2024/08/21 by Pollaci, Samuele, Kostopoulos, Babis, Denecker, Marc +1
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.2408.11712
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 . Under consideration in Theory and Practice of Logic Programming (TPLP).