Large Language Models (LLMs) have transformed natural language processing and hold growing promise for advancing science, healthcare, and decision-making. Yet their training paradigms remain dominated by affirmation-based inference, akin to \textit{modus ponens}, where accepted premises yield predicted consequents. While effective for generative fluency, this one-directional approach leaves models vulnerable to logical fallacies, adversarial manipulation, and failures in causal reasoning. This paper makes two contributions. First, it demonstrates how existing LLMs from major platforms exhibit systematic weaknesses when reasoning in scientific domains with negation, counterexamples, or faulty premises \footnote{Code to recreate these experiments are at https://github.com/hannahdavidsoncollege-maker/ScientificReasoningForEnvironment-MedicineWithLLMs. Second, it introduces a dual-reasoning training framework that integrates affirmative generation with structured counterfactual denial. Grounded in formal logic, cognitive science, and adversarial training, this training paradigm formalizes a computational analogue of ``denying the antecedent'' as a mechanism for disconfirmation and robustness. By coupling generative synthesis with explicit negation-aware objectives, the framework enables models that not only affirm valid inferences but also reject invalid ones, yielding systems that are more resilient, interpretable, and aligned with human reasoning.

Abductive reasoning in knowledge graphs aims to generate plausible logical hypotheses from observed entities, with broad applications in areas such as clinical diagnosis and scientific discovery. However, due to a lack of controllability, a single observation may yield numerous plausible but redundant or irrelevant hypotheses on large-scale knowledge graphs. To address this limitation, we introduce the task of controllable hypothesis generation to improve the practical utility of abductive reasoning. This task faces two key challenges when controlling for generating long and complex logical hypotheses: hypothesis space collapse and hypothesis oversensitivity. To address these challenges, we propose CtrlHGen, a Controllable logcial Hypothesis Generation framework for abductive reasoning over knowledge graphs, trained in a two-stage paradigm including supervised learning and subsequent reinforcement learning. To mitigate hypothesis space collapse, we design a dataset augmentation strategy based on sub-logical decomposition, enabling the model to learn complex logical structures by leveraging semantic patterns in simpler components. To address hypothesis oversensitivity, we incorporate smoothed semantic rewards including Dice and Overlap scores, and introduce a condition-adherence reward to guide the generation toward user-specified control constraints. Extensive experiments on three benchmark datasets demonstrate that our model not only better adheres to control conditions but also achieves superior semantic similarity performance compared to baselines.

Query embedding approaches answer complex logical queries over incomplete knowledge graphs (KGs) by computing and operating on low-dimensional vector representations of entities, relations, and queries. However, current query embedding models heavily rely on excessively parameterized neural networks and cannot explain the knowledge learned from the graph. We propose a novel query embedding method, AConE, which explains the knowledge learned from the graph in the form of SROI^{-} description logic axioms while being more parameter-efficient than most existing approaches. AConE associates queries to a SROI^{-} description logic concept. Every SROI^{-} concept is embedded as a cone in complex vector space, and each SROI^{-} relation is embedded as a transformation that rotates and scales cones. We show theoretically that AConE can learn SROI^{-} axioms, and defines an algebra whose operations correspond one to one to SROI^{-} description logic concept constructs. Our empirical study on multiple query datasets shows that AConE achieves superior results over previous baselines with fewer parameters. Notably on the WN18RR dataset, AConE achieves significant improvement over baseline models. We provide comprehensive analyses showing that the capability to represent axioms positively impacts the results of query answering.

