programs},
booktitle = {Logic Programming, 19th International Conference, {ICLP} 2003, Mumbai,
India, December 9-13, 2003, Proceedings},
series = {Lecture Notes in Computer Science},
volume = {2916},
pages = {451--465},
publisher = {Springer},
year = {2003},
url = {https://doi.org/10.1007/978-3-540-24599-5\_31},
doi = {10.1007/978-3-540-24599-5\_31},
timestamp = {Fri, 15 Jan 2021 08:34:36 +0100},
biburl = {https://dblp.org/rec/conf/iclp/LeeL03.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@misc{latticehomomorph,
title = {complete lattice homomorphism},
howpublished = {\url{https://planetmath.org/completelatticehomomorphism}},
note = {Accessed: 2023-08-03}
}
@inproceedings{gelfond1991disjunctive,
title={Disjunctive defaults},
author={Gelfond, Michael and Lifschitz, Vladimir and Przymusinska, Halina and Truszczynski, Miroslaw},
booktitle={Proc. Second International Conf. on Principles of Knowledge Representation and Reasoning},
pages={230--237},
year={1991}
}
@article{alviano2023aggregate,
title={Aggregate semantics for propositional answer set programs},
author={Alviano, Mario and Faber, Wolfgang and Gebser, Martin},
journal={Theory and Practice of Logic Programming},
volume={23},
number={1},
pages={157--194},
year={2023},
publisher={Cambridge University Press}
}
@article{heyninck2024operatorbasedsemanticschoiceprograms,
title={Operator-based semantics for choice programs: is choosing losing? (full version)},
author={Jesse Heyninck},
journal={arXiv},
number="2407.21556",
note ={A short version to appear in KR'24},
year={2024},
eprint={2407.21556},
archivePrefix={arXiv},
primaryClass={cs.AI},
url={https://arxiv.org/abs/2407.21556},
}
@article{DBLP:journals/tplp/HeyninckB23,
author = {Jesse Heyninck and
Bart Bogaerts},
title = {Non-deterministic Approximation Operators: Ultimate Operators, Semi-equilibrium
Semantics, and Aggregates},
journal = {Theory Pract. Log. Program.},
volume = {23},
number = {4},
pages = {632--647},
year = {2023},
url = {https://doi.org/10.1017/s1471068423000236},
doi = {10.1017/S1471068423000236},
timestamp = {Sat, 16 Mar 2024 15:10:17 +0100},
biburl = {https://dblp.org/rec/journals/tplp/HeyninckB23.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{wfs,
author = {Jo{\~{a}}o F. L. Alc{\^{a}}ntara and
Carlos Viegas Dam{\'{a}}sio and
Lu{\'{\i}}s Moniz Pereira},
editor = {Maurizio Gabbrielli and
Gopal Gupta},
title = {A Well-Founded Semantics with Disjunction},
booktitle = {Logic Programming, 21st International Conference, {ICLP} 2005, Sitges,
Spain, October 2-5, 2005, Proceedings},
series = {Lecture Notes in Computer Science},
volume = {3668},
pages = {341--355},
publisher = {Springer},
year = {2005},
url = {https://doi.org/10.1007/11562931\_26},
doi = {10.1007/11562931\_26},
timestamp = {Wed, 26 Oct 2022 11:14:38 +0200},
biburl = {https://dblp.org/rec/conf/iclp/AlcantaraDP05.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{wfsd,
author = {Alcantara, Joao and Damásio, Carlos and Pereira, Luís},
year = {2005},
month = {10},
pages = {341-355},
title = {A Well-Founded Semantics with Disjunction},
volume = {3668},
isbn = {978-3-540-29208-1},
journal = {Lecture Notes in Computer Science},
doi = {10.1007/11562931_26}
}
@inbook{belnapfour,
author = {Belnap, Nuel D.},
editor = {Dunn, J. Michael
and Epstein, George},
title = {A Useful Four-Valued Logic},
booktitle = {Modern Uses of Multiple-Valued Logic},
year = {1977},
publisher = {Springer Netherlands},
address = {Dordrecht},
pages = {5--37},
abstract = {It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead (as in classical logic) to irrelevant conclusions. The actual form of the four-valued logic is `deduced' from an interplay of this motivating consideration with certain ideas of Dana Scott concerning `approximation lattices.'},
isbn = {978-94-010-1161-7},
doi = {10.1007/978-94-010-1161-7_2},
url = {https://doi.org/10.1007/978-94-010-1161-7_2}
}
@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}
}
@book{paramcomplex,
author = {Rodney G. Downey and
Michael R. Fellows},
title = {Fundamentals of Parameterized Complexity},
series = {Texts in Computer Science},
publisher = {Springer},
year = {2013},
url = {https://doi.org/10.1007/978-1-4471-5559-1},
doi = {10.1007/978-1-4471-5559-1},
isbn = {978-1-4471-5558-4},
timestamp = {Tue, 16 May 2017 14:24:38 +0200},
biburl = {https://dblp.org/rec/series/txcs/DowneyF13.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@book{paramcomplexhigher,
author = {Haan, Ronald},
year = {2019},
month = {01},
pages = {},
title = {Parameterized Complexity in the Polynomial Hierarchy: Extending Parameterized Complexity Theory to Higher Levels of the Hierarchy},
isbn = {978-3-662-60669-8},
doi = {10.1007/978-3-662-60670-4}
}
@article{paramflum,
author = {J{\"{o}}rg Flum and
Martin Grohe},
title = {Describing parameterized complexity classes},
journal = {Inf. Comput.},
volume = {187},
number = {2},
pages = {291--319},
year = {2003},
url = {https://doi.org/10.1016/S0890-5401(03)00161-5},
