Abduction Prover in Isabelle/HOL

2026-06-03

AI Summary

This work addresses the limited automation and high cost of formal verification in highly expressive proof assistants by presenting the first systematic integration of abductive reasoning into Isabelle/HOL. The proposed approach synergistically combines abductive inference, automated theorem proving, and the interactive proof environment to automatically generate auxiliary conjectures and executable proof scripts from proof goals. Experimental results demonstrate that this technique substantially enhances Isabelle/HOL’s capacity to automate complex proof tasks and significantly reduces the need for manual intervention. By bridging abductive reasoning with interactive theorem proving, the method opens a new pathway toward scalable formal verification of high-assurance software and systems.

Abstract

Proof assistants based on expressive logics suffer limited automation for proof search, raising the cost of formal verification based on proof assistants. We address this problem by introducing the Abduction Prover for Isabelle/HOL. Given a challenging proof goal, the Abduction Prover constructs a proof script for the goal by identifying useful conjectures using abductive reasoning.

Problem

• proof assistants
• automation
• formal verification
• proof search
• Isabelle/HOL

Innovation

• abductive reasoning
• proof automation
• Isabelle/HOL
• conjecture generation
• proof script synthesis