Short Version of VERIFAI2026 Paper -- Learning Infused Formal Reasoning: Contract Synthesis, Artefact Reuse and Semantic Foundations

Abstract: Artificial intelligence systems have achieved remarkable capability in natural language processing, perception and decision-making tasks. However, their behaviour often remains opaque and difficult to verify, limiting their applicability in safety-critical systems. Formal methods provide mathematically rigorous mechanisms for specifying and verifying system behaviour, yet the creation and maintenance of formal specifications remains labour intensive and difficult to scale. This paper outlines a research vision called Learning-Infused Formal Reasoning (LIFR), which integrates machine learning techniques with formal verification workflows. The framework focuses on three complementary research directions: automated contract synthesis from natural language requirements, semantic reuse of verification artifacts using graph matching and learning-based embeddings, and mathematically grounded semantic foundations based on the Unifying Theories of Programming (UTP) and the Theory of Institutions. Together these research threads aim to transform verification from isolated correctness proofs into a cumulative knowledge-driven process where specifications, contracts and proofs can be synthesised, aligned and reused across systems.

• The paper demonstrates how integrating machine learning with formal methods automates contract synthesis by generating and refining logical predicates from natural language requirements.
• The paper shows that graph-based artifact reuse enables cumulative verification by structurally and semantically matching and adapting previous proofs and models.
• The paper establishes rigorous semantic foundations using UTP and institution theory to ensure that dynamically updated contracts remain mathematically sound and interoperable.

Learning-Infused Formal Reasoning: Integrating Machine Learning and Formal Methods for Contract Synthesis, Artifact Reuse, and Semantic Foundations

Research Agenda Overview

The paper "Learning-Infused Formal Reasoning: Contract Synthesis, Artefact Reuse and Semantic Foundations" (2604.12747) advances a compelling integration of ML with formal methods (FMs) for scalable, cumulative verification of safety-critical and high-assurance systems. The Learning-Infused Formal Reasoning (LIFR) framework targets existing impediments to the adoption of FMs—especially the cost and complexity of specification creation and the limited practical reuse of verification artifacts—by leveraging LLM-driven contract synthesis, graph-based artifact reuse, and robust semantic foundations. The synthesis of these approaches aims to construct a neuro-symbolic pipeline in which learning components enhance but do not replace formal rigor, preserving soundness and enabling interoperability across heterogeneous verification environments.

Automated Contract Synthesis via Neuro-Symbolic Pipelines

Manual translation of informal requirements into machine-verifiable contracts remains a principal bottleneck in formal verification workflows. LIFR addresses this by employing LLMs to generate candidate logical predicates from natural language requirements, thus automating the creation of preconditions, postconditions, and invariants. The generated specifications are then iteratively validated and refined using SMT solvers and proof assistants, creating an automated feedback loop that bridges the inductive pattern-learning abilities of ML models with deductive rigor from FMs.

A distinguishing claim is the promotion of dynamic contracts: contracts are no longer treated as static documentation, but as artifacts that can be inferred, updated, and repaired as the underlying system or its requirements evolve. The feedback-driven neuro-symbolic pipeline gives rise to specifications that adapt in real time, fundamentally shifting the FM development paradigm.

This approach operationalizes a neuro-symbolic symbiosis: LLMs propose candidate contracts, while symbolic tools verify logical consistency and drive further sample-efficient refinement. Such a pipeline promises to reduce the cost curve for industrial-scale adoption of formal specification engineering.

Artifact Reuse through Graph-Based Representations and Semantic Matching

A major open issue in verification is the lack of effective mechanisms for the reuse of specifications, proofs, and models across projects and development cycles. LIFR advances a hybrid reuse mechanism: all relevant artifacts are mapped to richly typed attributed graphs, enabling structural and semantic comparison using both graph matching algorithms and semantic embeddings derived from LLMs.

Graph nodes are enriched with semantic information (e.g., variable names, docstrings, comments), supporting approximate matching that considers both structure and meaning. This hybrid approach enables the identification and retrieval of relevant formal artifacts from a growing body of prior proofs, models, or contracts. Retrieved graphs are adapted through graph transformation rules, permitting refinement and fit to the current verification context.

The practical implication is the transformation of verification into a cumulative, knowledge-driven process: verification efforts are amortized across development lifecycles, and prior verification investments compound in value as they are reused and extended. This strategy is positioned as a scalable enabler for FM adoption in environments characterized by frequent requirement changes and complex system interdependencies.

Mathematical Rigor: UTP and Institution Theory as Semantic Foundations

While ML models can enhance synthesis and reuse, they lack intrinsic support for soundness and interoperability. LIFR anchors its neuro-symbolic processes in rigorous semantic frameworks: the Unifying Theories of Programming (UTP) and the Theory of Institutions.

UTP offers a relational semantic framework capable of subsuming disparate programming paradigms and specification styles under a single algebraic theory. With refinement relations and healthiness conditions, UTP enables cross-paradigm reasoning while enforcing fundamental semantic properties, which recent theorem-proving implementations such as Isabelle/UTP now mechanize.

The Theory of Institutions supplies a categorical abstraction for defining families of logics and specification languages, encoding their signatures, sentences, models, and satisfaction relations. This enables translation and interoperability of specifications across diverse formalisms.

By embedding AI-driven synthesis and adaptation mechanisms within the constraints imposed by UTP and institution theory, LIFR ensures that generated artifacts are not only expressive and adaptable, but also logically sound and semantically coherent. This governance mitigates the risk of unsound contracts or transformations, particularly important in high-assurance domains.

Numerical and Methodological Claims

The paper emphasizes that the LIFR framework does not simply automate existing FM procedures but fundamentally shifts the nature of contract management from static documents to dynamic, living artifacts responsive to change. It boldly asserts that neuro-symbolic feedback loops can close long-standing scalability and reusability gaps, transforming FM from isolated correctness proofs into a cumulative, evolving process.

Although the short version does not present empirical results, it claims that LIFR’s pipeline and ecosystem can yield substantial gains in specification reuse and reduction in manual effort, especially as the knowledge base of artifacts grows.

Implications and Future Outlook

The LIFR paradigm has multifaceted implications. Practically, it promises to accelerate the deployment of FMs in domains where verification has been traditionally viewed as prohibitively expensive or slow-moving—such as adaptive AI-enabled systems, autonomous platforms, and regulated cyber-physical environments. Theoretically, it provokes renewed interest in the integration of learning and logic, pushing toward robust neuro-symbolic systems where learning augments, but does not supplant, formal semantic guarantees.

If successfully implemented at scale, LIFR-style frameworks are poised to enable large-scale, collaborative verification workflows where contracts, proofs, and models become systematically discoverable, shareable, and incrementally improvable. This has potential to fundamentally alter best practices in verified software engineering and support the safe integration of advanced AI within critical systems.

Conclusion

LIFR delineates a cohesive research agenda at the intersection of machine learning and formal methods. Automated contract synthesis, graph-based artifact reuse, and strong semantic underpinnings via UTP and institutional logic together chart a pathway toward scalable, reusable, and mathematically sound verification. This cross-disciplinary integration reimagines formal methods as a cumulative, knowledge-driven scientific discipline, with profound implications for both the rigor and efficiency of software and AI system engineering.