An abstract fixed-point theorem for Horn formula equations
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914150894010368 |
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| author | Hetzl, Stefan Kloibhofer, Johannes |
| author_facet | Hetzl, Stefan Kloibhofer, Johannes |
| contents | We consider a class of formula equations in first-order logic, Horn formula equations, which are defined by a syntactic restriction on the occurrences of predicate variables. Horn formula equations play an important role in many applications in computer science. We state and prove a fixed-point theorem for Horn formula equations in first-order logic with a least fixed-point operator. Our fixed-point theorem is abstract in the sense that it applies to an abstract semantics which generalises standard semantics. We describe several corollaries of this fixed-point theorem in various areas of computational logic, ranging from the logical foundations of program verification to inductive theorem proving. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08162 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An abstract fixed-point theorem for Horn formula equations Hetzl, Stefan Kloibhofer, Johannes Logic in Computer Science Logic We consider a class of formula equations in first-order logic, Horn formula equations, which are defined by a syntactic restriction on the occurrences of predicate variables. Horn formula equations play an important role in many applications in computer science. We state and prove a fixed-point theorem for Horn formula equations in first-order logic with a least fixed-point operator. Our fixed-point theorem is abstract in the sense that it applies to an abstract semantics which generalises standard semantics. We describe several corollaries of this fixed-point theorem in various areas of computational logic, ranging from the logical foundations of program verification to inductive theorem proving. |
| title | An abstract fixed-point theorem for Horn formula equations |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2511.08162 |