Tootfinder

What You Code Is What We Prove: Translating BLE App Logic into Formal Models with LLMs for Vulnerability Detection
Biwei Yan, Yue Zhang, Minghui Xu, Runyu Pan, Jinku Li, Xiuzhen Cheng
https://arxiv.org/abs/2509.09291

What You Code Is What We Prove: Translating BLE App Logic into Formal Models with LLMs for Vulnerability Detection
The application layer of Bluetooth Low Energy (BLE) is a growing source of security vulnerabilities, as developers often neglect to implement critical protections such as encryption, authentication, and freshness. While formal verification offers a principled way to check these properties, the manual effort of constructing formal models makes it impractical for large-scale analysis. This paper introduces a key insight: BLE application security analysis can be reframed as a semantic translation …

Hammering Higher Order Set Theory
Chad E. Brown, Cezary Kaliszyk, Martin Suda, Josef Urban
https://arxiv.org/abs/2509.08264 https://arxiv.org/pdf/2509.0826…

Hammering Higher Order Set Theory
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of two. Higher order automated theorem provers are particularly useful here, since the underlying framework of higher order set theory coincides with the classical extensional higher order logic of (most) higher order automated theorem provers, so no significant tr…

Handling Open-Vocabulary Constructs in Formalizing Specifications: Retrieval-Augmented Parsing with Expert Knowledge
Mohammad Saqib Hasan, Sayontan Ghosh, Dhruv Verma, Geoff Kuenning, Erez Zadok, Scott A. Smolka, Niranjan Balasubramanian
https://arxiv.org/abs/2509.08808

Handling Open-Vocabulary Constructs in Formalizing Specifications: Retrieval-Augmented Parsing with Expert Knowledge
We study the problem of Open-Vocabulary Constructs(OVCs) -- ones not known beforehand -- in the context of converting natural language (NL) specifications into formal languages (e.g., temporal logic or code). Models fare poorly on OVCs due to a lack of necessary knowledge a priori. In such situations, a domain expert can provide correct constructs at inference time based on their preferences or domain knowledge. Our goal is to effectively reuse this inference-time, expert-provided knowledge for…

On the equivalence invariance of formal category theory
Paula Verdugo
https://arxiv.org/abs/2509.04255 https://arxiv.org/pdf/2509.04255

On the equivalence invariance of formal category theory
We prove a result of equivalence invariance of formal category theory for statements that can be expressed within an equipment. To do this, we exploit Henry and Bardomiano Martínez's link between Makkai's FOLDS (first order logic with dependent sorts) and abstract homotopy theory. In the process, we construct a model structure on the category DblCat of double categories and double functors, whose trivial fibrations are the double functors that are surjective on objects, full on horizontal and …

The analogy theorem in Hoare logic
Nikitin Nikita
https://arxiv.org/abs/2510.03685 https://arxiv.org/pdf/2510.03685…

The analogy theorem in Hoare logic
The introduction of machine learning methods has led to significant advances in automation, optimization, and discoveries in various fields of science and technology. However, their widespread application faces a fundamental limitation: the transfer of models between data domains generally lacks a rigorous mathematical justification. The key problem is the lack of formal criteria to guarantee that a model trained on one type of data will retain its properties on another.This paper proposes a so…

A Hoare Logic for Symmetry Properties
Vaibhav Mehta, Justin Hsu
https://arxiv.org/abs/2509.00587 https://arxiv.org/pdf/2509.00587

A Hoare Logic for Symmetry Properties
Many natural program correctness properties can be stated in terms of symmetries, but existing formal methods have little support for reasoning about such properties. We consider how to formally verify a broad class of symmetry properties expressed in terms of group actions. To specify these properties, we design a syntax for group actions, supporting standard constructions and a natural notion of entailment. Then, we develop a Hoare-style logic for verifying symmetry properties of …

Automaton Constrained Q-Learning
Anastasios Manganaris, Vittorio Giammarino, Ahmed H. Qureshi
https://arxiv.org/abs/2510.05061 https://arxiv.org/pdf/2510.0…

