A Unified Temporal Knowledge Graph Reasoning Model Towards Interpolation and Extrapolation (2024)

Abstract: Temporal knowledge graph (TKG) reasoning has two settings: interpolation reasoning and extrapolation reasoning. Both of them draw plenty of research interest and have great significance. Methods of the former de-emphasize the temporal correlations among facts sequences, while methods of the latter require strict chronological order of knowledge and ignore inferring clues provided by missing facts of the past. These limit the practicability of TKG applications as almost all of the existing TKG reasoning methods are designed specifically to address either one setting. To this end, this paper proposes an original Temporal PAth-based Reasoning (TPAR) model for both the interpolation and extrapolation reasoning settings. TPAR performs a neural-driven symbolic reasoning fashion that is robust to ambiguous and noisy temporal data, and with fine interpretability as well. Comprehensive experiments show that TPAR outperforms SOTA methods on the link prediction task for both the interpolation and the extrapolation settings. A novel pipeline experimental setting is designed to evaluate the performances of SOTA combinations and the proposed TPAR towards interpolation and extrapolation reasoning. And more diverse experiments are conducted to show the robustness and interpretability of TPAR.

## introduction knowledge graph (kg) is a semantic network that represents real-world facts in a structured way using entities and relations @xcite @xcite . typically, a fact is represented by a triple (s, r, o) in kg, consisting of a subject entity s, an object entity o, and a relation r between s and o. in the real world, many facts are closely associated with a particular time interval. for example, the fact "barack obama is the president of usa" is valid for the time period of 2009 january 20th -2017 january 20th and the fact "donald trump is the president of usa" is only valid for the following four years. to represent such time-sensitive facts, temporal knowledge graphs (tkgs) have recently gained significant attention from both academic and industrial communities. specifically, tkgs extend static kgs by incorporating the temporal information t into fact triples, represented as a quadruple (s, r, o, t), which allows for modelling the temporal dependencies and evolution of knowledge over time, being crucial for reasoning time-evolving facts in applications such as financial forecasting, social networks, and healthcare. tkg reasoning infers new knowledge with timesensitive facts in existing tkgs, which generally has two settings: the interpolation reasoning @xcite @xcite and the extrapolation reasoning @xcite @xcite . given a temporal knowledge graph with facts from time t 0 to time t t , the interpolation reasoning infers missing facts at any time in history (t 0 ≤ @xmath0. many approaches have been proposed to tackle the tkg reasoning problem, however, these two reasoning tasks are tackled in totally different and incompatible manners. on the one hand, interpolation methods de-emphasize the temporal correlations among fact sequences while training, thus it's difficult to cope with the challenges of invisible timestamps and invisible entities in extrapolation due to their poor inductive reasoning ability @xcite . on the other hand, most stateof-the-art (sota) extrapolation solutions require a strict chronological order of data during training. as a result, they can only predict unknown future facts, but they could hardly infer missing historical facts which are crucial for completing the overall knowledge landscape and providing more clues for predicting accurate future events. these limit the practicability of tkg applications as almost all of the existing tkg reasoning methods are designed specifically to address either one setting. experiments with a novel pipeline setting intuitively reveal that even with the sota methods from both settings, the composed methods show a frustrating decrease in reasoning performance. more in-depth analysis can be found in section 5.3 and appendix f. therefore, the motivation of this work is to propose a unified method that can accommodate two types of reasoning settings, enabling temporal knowledge graph reasoning to be conducted simultaneously for both the interpolation and the extrapolation. to this end, we take inspiration from recent neural @xcite and symbolic @xcite tkg reasoning approaches. neural network approaches can perform effective reasoning but lack interpretation as they cannot provide explicit rules to explain the reasoning results, while symbolic reasoning approaches use logical symbols and rules to perform reasoning tasks but are not suitable for handling ambiguous and noisy data due to their strict matching and discrete logic operations used during rule searching @xcite . in this paper, we propose a temporal path based reasoning (tpar) model with a neural-symbolic fashion applicable to both the interpolation and the extrapolation tkg reasoning. specifically, we utilize the @xcite @xcite and introduce a recursive encoding method to score the destination entities of various temporal paths, and then our tpar performs symbolic reasoning with the help of the obtained scores. it is noticeable that the neural-driven symbolic reasoning fashion we adopted is more robust to the uncertainty data compared to traditional pure symbolic reasoning methods, and comprehensible temporal paths with fine interpretability as well. we summarize our main contributions as follows: ## methodology in this section, we introduce a novel temporal pathbased reasoning model with a neural-driven symbolic fashion for both the interpolation and the extrapolation tkg reasoning settings. ## conclusion we propose a temporal path-based reasoning (tpar) model with a neural-symbolic fashion that can be applied to both interpolation and extrapolation tkg reasoning settings in this paper. introducing the bellman-ford algorithm and a recursive encoding method to score the destination entities of various temporal paths, tpar performs robustly on uncertain temporal knowledge with fine inter-pretability. comprehensive experiments demonstrate the superiority of our proposed model for both settings. a well-designed pipeline experiment further verified that tpar is capable of integrating two settings for a unified tkg reasoning.