arXiv subjects

Ioana Leuştean

Publications and source records attributed to Ioana Leuştean.

4 recordsLinked to original sources

arXiv2026

Formalizing a Many-Sorted Hybrid Polyadic Modal Logic in Lean

We present a Lean formalization of a general hybrid modal logic with many-sorted signatures and polyadic modal operators. The system borrows ideas from both algebraic specification and dynamic logics, and is designed to serve as a uniform axiomatic foundation for specifying and verifying programming languages and security protocols. We expose a DSL for users to define languages and protocols as many-sorted signatures, specify the relevant domain-specific axioms, and reason about program executions or protocol runs. We provide a machine-checked proof of its soundness theorem and showcase the framework's versatility through several applications: an imperative programming language for code verification, the BAN logic for security protocols, and the modal system S5. We have designed our formalization to be intrinsically sorted, that is, well-sorted formulas in the base language are well-typed terms in Lean. Thanks to intrinsic sorting, all domain specific applications can be easily embedded in our framework via the DSL, at no additional syntactic overhead required for the user to prove. All code presented in this paper is openly accessible in the following repository: https://github.com/alexoltean61/msphml-lean

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arXiv2025

Łukasiewicz Logic with Actions for Neural Networks training

Based on the already known connection between multilayer perceptrons and Lukasiewicz logic with rational coefficients, we take a step forward in analyzing its training process using a three-sorted hybrid modal logic: a multilayer perceptron is a logical formula; the actions of the training process are modal operators; the training process is a sequence of logical deductions. Using the proof assistant and the programming language Lean 4, the algorithmic implementation of the training process is certified by logical proofs.

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arXiv2020

Many-Sorted Hybrid Modal Languages

We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of the full logic, for which we prove sound and complete deduction and we show that it is powerful enough to represent both the programs and their semantics in an uniform way. Although weaker than other hybrid systems previously developed, this system is expected to have better computational properties. Finally, we provide a standard translation from full hybrid many-sorted logic to first-order logic.

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arXiv2019

From Hybrid Modal Logic to Matching Logic and Back

Building on our previous work on hybrid polyadic modal logic we identify modal logic equivalents for Matching Logic, a logic for program specification and verification. This provides a rigorous way to transfer results between the two approaches, which should benefit both systems.

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