An abstract fixed-point theorem for Horn formula equations

Stefan Hetzl; Johannes Kloibhofer

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arXiv · 2511.08162

An abstract fixed-point theorem for Horn formula equations

Stefan Hetzl·Johannes Kloibhofer

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Abstract

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.

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Stefan Hetzl, Johannes Kloibhofer. 2025-11-11. An abstract fixed-point theorem for Horn formula equations. https://arxiv.org/abs/2511.08162

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