Logic & Formal Reasoning
Challenges and Paths Towards AI for Software Engineering
Gu, Alex, Jain, Naman, Li, Wen-Ding, Shetty, Manish, Shao, Yijia, Li, Ziyang, Yang, Diyi, Ellis, Kevin, Sen, Koushik, Solar-Lezama, Armando
AI for software engineering has made remarkable progress recently, becoming a notable success within generative AI. Despite this, there are still many challenges that need to be addressed before automated software engineering reaches its full potential. It should be possible to reach high levels of automation where humans can focus on the critical decisions of what to build and how to balance difficult tradeoffs while most routine development effort is automated away. Reaching this level of automation will require substantial research and engineering efforts across academia and industry. In this paper, we aim to discuss progress towards this in a threefold manner. First, we provide a structured taxonomy of concrete tasks in AI for software engineering, emphasizing the many other tasks in software engineering beyond code generation and completion. Second, we outline several key bottlenecks that limit current approaches. Finally, we provide an opinionated list of promising research directions toward making progress on these bottlenecks, hoping to inspire future research in this rapidly maturing field.
Reasoning Under Threat: Symbolic and Neural Techniques for Cybersecurity Verification
Cybersecurity demands rigorous and scalable techniques to ensure system correctness, robustness, and resilience against evolving threats. Automated reasoning, encompassing formal logic, theorem proving, model checking, and symbolic analysis, provides a foundational framework for verifying security properties across diverse domains such as access control, protocol design, vulnerability detection, and adversarial modeling. This survey presents a comprehensive overview of the role of automated reasoning in cybersecurity, analyzing how logical systems, including temporal, deontic, and epistemic logics are employed to formalize and verify security guarantees. We examine SOTA tools and frameworks, explore integrations with AI for neural-symbolic reasoning, and highlight critical research gaps, particularly in scalability, compositionality, and multi-layered security modeling. The paper concludes with a set of well-grounded future research directions, aiming to foster the development of secure systems through formal, automated, and explainable reasoning techniques.
Monitoring Spatially Distributed Cyber-Physical Systems with Alternating Finite Automata
Balakrishnan, Anand, Paul, Sheryl, Silvetti, Simone, Nenzi, Laura, Deshmukh, Jyotirmoy V.
Modern cyber-physical systems (CPS) can consist of various networked components and agents interacting and communicating with each other. In the context of spatially distributed CPS, these connections can be dynamically dependent on the spatial configuration of the various components and agents. In these settings, robust monitoring of the distributed components is vital to ensuring complex behaviors are achieved, and safety properties are maintained. To this end, we look at defining the automaton semantics for the Spatio-Temporal Reach and Escape Logic (STREL), a formal logic designed to express and monitor spatio-temporal requirements over mobile, spatially distributed CPS. Specifically, STREL reasons about spatio-temporal behavior over dynamic weighted graphs. While STREL is endowed with well defined qualitative and quantitative semantics, in this paper, we propose a novel construction of (weighted) alternating finite automata from STREL specifications that efficiently encodes these semantics. Moreover, we demonstrate how this automaton semantics can be used to perform both, offline and online monitoring for STREL specifications using a simulated drone swarm environment.
Extracting Interpretable Logic Rules from Graph Neural Networks
Geng, Chuqin, Wang, Zhaoyue, Zhao, Ziyu, Ye, Haolin, Si, Xujie
Graph neural networks (GNNs) operate over both input feature spaces and combinatorial graph structures, making it challenging to understand the rationale behind their predictions. As GNNs gain widespread popularity and demonstrate success across various domains, such as drug discovery, studying their interpretability has become a critical task. To address this, many explainability methods have been proposed, with recent efforts shifting from instance-specific explanations to global concept-based explainability. However, these approaches face several limitations, such as relying on predefined concepts and explaining only a limited set of patterns. To address this, we propose a novel framework, LOGICXGNN, for extracting interpretable logic rules from GNNs. LOGICXGNN is model-agnostic, efficient, and data-driven, eliminating the need for predefined concepts. More importantly, it can serve as a rule-based classifier and even outperform the original neural models. Its interpretability facilitates knowledge discovery, as demonstrated by its ability to extract detailed and accurate chemistry knowledge that is often overlooked by existing methods. Another key advantage of LOGICXGNN is its ability to generate new graph instances in a controlled and transparent manner, offering significant potential for applications such as drug design. We empirically demonstrate these merits through experiments on real-world datasets such as MUTAG and BBBP.
Splitting Answer Set Programs with respect to Intensionality Statements (Extended Version)
Fandinno, Jorge, Lierler, Yuliya
Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under which this technique is applicable, by considering not only dependencies between predicates but also their arguments and context. This allows splitting programs commonly used in practice to which previous results were not applicable.