Automaton Constrained Q-Learning
Real-world robotic tasks often require agents to achieve sequences of goals while respecting time-varying safety constraints. However, standard Reinforcement Learning (RL) paradigms are fundamentally limited in these settings. A natural approach to these problems is to combine RL with Linear-time Temporal Logic (LTL), a formal language for specifying complex, temporally extended tasks and safety constraints. Yet, existing RL methods for LTL objectives exhibit poor empirical performance in compl…

Advancing Natural Language Formalization to First Order Logic with Fine-tuned LLMs
Felix Vossel, Till Mossakowski, Bj\"orn Gehrke
https://arxiv.org/abs/2509.22338 https://

Advancing Natural Language Formalization to First Order Logic with Fine-tuned LLMs
Automating the translation of natural language to first-order logic (FOL) is crucial for knowledge representation and formal methods, yet remains challenging. We present a systematic evaluation of fine-tuned LLMs for this task, comparing architectures (encoder-decoder vs. decoder-only) and training strategies. Using the MALLS and Willow datasets, we explore techniques like vocabulary extension, predicate conditioning, and multilingual training, introducing metrics for exact match, logical equiv…

Crosslisted article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- Bridging LLM Planning Agents and Formal Methods: A Case Study in Plan Verification
Keshav Ramani, Vali Tawosi, Salwa Alamir, Daniel Borrajo

From Grounding to Skolemization: A Logic-Constrained Vector Symbolic Architecture for Complex Query Answering
Yuyin Lu, Hegang Chen, Yanghui Rao
https://arxiv.org/abs/2509.10837

From Grounding to Skolemization: A Logic-Constrained Vector Symbolic Architecture for Complex Query Answering
Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs), typically formalized as reasoning with Existential First-Order predicate logic with one free variable (EFO$_1$), faces a fundamental trade-off between logical soundness and computational efficiency. This work establishes the Grounding-Skolemization dichotomy for systematically analyzing CQA methods through the lens of formal logic. While Grounding-based methods inherently suffer from combinatorial explosion, most Skolemizatio…

Assessing Trustworthiness of AI Training Dataset using Subjective Logic -- A Use Case on Bias
Koffi Ismael Ouattara, Ioannis Krontiris, Theo Dimitrakos, Frank Kargl
https://arxiv.org/abs/2508.13813

Assessing Trustworthiness of AI Training Dataset using Subjective Logic -- A Use Case on Bias
As AI systems increasingly rely on training data, assessing dataset trustworthiness has become critical, particularly for properties like fairness or bias that emerge at the dataset level. Prior work has used Subjective Logic to assess trustworthiness of individual data, but not to evaluate trustworthiness properties that emerge only at the level of the dataset as a whole. This paper introduces the first formal framework for assessing the trustworthiness of AI training datasets, enabling uncert…

Controller synthesis method for multi-agent system based on temporal logic specification
Ruohan Huang, Zining Cao
https://arxiv.org/abs/2509.00870 https://…

Controller synthesis method for multi-agent system based on temporal logic specification
Controller synthesis is a theoretical approach to the systematic design of discrete event systems. It constructs a controller to provide feedback and control to the system, ensuring it meets specified control specifications. Traditional controller synthesis methods often use formal languages to describe control specifications and are mainly oriented towards single-agent and non-probabilistic systems. With the increasing complexity of systems, the control requirements that need to be satisfied a…

PAT-Agent: Autoformalization for Model Checking
Xinyue Zuo, Yifan Zhang, Hongshu Wang, Yufan Cai, Zhe Hou, Jing Sun, Jin Song Dong
https://arxiv.org/abs/2509.23675 https://

PAT-Agent: Autoformalization for Model Checking
Recent advances in large language models (LLMs) offer promising potential for automating formal methods. However, applying them to formal verification remains challenging due to the complexity of specification languages, the risk of hallucinated output, and the semantic gap between natural language and formal logic. We introduce PAT-Agent, an end-to-end framework for natural language autoformalization and formal model repair that combines the generative capabilities of LLMs with the rigor of fo…

Proceedings of the 22nd International Conference on Quantum Physics and Logic
Alejandro D\'iaz-Caro, Ognyan Oreshkov, Ana Bel\'en Sainz
https://arxiv.org/abs/2508.13619 …