Generating coherent and credible explanations remains a significant challenge in the field of AI. In recent years, researchers have delved into the utilization of entailment trees to depict explanations, which exhibits a reasoning process of how a hypothesis is deduced from the supporting facts. However, existing models often overlook the importance of generating intermediate conclusions with logical consistency from the given facts, leading to inaccurate conclusions and undermining the overall credibility of entailment trees. To address this limitation, we propose the logical pattern memory pre-trained model (LMPM). LMPM incorporates an external memory structure to learn and store the latent representations of logical patterns, which aids in generating logically consistent conclusions. Furthermore, to mitigate the influence of logically irrelevant domain knowledge in the Wikipedia-based data, we introduce an entity abstraction approach to construct the dataset for pre-training LMPM. The experimental results highlight the effectiveness of our approach in improving the quality of entailment tree generation. By leveraging logical entailment patterns, our model produces more coherent and reasonable conclusions that closely align with the underlying premises.

Reasoning with knowledge graphs (KGs) has primarily focused on triple-shaped facts. Recent advancements have been explored to enhance the semantics of these facts by incorporating more potent representations, such as hyper-relational facts. However, these approaches are limited to \emph{atomic facts}, which describe a single piece of information. This paper extends beyond \emph{atomic facts} and delves into \emph{nested facts}, represented by quoted triples where subjects and objects are triples themselves (e.g., ((\emph{BarackObama}, \emph{holds\_position}, \emph{President}), \emph{succeed\_by}, (\emph{DonaldTrump}, \emph{holds\_position}, \emph{President}))). These nested facts enable the expression of complex semantics like \emph{situations} over time and \emph{logical patterns} over entities and relations. In response, we introduce NestE, a novel KG embedding approach that captures the semantics of both atomic and nested factual knowledge. NestE represents each atomic fact as a $1\times3$ matrix, and each nested relation is modeled as a $3\times3$ matrix that rotates the $1\times3$ atomic fact matrix through matrix multiplication. Each element of the matrix is represented as a complex number in the generalized 4D hypercomplex space, including (spherical) quaternions, hyperbolic quaternions, and split-quaternions. Through thorough analysis, we demonstrate the embedding's efficacy in capturing diverse logical patterns over nested facts, surpassing the confines of first-order logic-like expressions. Our experimental results showcase NestE's significant performance gains over current baselines in triple prediction and conditional link prediction. The code and pre-trained models are open available at https://github.com/xiongbo010/NestE.

Knowledge enriched language representation learning has shown promising performance across various knowledge-intensive NLP tasks. However, existing knowledge based language models are all trained with monolingual knowledge graph data, which limits their application to more languages. In this work, we present a novel framework to pretrain knowledge based multilingual language models (KMLMs). We first generate a large amount of code-switched synthetic sentences and reasoning-based multilingual training data using the Wikidata knowledge graphs. Then based on the intra-and inter-sentence structures of the generated data, we design pretraining tasks to facilitate knowledge learning, which allows the language models to not only memorize the factual knowledge but also learn useful logical patterns. Our pretrained KMLMs demonstrate significant performance improvements on a wide range of knowledge-intensive cross-lingual NLP tasks, including named entity recognition, factual knowledge retrieval, relation classification, and a new task designed by us, namely, logic reasoning. Our code and pretrained language models will be made publicly available. Pretrained language models (PTLMs) such as BERT (Devlin et al., 2019) and RoBERTa (Liu et al., 2019) have achieved superior performances on a wide range of natural language processing (NLP) tasks.

Real-world knowledge graphs are often characterized by low-frequency relations - a challenge that has prompted an increasing interest in few-shot link prediction methods. These methods perform link prediction for a set of new relations, unseen during training, given only a few example facts of each relation at test time. In this work, we perform a systematic study on a spectrum of models derived by generalizing the current state of the art for few-shot link prediction, with the goal of probing the limits of learning in this few-shot setting. We find that a simple zero-shot baseline - which ignores any relation-specific information - achieves surprisingly strong performance. Moreover, experiments on carefully crafted synthetic datasets show that having only a few examples of a relation fundamentally limits models from using fine-grained structural information and only allows for exploiting the coarse-grained positional information of entities. Together, our findings challenge the implicit assumptions and inductive biases of prior work and highlight new directions for research in this area.

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention-based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.