Papers

Retrieval-augmented generation (RAG) improves question answering by grounding large language models (LLMs) in external knowledge such as text corpora. However, its reasoning process remains largely opaque: intermediate reasoning steps are difficult to verify and cannot be reliably attributed to specific evidence. Moreover, missing user-specific context is rarely detected systematically, often leading to incomplete or incorrect output. We propose NeSy-RAG, a modular neuro-symbolic RAG framework that synthesizes attributable Prolog modules from retrieved text chunks. For each chunk, the system generates semantically meaningful predicates that encode Boolean claims, which may depend on user facts. Using joint natural language-code embeddings, predicates are retrieved and composed into Prolog queries. To address incomplete user context, we introduce a symbolic knowledge-gap detection mechanism that identifies missing user facts whose truth values affect the query outcome and automatically triggers follow-up interactions. Executing the resulting Prolog queries yields deterministic answers together with transparent execution traces that link each reasoning step to its originating source. On the ShARC benchmark, without domain-specific training, NeSy-RAG achieves 61.1% accuracy, outperforming a same-model RAG baseline that achieves 42.8% accuracy.

Prime implicants (PIs) are central in computer science, with applications in logic minimization, diagnosis, explainable formal methods and AI. Algorithms for the computation of PIs were first-and-foremost considered on the full input space, not considering the case where the input space might be constrained by context or structural dependencies. To filter out those PIs that do not fulfill the constraints, existing methods rely on an explicit post-processing step after computing all PIs, which leads to scalability issues due to the number of PIs being exponential. We propose end-to-end symbolic algorithms that implicitly represent the set of PIs under side constraints. For this, we extend the prominent method based on decision diagrams by Coudert and Madre and implement a modular tool chain that separates decision-diagram construction, PI computation, and filtering.

Large language models can derive a plausible mathematical object yet still violate explicit requirements–for example, by omitting a modular reduction, returning a non-integer, or using the wrong encoded answer form. We introduce Constraint-First Reasoning (CFR), a training-free two-stage prompting protocol: Stage 1 extracts and summarizes constraints entailed by the problem, and Stage 2 solves while checking intermediate and final results against that summary. Routed-CFR activates the two-stage protocol only when a text-only regex router detects restrictive cues; otherwise it uses direct chain-of-thought (CoT). Across AIME, CMIMC, BRUMO, and AIMO_AMC, the method improves direct CoT on multiple backbones. We further report convention-controlled routing experiments, matched prompting baselines, problem-level paired tests, decoding robustness, constraint-quality audits, total-token accounting, and an OlympiadBench evaluation. These analyses position CFR as a targeted test-time intervention whose benefit depends on recoverable constraints and reliable Stage 1 extraction, rather than as a general-purpose replacement for mathematical reasoning.

Kinetic model discovery is a central challenge in chemical engineering, as accurate rate expressions are essential for understanding and controlling chemical and biological processes. Symbolic regression (SR) has emerged as a powerful data-driven approach for identifying interpretable kinetic models, but usually operates without domain knowledge, often exploring physicochemically implausible models. Large language models (LLMs) offer a promising avenue for injecting domain expertise into this search. Here, we introduce an LLM-guided SR framework, embedding an LLM module within an iterative SR algorithm for automated kinetic model discovery. The LLM performs two roles at each iteration: (1) a qualitative physicochemical critique of the best SR candidates, and (2) the proposal of new candidate rate expressions guided by the SR-generated models and embedded chemical knowledge. Our framework is evaluated on four in silico case studies of increasing complexity, spanning heterogeneous catalysis and bioprocess systems. Results show the LLM-guided framework reduces iterations to identify the ground-truth model by $41.7-79.3\%$ versus a state-of-the-art SR framework, with the LLM directly proposing the correct model structure in over half of the guided runs. In practical settings, where each iteration typically requires a new wet-lab experiment, this translates into a substantial reduction in experimental effort. Predictive performance on an independent validation set is equivalent between both approaches, with $R^2>0.98$ in all case studies. Ablation studies indicate that both the SR component and the LLM scale contribute to this performance, with a reduced-size LLM largely retaining discovery efficiency. These findings demonstrate that LLMs can effectively inject domain knowledge into scientific model discovery, paving the way toward fully automated, domain-aware kinetic modelling pipelines.

Symbolic execution plays a critical role in software reliability, as they are used to find bugs, generate test cases, and provide correctness guarantees, particularly for safety-critical systems. Yet their own correctness is rarely subject to formal scrutiny, as it is typically established empirically by evaluating tool behavior across many programs. This leaves open the possibility that the tools themselves introduce unsoundness, potentially invalidating the verification results they produce and undermining the very guarantees they are meant to provide. In this paper, we address this gap by providing the formal treatment of symbolic execution with path-merging, an optimization that improves path explosion by summarizing branching code regions into disjunctive constraints rather than exploring each path independently. Specifically, we target Java Ranger, a path-merging tool for Java programs that progressively transforms imperative Java code toward the language of formal logic through a series of code transformations. We formalize each of these transformations and prove their soundness with respect to a simplified version of the Java concrete semantics, establishing that Java Ranger's path-merging process preserves program semantics.

Given an algebraic statistical model, a challenging problem is classifying the data according to the number of positive critical points of the likelihood function. The positive critical points are the positive solutions to an algebraic system, say likelihood equations. So, identifying the number of positive critical points is a real root classification problem for the likelihood equations. A discriminant variety of a likelihood-equation system geometrically describes the data for which the number of real solutions becomes unusual. As an essential component of the discriminant variety, the nonproperness set collects the data such that the likelihood-equation system has a solution at infinity. So, the number of real solutions varies when the data passes the nonproperness set, and identifying the nonproperness set plays a crucial role in the real root classification. In this work, we develop a novel method for computing nonproperness sets of likelihood-equation systems. We prove the correctness of this method. We show experimentally that it is far more efficient than the known methods in the literature.