Extrapolation reasoning on temporal knowledge graphs (TKGs) aims to forecast future facts based on past counterparts. There are two main challenges: (1) incorporating the complex information, including structural dependencies, temporal dynamics, and hidden logical rules; (2) implementing differentiable logical rule learning and reasoning for explainability. To this end, we propose an explainable extrapolation reasoning framework TEemporal logiCal grapH networkS (TECHS), which mainly contains a temporal graph encoder and a logical decoder. The former employs a graph convolutional network with temporal encoding and heterogeneous attention to embed topological structures and temporal dynamics. The latter integrates propositional reasoning and first-order reasoning by introducing a reasoning graph that iteratively expands to find the answer. A forward message-passing mechanism is also proposed to update node representations, and their propositional and first-order attention scores. Experimental results demonstrate that it outperforms state-of-the-art baselines.

Relation prediction in knowledge graphs (KGs) aims at predicting missing relations in incomplete triples, whereas the dominant embedding paradigm has a restriction on handling unseen entities during testing. In the real-world scenario, the inductive setting is more common because entities in the training process are finite. Previous methods capture an inductive ability by implicit logic in KGs. However, it would be challenging to preciously acquire entity-independent relational semantics of compositional logic rules and to deal with the deficient supervision of logic caused by the scarcity of relational semantics. To this end, we propose a novel graph convolutional network (GCN)-based model LogCo with logical reasoning by contrastive representations. LogCo firstly extracts enclosing subgraphs and relational paths between two entities to supply the entity-independence. Then a contrastive strategy for relational path instances and the subgraph is proposed for the issue of deficient supervision. The contrastive representations are learned for a joint training regime. Finally, prediction results and logic rules for reasoning are attained. Comprehensive experiments on twelve inductive datasets show that LogCo achieves outstanding performance comparing with state-of-the-art inductive relation prediction baselines.