Our work presents a novel reinforcement learning (RL) based framework to optimize heuristic selection within the conflict-driven clause learning (CDCL) process, improving the efficiency of Boolean satisfia-bility (SAT) solving. The proposed system, LangSAT, bridges the gap between natural language inputs and propositional logic by converting English descriptions into Conjunctive Normal Form (CNF) expressions and solving them using an RL-enhanced CDCL SAT solver. Unlike existing SAT-solving platforms that require CNF as input, LangSAT enables users to input standard English descriptions, making SAT-solving more accessible. The framework comprises two key components: Lang2Logic, which translates English sentences into CNF expressions, and SmartSAT, an RL-based SAT solver. SmartSAT encodes clause-variable relationships as structured graph representations and extracts global features specific to the SAT problem. This implementation provides the RL agent with deeper contextual information, enabling SAT problems to be solved more efficiently. Lang2Logic was evaluated on diverse natural language inputs, processing descriptions up to 450 words. The generated CNFs were solved by SmartSAT, which demonstrated comparable performance to traditional CDCL heuristics with respect to solving time. The combined LangSAT framework offers a more accessible and scalable solution for SAT-solving tasks across reasoning, formal verification, and debugging.

Recent advances in natural language processing (NLP), particularly large language models (LLMs), have motivated the automatic translation of natural language statements into formal logic without human intervention. This enables automated reasoning and facilitates debugging, finding loop invariants, and adhering to specifications in software systems. However, hallucinations-incorrect outputs generated by LLMs are challenging, particularly for logical translation tasks requiring precision. This work introduces a novel framework that inputs English sentences, converts them into logical expressions, and then translates them into Conjunctive Normal Form (CNF) for satisfiability solving. It employs classical NLP techniques with self-defined grammar, symbolic computation libraries, and a fine-tuned language model to reduce hallucinations. In the early experiments, we observed that the fine-tuned model, trained on different grammar settings, could intentionally correct the same types of hallucinations made by the original model. Thus, it provides reliable CNF generation.

Large language models (LLMs) undergo safety alignment after training and tuning, yet recent work shows that safety can be bypassed through jailbreak attacks. While many jailbreaks and defenses exist, their cross-lingual generalization remains underexplored. This paper presents the first systematic multilingual evaluation of jailbreaks and defenses across ten languages -- spanning high-, medium-, and low-resource languages -- using six LLMs on HarmBench and AdvBench. We assess two jailbreak types: logical-expression-based and adversarial-prompt-based. For both types, attack success and defense robustness vary across languages: high-resource languages are safer under standard queries but more vulnerable to adversarial ones. Simple defenses can be effective, but are language- and model-dependent. These findings call for language-aware and cross-lingual safety benchmarks for LLMs.

Constructing comprehensive knowledge graphs requires the use of multiple ontologies in order to fully contextualize data into a domain. Ontology matching finds equivalences between concepts interconnecting ontologies and creating a cohesive semantic layer. While the simple pairwise state of the art is well established, simple equivalence mappings cannot provide full semantic integration of related but disjoint ontologies. Complex multi-ontology matching (CMOM) aligns one source entity to composite logical expressions of multiple target entities, establishing more nuanced equivalences and provenance along the ontological hierarchy. We present CMOMgen, the first end-to-end CMOM strategy that generates complete and semantically sound mappings, without establishing any restrictions on the number of target ontologies or entities. Retrieval-Augmented Generation selects relevant classes to compose the mapping and filters matching reference mappings to serve as examples, enhancing In-Context Learning. The strategy was evaluated in three biomedical tasks with partial reference alignments. CMOMgen outperforms baselines in class selection, demonstrating the impact of having a dedicated strategy. Our strategy also achieves a minimum of 63% in F1-score, outperforming all baselines and ablated versions in two out of three tasks and placing second in the third. Furthermore, a manual evaluation of non-reference mappings showed that 46% of the mappings achieve the maximum score, further substantiating its ability to construct semantically sound mappings.

Despite substantial advancements in aligning large language models (LLMs) with human values, current safety mechanisms remain susceptible to jailbreak attacks. We hypothesize that this vulnerability stems from distributional discrepancies between alignment-oriented prompts and malicious prompts. To investigate this, we introduce LogiBreak, a novel and universal black-box jailbreak method that leverages logical expression translation to circumvent LLM safety systems. By converting harmful natural language prompts into formal logical expressions, LogiBreak exploits the distributional gap between alignment data and logic-based inputs, preserving the underlying semantic intent and readability while evading safety constraints. We evaluate LogiBreak on a multilingual jailbreak dataset spanning three languages, demonstrating its effectiveness across various evaluation settings and linguistic contexts.