doi = {10.1016/S0890-5401(03)00161-5},
timestamp = {Fri, 12 Feb 2021 22:16:44 +0100},
biburl = {https://dblp.org/rec/journals/iandc/FlumG03.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@inproceedings{pelov_semantics_2004,
title = {Semantics of disjunctive programs with monotone aggregates - an operator-based approach},
url = {http://www.pims.math.ca/science/2004/NMR/papers/paper43.pdf},
pages = {327--334},
booktitle = {10th International Workshop on Non-Monotonic Reasoning ({NMR} 2004), Whistler, Canada, June 6-8, 2004, Proceedings},
author = {Pelov, Nikolay and Truszczynski, Miroslaw},
editor = {Delgrande, James P. and Schaub, Torsten},
date = {2004},
file = {Pelov - Semantics of Disjunctive Programs with Monotone Ag.pdf:/home/squirrel/Zotero/storage/VZCMFV2Q/Pelov - Semantics of Disjunctive Programs with Monotone Ag.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{nondet2,
title = {Non-deterministic approximation fixpoint theory and its application in disjunctive logic programming},
journal = {Artificial Intelligence},
volume = {331},
pages = {104110},
year = {2024},
issn = {0004-3702},
doi = {https://doi.org/10.1016/j.artint.2024.104110},
url = {https://www.sciencedirect.com/science/article/pii/S0004370224000468},
author = {Jesse Heyninck and Ofer Arieli and Bart Bogaerts},
keywords = {Logic Programming, Answer Set Programming, Approximation Fixpoint Theory, Knowledge Representation},
abstract = {Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.}
}
@article{aftjustif,
title = {Embedding justification theory in approximation fixpoint theory},
journal = {Artificial Intelligence},
volume = {331},
pages = {104112},
year = {2024},
issn = {0004-3702},
doi = {https://doi.org/10.1016/j.artint.2024.104112},
url = {https://www.sciencedirect.com/science/article/pii/S0004370224000481},
author = {Simon Marynissen and Bart Bogaerts and Marc Denecker},
keywords = {Justification theory, Approximation fixpoint theory, Knowledge representation},
abstract = {Approximation Fixpoint Theory (AFT) and Justification Theory (JT) are two frameworks to unify logical formalisms. AFT studies semantics in terms of fixpoints of lattice operators, and JT in terms of so-called justifications, which are explanations of why certain facts do or do not hold in a model. While the approaches differ, the frameworks were designed with similar goals in mind, namely to study the different semantics that arise in (mainly) non-monotonic logics. The first contribution of our current paper is to provide a formal link between the two frameworks. To be precise, we show that every justification frame induces an approximator and that this mapping from JT to AFT preserves all major semantics. The second contribution exploits this correspondence to extend JT with a novel class of semantics, namely ultimate semantics: we formally show that ultimate semantics can be obtained in JT by a syntactic transformation on the justification frame, essentially performing a sort of resolution on the rules.}
}
@misc{williams2023survey,
title = {A survey of congruences and quotients of partially ordered sets},
author = {Nicholas J. Williams},
year = {2023},
eprint = {2303.03765},
archiveprefix = {arXiv},
primaryclass = {math.CO}
}
@article{partial_conruence,
author = {Moorthy, C.Ganesa and Karpagavalli, S.G.},
year = {2015},
month = {08},
pages = {401-405},
title = {A congruence relation in partially ordered sets},
volume = {13}
}
@book{sipser,
author = {Michael Sipser},
title = {Introduction to the theory of computation},
publisher = {{PWS} Publishing Company},
year = {1997},
isbn = {978-0-534-94728-6},
timestamp = {Thu, 21 Apr 2011 19:59:45 +0200},
biburl = {https://dblp.org/rec/books/daglib/0086373.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@misc{pos_restriction_defn,
title = {Turning preorders into partial orders},
author = {Xodarap (https://math.stackexchange.com/users/2549/xodarap)},
howpublished = {Mathematics Stack Exchange},
note = {URL:https://math.stackexchange.com/q/471971 (version: 2013-10-05)},
eprint = {https://math.stackexchange.com/q/471971},
url = {https://math.stackexchange.com/q/471971}
}
@misc{po_restriction_name,
title = {Turning preorders into partial orders},
author = {Dan Rust (https://math.stackexchange.com/users/29059/dan-rust)},
howpublished = {Mathematics Stack Exchange},
note = {URL:https://math.stackexchange.com/q/471990 (version: 2013-08-20)},
eprint = {https://math.stackexchange.com/q/471990},
url = {https://math.stackexchange.com/q/471990}
}
@article{disjunctive_complexity,
author = {Thomas Eiter and
Georg Gottlob},
title = {On the Computational Cost of Disjunctive Logic Programming: Propositional
Case},
journal = {Ann. Math. Artif. Intell.},
volume = {15},
number = {3-4},
pages = {289--323},
year = {1995},
url = {https://doi.org/10.1007/BF01536399},
doi = {10.1007/BF01536399},
timestamp = {Sun, 02 Jun 2019 20:45:55 +0200},
