Temporal knowledge graph (TKG) forecasting aims to infer future facts from historical observations in time-evolving graphs. Traditional rule-based methods often rely on statistical co-occurrences and extensive path enumeration, suffering from rule sparsity and search-space explosion, while recent LLM-based rule reasoning can produce linguistically plausible rules that are weakly constrained by graph evidence and thus may reflect spurious correlations or violate temporal constraints.To address these challenges, we propose Critic-Guided Rule Induction (CRI), which treats temporal rules as rule hypotheses to be examined and adopts a decoupled Generation-Discrimination pipeline to induce rules that are both high-coverage and high-precision. CRI first mines seed rules and path evidence from the historical graph and uses an LLM-based generator to abstract and generalize them into broader raw rule hypotheses. It then introduces a Fact-Grounded Rule Evaluator to perform fact-grounded discrimination of rule hypotheses from complementary perspectives together with necessary temporal and statistical constraints. Finally, CRI performs symbolic reasoning over the refined rule set to produce forecasts with traceable reasoning evidence. Experiments on three benchmarks show that CRI outperforms strong baselines, achieving state-of-the-art performance on TKG forecasting.

Multi-modal Knowledge Graph Completion (MKGC) aims to infer missing links in multimodal knowledge graphs by leveraging structured triples together with auxiliary modalities such as text and images. Existing MKGC methods typically train with all modalities available, implicitly assuming consistent complementarity; however, this practice often induces modality dependence and modality competition under heterogeneous noise, which can hinder robust multi-modal fusion and limit overall performance.To address these issues, we propose **MDBGF**, a **M**odality **D**ropout and **B**idirectional **G**ated **F**usion framework for MKGC. MDBGF introduces a *dynamic, probability-based modality dropout* schedule. When the dropout is activated, MDBGF drops either the textual or visual modality during training while always preserving the structural information, encouraging the model to reduce over-reliance on any single auxiliary modality and to learn complementary cues under missing-modality conditions. When the dropout is not activated (i.e., all modalities are present), we further design a *bidirectional gated fusion* mechanism that enables mutual modulation between textual and visual modalities, enhancing cross-modal interaction and flexible fusion. In addition, we propose an *adaptive proportional hybrid negative sampling* strategy to strengthen MDBGF’s discriminative ability on hard negatives. Experiments on three benchmarks show that MDBGF consistently outperforms existing baselines and achieves new state-of-the-art results. Our code is available at https://anonymous.4open.science/r/MDBGF-AHNS.

Temporal knowledge graph (TKG) reasoning, a central task in temporal knowledge representation, focuses on predicting future facts by leveraging historical temporal contexts. However, current approaches face two major challenges: limited generalization to unseen facts and insufficient interpretability of reasoning processes. To address these challenges, this paper proposes the **D**enoising **L**ogic-based **T**emporal **K**nowledge **G**raph (DLTKG) framework, which employs a denoising diffusion process to complete reasoning tasks by introducing a noise source and a historical conditionguiding mechanism. Specifically, DLTKG constructs fuzzy entity representations by treating historical facts as noise sources, thereby enhancing the semantic associations between entities and the generalization ability for unseen facts. Additionally, the condition-based guidance mechanism, rooted in the relationship evolutionary paths, is designed to improve the interpretability of the reasoning process. Furthermore, we introduce a fine-tuning strategy that optimizes the denoising process by leveraging shortest path information between the head entity and candidate entities. Experimental results on three benchmark datasets demonstrate that DLTKG outperforms state-of-the-art methods across multiple evaluation metrics. Our code is available at: https://github.com/NEU-IDKE/DLTKG