Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics

Pascal KettmannPascal Kettmann, Jesse HeyninckJesse Heyninck, Hannes StraßHannes Straß

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Pascal Kettmann, Jesse Heyninck, Hannes Straß
Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics
Proceedings of the 34th International Joint Conference on Artificial Intelligence, IJCAI 2025, to appear

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KurzfassungAbstract
Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of the most prominent classical semantics, namely the stable model and the well-founded semantics, can be reconstructed within the general framework of approximation fixpoint theory (AFT). This not only widens the scope of AFT from two- to many-valued logics, but allows a wide range of existing AFT results to be applied to fuzzy logic programming. As first examples of such applications, we clarify the formal relationship between existing semantics, generalize the notion of stratification from classical to fuzzy logic programs, and devise “more precise” variants of the semantics.
Projekt:Project: KIMEDS, MEDGE, SECAI, SEMECO-Q2
Forschungsgruppe:Research Group: Computational LogicComputational Logic

@inproceedings{KHS2025,
  author    = {Pascal Kettmann and Jesse Heyninck and Hannes Stra{\ss}},
  title     = {Approximation Fixpoint Theory as a Unifying Framework for Fuzzy
               Logic Programming Semantics},
  booktitle = {Proceedings of the 34th International Joint Conference on
               Artificial Intelligence,  {IJCAI} 2025},
  year      = {2025}
}