References

  1. M. Andreşel, J. Corman, M. Ortiz, J.L. Reutter, O. Savkovic & M. Simkus (2020): Stable model semantics for recursive SHACL. In: Proceedings of WWW, pp. 1570–1580, doi:10.1145/3366423.3380229.
  2. Grigoris Antoniou, Paul Groth, Frank van Harmelen & Rinke Hoekstra (2012): A Semantic Web Primer, 3rd Edition. MIT Press.
  3. F. Baader, I. Horrocks, C. Lutz & U. Sattler (2017): An Introduction to Description Logic. Cambridge University Press, doi:10.1017/9781139025355.
  4. Bart Bogaerts (2019): Weighted Abstract Dialectical Frameworks through the Lens of Approximation Fixpoint Theory. In: Proceedings of AAAI, pp. 2686–2693, doi:10.1609/aaai.v33i01.33012686.
  5. Bart Bogaerts & Luís Cruz-Filipe (2018): Fixpoint Semantics for Active Integrity Constraints. AIJ 255, pp. 43–70, doi:10.1016/j.artint.2017.11.003.
  6. Bart Bogaerts & Luís Cruz-Filipe (2021): Stratification in Approximation Fixpoint Theory and Its Application to Active Integrity Constraints. ACM Trans. Comput. Log. 22(1), pp. 6:1–6:19, doi:10.1145/3430750.
  7. Bart Bogaerts, Maxime Jakubowski & Jan Van den Bussche (2021): SHACL: A Description Logic in Disguise. CoRR abs/2108.06096.
  8. Bart Bogaerts, Joost Vennekens & Marc Denecker (2015): Grounded fixpoints and their applications in knowledge representation. AIJ 224, pp. 51–71, doi:10.1016/j.artint.2015.03.006.
  9. I. Boneva, J.E. Labro Gayo & E.G. Prud'hommeaux (2017): Semantics and validation of shape schemas for RDF. In: Proceedings of ISWC, pp. 104–120, doi:10.1007/978-3-319-68288-4_7.
  10. Gerhard Brewka, Hannes Strass, Stefan Ellmauthaler, Johannes Peter Wallner & Stefan Woltran (2013): Abstract Dialectical Frameworks Revisited. In: Proceedings of IJCAI, pp. 803–809, doi:10.5555/2540128.2540245.
  11. Angelos Charalambidis, Panos Rondogiannis & Ioanna Symeonidou (2018): Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs. TPLP 18(3-4), pp. 421–437, doi:10.1017/S1471068418000108.
  12. J. Corman, J.L. Reutter & O. Savkovic (2018): Semantics and validation of recursive SHACL. In: Proceedings of ISWC, pp. 318–336. Extended version, technical report KRDB18-01.
  13. Broes De Cat, Bart Bogaerts, Maurice Bruynooghe, Gerda Janssens & Marc Denecker (2016): Predicate Logic as a Modelling Language: The IDP System. CoRR abs/1401.6312v2, doi:10.1145/3191315.3191321.
  14. Marc Denecker, Victor Marek & Mirosław Truszczyński (2000): Approximations, Stable Operators, Well-Founded Fixpoints and Applications in Nonmonotonic Reasoning. In: Logic-Based Artificial Intelligence, pp. 127–144, doi:10.1007/978-1-4615-1567-8_6.
  15. Marc Denecker, Victor Marek & Mirosław Truszczyński (2003): Uniform semantic treatment of default and autoepistemic logics. AIJ 143(1), pp. 79–122, doi:10.1016/S0004-3702(02)00293-X.
  16. Marc Denecker, Victor Marek & Mirosław Truszczyński (2004): Ultimate approximation and its application in nonmonotonic knowledge representation systems. Information and Computation 192(1), pp. 84–121, doi:10.1016/j.ic.2004.02.004.
  17. Marc Denecker & Joost Vennekens (2014): The Well-Founded Semantics Is the Principle of Inductive Definition, Revisited. In: Proceedings of KR, pp. 22–31, doi:10.5555/3031929.3031933.
  18. Melvin Fitting (2002): Fixpoint semantics for logic programming — A survey. Theoretical Computer Science 278(1-2), pp. 25–51, doi:10.1016/S0304-3975(00)00330-3.
  19. Fangfang Liu, Yi Bi, Md. Solimul Chowdhury, Jia-Huai You & Zhiyong Feng (2016): Flexible Approximators for Approximating Fixpoint Theory. In: Proceedings of Canadian AI, pp. 224–236, doi:10.1007/978-3-319-34111-8_28.
  20. (2012): OWL 2 Web Ontology Language: Structural Specification and Functional-Style Syntax. W3C Recommendation.
  21. Nikolay Pelov, Marc Denecker & Maurice Bruynooghe (2007): Well-founded and Stable Semantics of Logic Programs with Aggregates. TPLP 7(3), pp. 301–353, doi:10.1017/S1471068406002973.
  22. (2014): RDF 1.1 Primer. W3C Working Group Note. Available at https://www.w3.org/TR/rdf11-primer/.
  23. (2017): Shapes Constraint Language (SHACL). W3C Recommendation. Available at https://www.w3.org/TR/shacl/.
  24. Hannes Strass (2013): Approximating operators and semantics for abstract dialectical frameworks. AIJ 205, pp. 39–70, doi:10.1016/j.artint.2013.09.004.
  25. Mirosław Truszczyński (2006): Strong and uniform equivalence of nonmonotonic theories - an algebraic approach. Ann. Math. Artif. Intell. 48(3-4), pp. 245–265, doi:10.1007/s10472-007-9049-2.
  26. Maarten H. van Emden & Robert A. Kowalski (1976): The Semantics of Predicate Logic as a Programming Language. J. ACM 23(4), pp. 733–742, doi:10.1145/321978.321991.
  27. Joost Vennekens, David Gilis & Marc Denecker (2006): Splitting an operator: Algebraic modularity results for logics with fixpoint semantics. ACM Trans. Comput. Log. 7(4), pp. 765–797, doi:10.1145/1182613.1189735.
  28. Joost Vennekens, Maarten Mariën, Johan Wittocx & Marc Denecker (2007): Predicate Introduction for Logics With a Fixpoint Semantics. Parts I and II. Fundamenta Informaticae 79(1-2), pp. 187–227, doi:10.5555/2366527.2366536.
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