Traditional retrieval methods rely on transforming user queries into vector representations and retrieving documents based on cosine similarity within an embedding space. While efficient and scalable, this approach often fails to handle complex queries involving logical constructs such as negations, conjunctions, and disjunctions. In this paper, we propose a novel inference-time logical reasoning framework that explicitly incorporates logical reasoning into the retrieval process. Our method extracts logical reasoning structures from natural language queries and then composes the individual cosine similarity scores to formulate the final document scores. This approach enables the retrieval process to handle complex logical reasoning without compromising computational efficiency. Our results on both synthetic and real-world benchmarks demonstrate that the proposed method consistently outperforms traditional retrieval methods across different models and datasets, significantly improving retrieval performance for complex queries.

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks but their performance in complex logical reasoning tasks remains unsatisfactory. Although some prompting methods, such as Chain-of-Thought, can improve the reasoning ability of LLMs to some extent, they suffer from an unfaithful issue where derived conclusions may not align with the generated reasoning chain. To address this issue, some studies employ the approach of propositional logic to further enhance logical reasoning abilities of LLMs. However, the potential omissions in the extraction of logical expressions in these methods can cause information loss in the logical reasoning process, thereby generating incorrect results. To this end, we propose Logic-of-Thought (LoT) prompting which employs propositional logic to generate expanded logical information from input context, and utilizes the generated logical information as an additional augmentation to the input prompts, thereby enhancing the capability of logical reasoning. The LoT is orthogonal to existing prompting methods and can be seamlessly integrated with them. Extensive experiments demonstrate that LoT boosts the performance of various prompting methods with a striking margin across five logical reasoning tasks.

Using computerized verifiable formal languages like Lean 4 to prove mathematical theorems has a significant impact on mathematical formalization. Lean 4 offers prominent potential for advancing mathematical reasoning. However, existing efforts are limited to mathematical formalization languages in substantial online corpora and are dedicated to keeping pace with rapidly evolving languages. To bridge the gap between the traditional and computerized proof, my approach to formalizing theorem proving involves generating formal steps and complete proofs using Large Language Models (LLMs) based on Natural Language (NL) proofs. The method is to introduce the basic structure and tactics in general, determine how AI can assist the mathematical formalization process to improve its performance, and give examples of solving problems in Lean 4 comparing to NL, mainly in IMO, and a sample theorem proving in abstract algebra.

Large-scale knowledge bases (KBs) like Freebase and Wikidata house millions of structured knowledge. Knowledge Base Question Answering (KBQA) provides a user-friendly way to access these valuable KBs via asking natural language questions. In order to improve the generalization capabilities of KBQA models, extensive research has embraced a retrieve-then-reason framework to retrieve relevant evidence for logical expression generation. These multi-stage efforts prioritize acquiring external sources but overlook the incorporation of new knowledge into their model parameters. In effect, even advanced language models and retrievers have knowledge boundaries, thereby limiting the generalization capabilities of previous KBQA models. Therefore, this paper develops KBLLaMA, which follows a learn-then-reason framework to inject new KB knowledge into a large language model for flexible end-to-end KBQA. At the core of KBLLaMA, we study (1) how to organize new knowledge about KBQA and (2) how to facilitate the learning of the organized knowledge. Extensive experiments on various KBQA generalization tasks showcase the state-of-the-art performance of KBLLaMA. Especially on the general benchmark GrailQA and domain-specific benchmark Bio-chemical, KBLLaMA respectively derives a performance gain of up to 3.8% and 9.8% compared to the baselines.

Rule-based reasoning, a fundamental type of legal reasoning, enables us to draw conclusions by accurately applying a rule to a set of facts. We explore causal language models as rule-based reasoners, specifically with respect to compositional rules - rules consisting of multiple elements which form a complex logical expression. Reasoning about compositional rules is challenging because it requires multiple reasoning steps, and attending to the logical relationships between elements. We introduce a new prompting method, Chain of Logic, which elicits rule-based reasoning through decomposition (solving elements as independent threads of logic), and recomposition (recombining these sub-answers to resolve the underlying logical expression). This method was inspired by the IRAC (Issue, Rule, Application, Conclusion) framework, a sequential reasoning approach used by lawyers. We evaluate chain of logic across eight rule-based reasoning tasks involving three distinct compositional rules from the LegalBench benchmark and demonstrate it consistently outperforms other prompting methods, including chain of thought and self-ask, using open-source and commercial language models.