biburl = {https://dblp.org/rec/journals/amai/EiterG95.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@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{DBLP:journals/tplp/LiuY22,
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},
url = {https://doi.org/10.1017/S1471068421000168},
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}
}
@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}
}
@inproceedings{DBLP:conf/kr/HeyninckA21,
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},
url = {https://doi.org/10.24963/kr.2021/32},
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}
}
@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{backdoorsnormality,
author = {Johannes Klaus Fichte and
Stefan Szeider},
title = {Backdoors to Normality for Disjunctive Logic Programs},
journal = {{ACM} Trans. Comput. Log.},
volume = {17},
number = {1},
pages = {7},
year = {2015},
url = {https://doi.org/10.1145/2818646},
doi = {10.1145/2818646},
timestamp = {Fri, 10 Jun 2022 10:35:17 +0200},
biburl = {https://dblp.org/rec/journals/tocl/FichteS15.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
}
@article{van1991well,
title={The well-founded semantics for general logic programs},
author={Van Gelder, Allen and Ross, Kenneth A and Schlipf, John S},
journal={Journal of the ACM (JACM)},
volume={38},
number={3},
pages={619--649},
year={1991},
publisher={ACM New York, NY, USA}
}
@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{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{anonkillen2022,
author = {Anonymized},
title = {Anonymized},
}
@article{leone_disjunctive_1997,
title = {Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation},
volume = {135},
issn = {0890-5401},
url = {https://www.sciencedirect.com/science/article/pii/S0890540197926304},
doi = {https://doi.org/10.1006/inco.1997.2630},
abstract = {Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunctive logic programs, we provide two declarative characterizations of stable models in terms of unfounded sets. One shows that the set of stable models coincides with the family of unfounded-free models (i.e., a model is stable iff it contains no unfounded atoms). The other proves that stable models can be defined equivalently by a property of their false literals, as a model is stable iff the set of its false literals coincides with its greatest unfounded set. We then generalize the well-founded {WPoperator} to disjunctive logic programs, give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of function-free programs. The algorithm's soundness and completeness are proved and some complexity issues are discussed.},
pages = {69--112},
number = {2},
journaltitle = {Information and Computation},
author = {Leone, Nicola and Rullo, Pasquale and Scarcello, Francesco},
year = {1997}
}
@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},
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biburl = {https://dblp.org/rec/conf/kr/KillenY21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
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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},
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biburl = {https://dblp.org/rec/conf/kr/HeyninckA21.bib},
bibsource = {dblp computer science bibliography, https://dblp.org}
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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}
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author = {Christian Antic and
Thomas Eiter and
Michael Fink},
editor = {Pedro Cabalar and
Tran Cao Son},
title = {Hex Semantics via Approximation Fixpoint Theory},
booktitle = {Logic Programming and Nonmonotonic Reasoning, 12th International Conference,
{LPNMR} 2013, Corunna, Spain, September 15-19, 2013. Proceedings},
series = {Lecture Notes in Computer Science},
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doi = {10.1007/978-3-642-40564-8\_11},
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bibsource = {dblp computer science bibliography, https://dblp.org}
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title = {Possible model semantics for disjunctive databases},
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year = {1990},
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@inproceedings{sakama1992extended,
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author = {Marc Denecker and
Maurice Bruynooghe and
Joost Vennekens},
editor = {Esra Erdem and
Joohyung Lee and
Yuliya Lierler and
David Pearce},
title = {Approximation Fixpoint Theory and the Semantics of Logic and Answers
Set Programs},
booktitle = {Correct Reasoning - Essays on Logic-Based {AI} in Honour of Vladimir
Lifschitz},
series = {Lecture Notes in Computer Science},
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publisher = {Springer},
year = {2012},
url = {https://doi.org/10.1007/978-3-642-30743-0\_13},
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@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},
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