A Category-Theoretic Perspective on Higher-Order Approximation Fixpoint Theory
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917200336519168 |
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| author | Pollaci, Samuele Kostopoulos, Babis Denecker, Marc Bogaerts, Bart |
| author_facet | Pollaci, Samuele Kostopoulos, Babis Denecker, Marc Bogaerts, Bart |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Category-Theoretic Perspective on Higher-Order Approximation Fixpoint Theory Pollaci, Samuele Kostopoulos, Babis Denecker, Marc Bogaerts, Bart Logic in Computer Science 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). |
| title | A Category-Theoretic Perspective on Higher-Order Approximation Fixpoint Theory |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2408.11712 |