Proceedings of the 22nd International Conference on Quantum Physics and Logic
This volume contains the proceedings of the 22nd International Conference on Quantum Physics and Logic (QPL 2025), which was held from 14th to 18th July 2025, in Varna, Bulgaria, organised by Université libre de Bruxelles. QPL is an annual conference that brings together academic and industry researchers working on the mathematical foundations of quantum computation, quantum physics, and related areas. The main focus is on the use of algebraic and categorical structures, formal languages, sema…

An Iterative Approach for Heterogeneous Multi-Agent Route Planning with Resource Transportation Uncertainty and Temporal Logic Goals
Gustavo A. Cardona, Kaier Liang, Cristian-Ioan Vasile
https://arxiv.org/abs/2508.19429

An Iterative Approach for Heterogeneous Multi-Agent Route Planning with Resource Transportation Uncertainty and Temporal Logic Goals
This paper presents an iterative approach for heterogeneous multi-agent route planning in environments with unknown resource distributions. We focus on a team of robots with diverse capabilities tasked with executing missions specified using Capability Temporal Logic (CaTL), a formal framework built on Signal Temporal Logic to handle spatial, temporal, capability, and resource constraints. The key challenge arises from the uncertainty in the initial distribution and quantity of resources in the…

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Multi-representation associated to the numbering of a subbasis and formal inclusion relations
Emmanuel Rauzy

Crosslisted article(s) found for cs.LO. https://arxiv.org/list/cs.LO/new
[1/1]:
- Vision: An Extensible Methodology for Formal Software Verification in Microservice Systems
Connor Wojtak, Darek Gajewski, Tomas Cerny

Bridging Threat Models and Detections: Formal Verification via CADP
Dumitru-Bogdan Prelipcean (Bitdefender, Ia\c{s}i, Romania, Alexandru Ioan Cuza University, Iasi, Romania, LACL, Universite Paris-Est Creteil, France), C\u{a}t\u{a}lin Dima (LACL, Universit\'e Paris-Est Cr\'et\'eil, France)
https://arxiv.org/abs/2509.13035

Bridging Threat Models and Detections: Formal Verification via CADP
Threat detection systems rely on rule-based logic to identify adversarial behaviors, yet the conformance of these rules to high-level threat models is rarely verified formally. We present a formal verification framework that models both detection logic and attack trees as labeled transition systems (LTSs), enabling automated conformance checking via bisimulation and weak trace inclusion. Detection rules specified in the Generic Threat Detection Language (GTDL, a general-purpose detection langua…

On a Dependently Typed Encoding of Matching Logic
\'Ad\'am Kurucz (E\"otv\"os Lor\'and University, Hungary), P\'eter Bereczky (E\"otv\"os Lor\'and University, Hungary), D\'aniel Horp\'acsi (E\"otv\"os Lor\'and University, Hungary)
https://arxiv.org/abs/2509.13018

On a Dependently Typed Encoding of Matching Logic
Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of matching $μ$-logic, a sorted, polyadic variant of the logic. Metatheoretic reasoning requires the logic to be expressed within a foundational theory; opting for a dependently typed one enables well-sortedness in the object theory to correspond directly to well-typ…

Transition-based vs stated-based acceptance for automata over infinite words
Antonio Casares
https://arxiv.org/abs/2508.15402 https://arxiv.org/pdf/2508.15…

Transition-based vs stated-based acceptance for automata over infinite words
Automata over infinite objects are a well-established model with applications in logic and formal verification. Traditionally, acceptance in such automata is defined based on the set of states visited infinitely often during a run. However, there is a growing trend towards defining acceptance based on transitions rather than states. In this survey, we analyse the reasons for this shift and advocate using transition-based acceptance in the context of automata over infinite words. We present a …

Formal Reasoning for Intelligent QA Systems: A Case Study in the Educational Domain
Tuan Bui, An Nguyen, Phat Thai, Minh Hua, Ngan Pham L. N., Ngan Pham T. B., Dung Le, Long Nguyen, Thanh-Tung Tran, Thang Bui, Tho Quan
https://arxiv.org/abs/2509.11572

