Logical reasoning task has attracted great interest since it was proposed. Faced with such a task, current competitive models, even large language models (e.g., ChatGPT and PaLM 2), still perform badly. Previous promising LMs struggle in logical consistency modeling and logical structure perception. To this end, we model the logical reasoning task by transforming each logical sample into reasoning paths and propose an architecture PathReasoner. It addresses the task from the views of both data and model. To expand the diversity of the logical samples, we propose an atom extension strategy supported by equivalent logical formulas, to form new reasoning paths. From the model perspective, we design a stack of transformer-style blocks. In particular, we propose a path-attention module to joint model in-atom and cross-atom relations with the high-order diffusion strategy. Experiments show that PathReasoner achieves competitive performances on two logical reasoning benchmarks and great generalization abilities.

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.