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

Kettmann, Pascal; Heyninck, Jesse; Strass, Hannes

doi:10.24963/ijcai.2025/506

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

Pascal Kettmann, Jesse Heyninck, Hannes Strass

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Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence. Main Track. Pages 4544-4552.

https://doi.org/10.24963/ijcai.2025/506

Keywords

Uncertainty in AI: UAI: Uncertainty representations
Knowledge Representation and Reasoning: KRR: Logic programming
Knowledge Representation and Reasoning: KRR: Non-monotonic reasoning

Abstract

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.

Pascal Kettmann, Jesse Heyninck, and Hannes Strass. 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-25. IJCAI, 4544–4552. https://doi.org/10.24963/ijcai.2025/506

@inproceedings{ijcai2025p506,
  title     = {Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics},
  author    = {Kettmann, Pascal and Heyninck, Jesse and Strass, Hannes},
  booktitle = {Proceedings of the Thirty-Fourth International Joint Conference on
               Artificial Intelligence, {IJCAI-25}},
  publisher = {International Joint Conferences on Artificial Intelligence Organization},
  editor    = {James Kwok},
  pages     = {4544--4552},
  year      = {2025},
  month     = {8},
  note      = {Main Track},
  doi       = {10.24963/ijcai.2025/506},
  url       = {https://doi.org/10.24963/ijcai.2025/506},
}

TY  - CPAPER
TI  - Approximation Fixpoint Theory as a Unifying Framework for Fuzzy Logic Programming Semantics
AU  - Kettmann, Pascal
AU  - Heyninck, Jesse
AU  - Strass, Hannes
T2  - Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence, IJCAI-25
PB  - International Joint Conferences on Artificial Intelligence Organization
PY  - 2025
SP  - 4544
EP  - 4552
DO  - 10.24963/ijcai.2025/506
UR  - https://doi.org/10.24963/ijcai.2025/506
ER  -