Formal Reasoning for Intelligent QA Systems: A Case Study in the Educational Domain
Reasoning is essential for closed-domain QA systems in which procedural correctness and policy compliance are critical. While large language models (LLMs) have shown strong performance on many reasoning tasks, recent work reveals that their reasoning traces are often unfaithful - serving more as plausible justifications than as causally grounded derivations. Efforts to combine LLMs with symbolic engines (e.g., Prover9, Z3) have improved reliability but remain limited to static forms of logic, s…

Replaced article(s) found for math.LO. https://arxiv.org/list/math.LO/new
[1/1]:
- Multi-representation associated to the numbering of a subbasis and formal inclusion relations
Emmanuel Rauzy

Inference of Human-derived Specifications of Object Placement via Demonstration
Alex Cuellar, Ho Chit Siu, Julie A Shah
https://arxiv.org/abs/2508.19367 https://

Inference of Human-derived Specifications of Object Placement via Demonstration
As robots' manipulation capabilities improve for pick-and-place tasks (e.g., object packing, sorting, and kitting), methods focused on understanding human-acceptable object configurations remain limited expressively with regard to capturing spatial relationships important to humans. To advance robotic understanding of human rules for object arrangement, we introduce positionally-augmented RCC (PARCC), a formal logic framework based on region connection calculus (RCC) for describing the relative…

Reasoning Core: A Scalable RL Environment for LLM Symbolic Reasoning
Valentin Lacombe, Valentin Quesnel, Damien Sileo
https://arxiv.org/abs/2509.18083 https://

Reasoning Core: A Scalable RL Environment for LLM Symbolic Reasoning
We introduce Reasoning Core, a new scalable environment for Reinforcement Learning with Verifiable Rewards (RLVR), designed to advance foundational symbolic reasoning in Large Language Models (LLMs). Unlike existing benchmarks that focus on games or isolated puzzles, Reasoning Core procedurally generates problems across core formal domains, including PDDL planning, first-order logic, context-free grammar parsing, causal reasoning, and system equation solving. The environment is built on key des…

A Correct by Construction Fault Tolerant Voter for Input Selection of a Control System
Arif Ali AP, Jasine Babu, Deepa Sara John
https://arxiv.org/abs/2509.22236 https://…

A Correct by Construction Fault Tolerant Voter for Input Selection of a Control System
Safety-critical systems use redundant input units to improve their reliability and fault tolerance. A voting logic is then used to select a reliable input from the redundant sources. A fault detection and isolation rules help in selecting input units that can participate in voting. This work deals with the formal requirement formulation, design, verification and synthesis of a generic voting unit for an $N$-modular redundant measurement system used for control applications in avionics systems. …

e-boost: Boosted E-Graph Extraction with Adaptive Heuristics and Exact Solving
Jiaqi Yin, Zhan Song, Chen Chen, Yaohui Cai, Zhiru Zhang, Cunxi Yu
https://arxiv.org/abs/2508.13020

e-boost: Boosted E-Graph Extraction with Adaptive Heuristics and Exact Solving
E-graphs have attracted growing interest in many fields, particularly in logic synthesis and formal verification. E-graph extraction is a challenging NP-hard combinatorial optimization problem. It requires identifying optimal terms from exponentially many equivalent expressions, serving as the primary performance bottleneck in e-graph based optimization tasks. However, traditional extraction methods face a critical trade-off: heuristic approaches offer speed but sacrifice optimality, while exac…

Representations
Paul Brunet (UPEC UP12, LACL)
https://arxiv.org/abs/2510.11419 https://arxiv.org/pdf/2510.11419

Representations
The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often, one particular property can prove frustrating to establish: completeness of the logic with respect to the semantics. In this paper, we try and make such developments easier, with a particular attention on completeness. Towards that aim, we propose a formal (…

On Middle Grounds for Preference Statements
Anne-Marie George, Ana Ozaki
https://arxiv.org/abs/2508.09553 https://arxiv.org/pdf/2508.09553

On Middle Grounds for Preference Statements
In group decisions or deliberations, stakeholders are often confronted with conflicting opinions. We investigate a logic-based way of expressing such opinions and a formal general notion of a middle ground between stakeholders. Inspired by the literature on preferences with hierarchical and lexicographic models, we instantiate our general framework to the case where stakeholders express their opinions using preference statements of the form I prefer 'a' to 'b', where 'a' and 'b' are alternative…