LogicLearner: A Tool for the Guided Practice of Propositional Logic Proofs
Inamdar, Amogh, Macar, Uzay, Vazirani, Michel, Tarnow, Michael, Mustapha, Zarina, Dittren, Natalia, Sadeh, Sam, Verma, Nakul, Salleb-Aouissi, Ansaf
The study of propositional logic -- fundamental to the theory of computing -- is a cornerstone of the undergraduate computer science curriculum. Learning to solve logical proofs requires repeated guided practice, but undergraduate students often lack access to on-demand tutoring in a judgment-free environment. In this work, we highlight the need for guided practice tools in undergraduate mathematics education and outline the desiderata of an effective practice tool. We accordingly develop LogicLearner, a web application for guided logic proof practice. LogicLearner consists of an interface to attempt logic proofs step-by-step and an automated proof solver to generate solutions on the fly, allowing users to request guidance as needed. We pilot LogicLearner as a practice tool in two semesters of an undergraduate discrete mathematics course and receive strongly positive feedback for usability and pedagogical value in student surveys. To the best of our knowledge, LogicLearner is the only learning tool that provides an end-to-end practice environment for logic proofs with immediate, judgment-free feedback.
Neuro-symbolic Weak Supervision: Theory and Semantics
Upreti, Nijesh, Belle, Vaishak
Weak supervision allows machine learning models to learn from limited or noisy labels, but it introduces challenges in interpretability and reliability - particularly in multi-instance partial label learning (MI-PLL), where models must resolve both ambiguous labels and uncertain instance-label mappings. We propose a semantics for neuro-symbolic framework that integrates Inductive Logic Programming (ILP) to improve MI-PLL by providing structured relational constraints that guide learning. Within our semantic characterization, ILP defines a logical hypothesis space for label transitions, clarifies classifier semantics, and establishes interpretable performance standards. This hybrid approach improves robustness, transparency, and accountability in weakly supervised settings, ensuring neural predictions align with domain knowledge. By embedding weak supervision into a logical framework, we enhance both interpretability and learning, making weak supervision more suitable for real-world, high-stakes applications.
Can AI expose tax loopholes? Towards a new generation of legal policy assistants
Fratrič, Peter, Holzenberger, Nils, Amariles, David Restrepo
The legislative process is the backbone of a state built on solid institutions. Yet, due to the complexity of laws -- particularly tax law -- policies may lead to inequality and social tensions. In this study, we introduce a novel prototype system designed to address the issues of tax loopholes and tax avoidance. Our hybrid solution integrates a natural language interface with a domain-specific language tailored for planning. We demonstrate on a case study how tax loopholes and avoidance schemes can be exposed. We conclude that our prototype can help enhance social welfare by systematically identifying and addressing tax gaps stemming from loopholes.
Shedding Light in Task Decomposition in Program Synthesis: The Driving Force of the Synthesizer Model
Zenkner, Janis, Sesterhenn, Tobias, Bartelt, Christian
Task decomposition is a fundamental mechanism in program synthesis, enabling complex problems to be broken down into manageable subtasks. ExeDec, a state-of-the-art program synthesis framework, employs this approach by combining a Subgoal Model for decomposition and a Synthesizer Model for program generation to facilitate compositional generalization. In this work, we develop REGISM, an adaptation of ExeDec that removes decomposition guidance and relies solely on iterative execution-driven synthesis. By comparing these two exemplary approaches-ExeDec, which leverages task decomposition, and REGISM, which does not-we investigate the interplay between task decomposition and program generation. Our findings indicate that ExeDec exhibits significant advantages in length generalization and concept composition tasks, likely due to its explicit decomposition strategies. At the same time, REGISM frequently matches or surpasses ExeDec's performance across various scenarios, with its solutions often aligning more closely with ground truth decompositions. These observations highlight the importance of repeated execution-guided synthesis in driving task-solving performance, even within frameworks that incorporate explicit decomposition strategies. Our analysis suggests that task decomposition approaches like ExeDec hold significant potential for advancing program synthesis, though further work is needed to clarify when and why these strategies are most effective.
Unique Hard Attention: A Tale of Two Sides
Jerad, Selim, Svete, Anej, Li, Jiaoda, Cotterell, Ryan
Understanding the expressive power of transformers has recently attracted attention, as it offers insights into their abilities and limitations. Many studies analyze unique hard attention transformers, where attention selects a single position that maximizes the attention scores. When multiple positions achieve the maximum score, either the rightmost or the leftmost of those is chosen. In this paper, we highlight the importance of this seeming triviality. Recently, finite-precision transformers with both leftmost- and rightmost-hard attention were shown to be equivalent to Linear Temporal Logic (LTL). We show that this no longer holds with only leftmost-hard attention -- in that case, they correspond to a \emph{strictly weaker} fragment of LTL. Furthermore, we show that models with leftmost-hard attention are equivalent to \emph{soft} attention, suggesting they may better approximate real-world transformers than right-attention models. These findings refine the landscape of transformer expressivity and underscore the role of attention directionality.