Tootfinder

From Logic to Language: A Trust Index for Problem Solving with LLMs
Tehseen Rug, Felix B\"ohmer, Tessa Pfattheicher
https://arxiv.org/abs/2507.16028 h…

From Logic to Language: A Trust Index for Problem Solving with LLMs
Classical computation, grounded in formal, logical systems, has been the engine of technological progress for decades, excelling at problems that can be described with unambiguous rules. This paradigm, however, leaves a vast ocean of human problems -- those characterized by ambiguity, dynamic environments, and subjective context -- largely untouched. The advent of Large Language Models (LLMs) represents a fundamental shift, enabling computational systems to engage with this previously inaccessi…

Formal Analysis of Networked PLC Controllers Interacting with Physical Environments
Jaeseo Lee, Kyungmin Bae
https://arxiv.org/abs/2507.15596 https://

Formal Analysis of Networked PLC Controllers Interacting with Physical Environments
Programmable Logic Controllers (PLCs) are widely used in industrial automation to control physical systems. As PLC applications become increasingly complex, ensuring their correctness is crucial. Existing formal verification techniques focus on individual PLC programs in isolation, often neglecting interactions with physical environments and network communication between controllers. This limitation poses significant challenges in analyzing real-world industrial systems, where continuous dynami…

Notes on applicative matching logic
Laurentiu Leustean
https://arxiv.org/abs/2506.10088 https://arxiv.org/pdf/2506.10088

Notes on applicative matching logic
Matching logic (ML) was developed by Grigore Roşu and collaborators as a logic for defining the formal semantics of programming languages and for specifying and reasoning about the behavior of programs. These lecture notes present basic definitions and results on applicative matching logic (AML), a functional variant of ML introduced recently by Xiaohong Chen and Grigore Roşu. They can be used as an introductory text in the theory of AML. Monk's textbook on mathematical logic has an enormous …

Cognitive Castes: Artificial Intelligence, Epistemic Stratification, and the Dissolution of Democratic Discourse
Craig S Wright
https://arxiv.org/abs/2507.14218

Cognitive Castes: Artificial Intelligence, Epistemic Stratification, and the Dissolution of Democratic Discourse
Artificial intelligence functions not as an epistemic leveller, but as an accelerant of cognitive stratification, entrenching and formalising informational castes within liberal-democratic societies. Synthesising formal epistemology, political theory, algorithmic architecture, and economic incentive structures, the argument traces how contemporary AI systems selectively amplify the reasoning capacity of individuals equipped with recursive abstraction, symbolic logic, and adversarial interrogati…

To add a single example here (feel free to chime in with your own):
Problem: editing code is sometimes tedious because external APIs require boilerplate.
Solutions:
- Use LLM-generated code. Downsides: energy use, code theft, potential for legal liability, makes mistakes, etc. Upsides: popular among some peers, seems easy to use.
- Pick a better library (not always possible).
- Build internal functions to centralize boilerplate code, then use those (benefits: you get a better understanding of the external API, and a more-unit-testable internal code surface; probably less amortized effort).
- Develop a non-LLM system that actually reasons about code at something like the formal semantics level and suggests boilerplate fill-ins based on rules, while foregrounding which rules it's applying so you can see the logic behind the suggestions (needs research).
Obviously LLM use in coding goes beyond this single issue, but there are similar analyses for each potential use of LLMs in coding. I'm all cases there are:
1. Existing practical solutions that require more effort (or in many cases just seem to but are less-effort when amortized).
2. Near-term researchable solutions that directly address the problem and which would be much more desirable in the long term.
Thus in addition to disastrous LLM effects on the climate, on data laborers, and on the digital commons, they tend to suck us into cheap-seeming but ultimately costly design practices while also crowding out better long-term solutions. Next time someone suggests how useful LLMs are for some task, try asking yourself (or them) what an ideal solution for that task would look like, and whether LLM use moves us closer to or father from a world in which that solution exists.

Fuzzy Lattice-based Description Logic
Yiwen Ding, Krishna Manoorkar
https://arxiv.org/abs/2506.05833 https://arxiv.org/pdf/2506.05833…

Fuzzy Lattice-based Description Logic
Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes. In this work, we introduce a fuzzy generalization of LE-ALC called LE-FALC which provides a description logic counterpart of many-valued normal non-distributive logic a.k.a. many-valued LE-logic. This description logic can be used to represent and reason a…

Logic Mining from Process Logs: Towards Automated Specification and Verification
Radoslaw Klimek, Julia Witek
https://arxiv.org/abs/2506.08628 https://

Logic Mining from Process Logs: Towards Automated Specification and Verification
Logical specifications play a key role in the formal analysis of behavioural models. Automating the derivation of such specifications is particularly valuable in complex systems, where manual construction is time-consuming and error-prone. This article presents an approach for generating logical specifications from process models discovered via workflow mining, combining pattern-based translation with automated reasoning techniques. In contrast to earlier work, we evaluate the method on both ge…

A Formal Refutation of the Blockchain Trilemma
Craig Wright
https://arxiv.org/abs/2507.05809 https://arxiv.org/pdf/2507.05809

