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arXiv · 2408.11712

A Category-Theoretic Perspective on Higher-Order Approximation Fixpoint Theory

Samuele Pollaci·Babis Kostopoulos·Marc Denecker·Bart Bogaerts
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Abstract

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).

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Samuele Pollaci, Babis Kostopoulos, Marc Denecker, Bart Bogaerts. 2024-08-21. A Category-Theoretic Perspective on Higher-Order Approximation Fixpoint Theory. https://doi.org/10.1017/s1471068425100367

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