Learning-Infused Formal Reasoning: From Contract Synthesis to Artifact Reuse and Formal Semantics

TL;DR

The paper addresses the challenge that AI systems lack strong, formal guarantees and that traditional formal methods struggle to scale with learned components. It proposes Learning-Infused Formal Reasoning (LIFR), a framework that unifies automated contract synthesis, semantic artifact reuse via graph-based representations, and a unifying semantic theory (based on Unifying Theories of Programming and the Theory of Institutions) to enable cross-formalism verification. It introduces VERIFYAI as a contract-synthesis architecture, a graph-augmented reuse pipeline with LLM-guided semantic enrichment, and a theory-driven interoperability foundation aimed at scalable, traceable verification ecosystems. The work envisions verification knowledge progressively accumulated and propagated across projects and lifecycles, enhancing safety-critical AI and cyber-physical systems through principled semantic grounding and cooperative human-machine oversight.

Abstract

This vision paper articulates a long-term research agenda for formal methods at the intersection with artificial intelligence, outlining multiple conceptual and technical dimensions and reporting on our ongoing work toward realising this agenda. It advances a forward-looking perspective on the next generation of formal methods based on the integration of automated contract synthesis, semantic artifact reuse, and refinement-based theory. We argue that future verification systems must move beyond isolated correctness proofs toward a cumulative, knowledge-driven paradigm in which specifications, contracts, and proofs are continuously synthesised and transferred across systems. To support this shift, we outline a hybrid framework combining large language models with graph-based representations to enable scalable semantic matching and principled reuse of verification artifacts. Learning-based components provide semantic guidance across heterogeneous notations and abstraction levels, while symbolic matching ensures formal soundness. Grounded in compositional reasoning, this vision points toward verification ecosystems that evolve systematically, leveraging past verification efforts to accelerate future assurance.

Figures (2)

• Figure 1: High-level conceptual architecture of the LIFR framework.
• Figure 2: Visionary workflow for verification artefact reuse via hybrid graph matching and LLM-based semantic enrichment.