The Stable Model Semantics for Higher-Order Logic Programming
<|reference_start|>The Stable Model Semantics for Higher-Order Logic Programming: We propose a stable model semantics for higher-order logic programs. Our semantics is developed using Approximation Fixpoint Theory (AFT), a powerful formalism that has successfully been used to give meaning to diverse non-monotonic formalisms. The proposed semantics generalizes the classical two-valued stable model semantics of (Gelfond and Lifschitz 1988) as-well-as the three-valued one of (Przymusinski 1990), retaining their desirable properties. Due to the use of AFT, we also get for free alternative semantics for higher-order logic programs, namely supported model, Kripke-Kleene, and well-founded. Additionally, we define a broad class of stratified higher-order logic programs and demonstrate that they have a unique two-valued higher-order stable model which coincides with the well-founded semantics of such programs. We provide a number of examples in different application domains, which demonstrate that higher-order logic programming under the stable model semantics is a powerful and versatile formalism, which can potentially form the basis of novel ASP systems.<|reference_end|>
@article{bogaerts2024the,
    title={The Stable Model Semantics for Higher-Order Logic Programming},
    author={Bart Bogaerts, Angelos Charalambidis, Giannos Chatziagapis, Babis
  Kostopoulos, Samuele Pollaci, Panos Rondogiannis},
    journal={arXiv preprint arXiv:2408.10563},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.10563},
    primaryClass={cs.LO cs.AI cs.PL}
}