A Category-Theoretic Perspective on Higher-Order Approximation Fixpoint Theory (Extended Version)
<|reference_start|>A Category-Theoretic Perspective on Higher-Order Approximation Fixpoint Theory (Extended Version): Approximation Fixpoint Theory (AFT) is an algebraic framework designed to study the semantics of non-monotonic logics. Despite its success, AFT is not readily applicable to higher-order definitions. To solve such an issue, we devise a formal mathematical framework employing concepts drawn from Category Theory. In particular, we make use of the notion of Cartesian closed category to inductively construct higher-order approximation spaces while preserving the structures necessary for the correct application of AFT. We show that this novel theoretical approach extends standard AFT to a higher-order environment, and generalizes the AFT setting of arXiv:1804.08335 .<|reference_end|>
@article{pollaci2024a,
    title={A Category-Theoretic Perspective on Higher-Order Approximation Fixpoint
  Theory (Extended Version)},
    author={Samuele Pollaci, Babis Kostopoulos, Marc Denecker, Bart Bogaerts},
    journal={arXiv preprint arXiv:2408.11712},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.11712},
    primaryClass={cs.LO}
}