A Formal Refutation of the Blockchain Trilemma
The so-called blockchain trilemma asserts the impossibility of simultaneously achieving scalability, security, and decentralisation within a single blockchain protocol. In this paper, we formally refute that proposition. Employing predicate logic, formal automata theory, computational complexity analysis, and graph-theoretic measures of relay topology--specifically Baran's model of network path redundancy--we demonstrate that the trilemma constitutes a category error, conflates distinct analyti…

Swarm-STL: A Framework for Motion Planning in Large-Scale, Multi-Swarm Systems
Shiyu Cheng, Luyao Niu, Bhaskar Ramasubramanian, Andrew Clark, Radha Poovendran
https://arxiv.org/abs/2506.14749

Swarm-STL: A Framework for Motion Planning in Large-Scale, Multi-Swarm Systems
In multi-agent systems, signal temporal logic (STL) is widely used for path planning to accomplish complex objectives with formal safety guarantees. However, as the number of agents increases, existing approaches encounter significant computational challenges. Recognizing that many complex tasks require cooperation among multiple agents, we propose swarm STL specifications to describe the collective tasks that need to be achieved by a team of agents. Next, we address the motion planning problem…

Trajectory Optimization for UAV-Based Medical Delivery with Temporal Logic Constraints and Convex Feasible Set Collision Avoidance
Kaiyuan Chen, Yuhan Suo, Shaowei Cui, Yuanqing Xia, Wannian Liang, Shuo Wang
https://arxiv.org/abs/2506.06038

Trajectory Optimization for UAV-Based Medical Delivery with Temporal Logic Constraints and Convex Feasible Set Collision Avoidance
This paper addresses the problem of trajectory optimization for unmanned aerial vehicles (UAVs) performing time-sensitive medical deliveries in urban environments. Specifically, we consider a single UAV with 3 degree-of-freedom dynamics tasked with delivering blood packages to multiple hospitals, each with a predefined time window and priority. Mission objectives are encoded using Signal Temporal Logic (STL), enabling the formal specification of spatial-temporal constraints. To ensure safety, c…

Hazel Deriver: A Live Editor for Constructing Rule-Based Derivations
Zhiyao Zhong, Cyrus Omar
https://arxiv.org/abs/2506.10781 https://

Hazel Deriver: A Live Editor for Constructing Rule-Based Derivations
Students in programming languages and formal logic courses often struggle with constructing rule-based derivation trees due to the complexity of applying inference rules, the lack of immediate feedback, and the manual effort required for handwritten proofs. We present Hazel Deriver, a live, web-based editor designed to scaffold derivation construction through multiple layers of support. Built on the Hazel live programming environment, it provides a structured, interactive experience that encour…

This https://arxiv.org/abs/2504.07732 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csPL_…

Efficient Formal Verification of Quantum Error Correcting Programs
Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion logic and a program logic specifically crafted for QEC programs and establish a sound proof system. We then develop an efficient method for handling verification conditions (VCs) of QEC programs: for Pauli errors, the VCs are reduced to classical assertions t…

Verifiable Natural Language to Linear Temporal Logic Translation: A Benchmark Dataset and Evaluation Suite
William H English, Chase Walker, Dominic Simon, Sumit Kumar Jha, Rickard Ewetz
https://arxiv.org/abs/2507.00877

Verifiable Natural Language to Linear Temporal Logic Translation: A Benchmark Dataset and Evaluation Suite
Empirical evaluation of state-of-the-art natural-language (NL) to temporal-logic (TL) translation systems reveals near-perfect performance on existing benchmarks. However, current studies measure only the accuracy of the translation of NL logic into formal TL, ignoring a system's capacity to ground atomic propositions into new scenarios or environments. This is a critical feature, necessary for the verification of resulting formulas in a concrete state space. Consequently, most NL-to-TL transla…

AI's Euclid's Elements Moment: From Language Models to Computable Thought
Xinmin Fang, Lingfeng Tao, Zhengxiong Li
https://arxiv.org/abs/2506.23080

AI's Euclid's Elements Moment: From Language Models to Computable Thought
This paper presents a comprehensive five-stage evolutionary framework for understanding the development of artificial intelligence, arguing that its trajectory mirrors the historical progression of human cognitive technologies. We posit that AI is advancing through distinct epochs, each defined by a revolutionary shift in its capacity for representation and reasoning, analogous to the inventions of cuneiform, the alphabet, grammar and logic, mathematical calculus, and formal logical systems. Th…

CCR 2.0: High-level Reasoning for Conditional Refinements
Youngju Song, Minki Cho
https://arxiv.org/abs/2507.04298 https://arxiv.org/…

CCR 2.0: High-level Reasoning for Conditional Refinements
In recent years, great progress has been made in the field of formal verification for low-level systems. Many of them are based on one of two popular approaches: refinement or separation logic. These two approaches are very different in nature and offer complementary benefits in terms of compositionality. Recently, to fuse these benefits in a unified mechanism, a new approach called Conditional Contextual Refinement (CCR 1.0 for short) was proposed. In this paper, we advance the model of CCR 1.…