Verifying the correctness of a textual statement requires not only semantic reasoning about the meaning of words, but also symbolic reasoning about logical operations like count, superlative, aggregation, etc. In this work, we propose LogicalFactChecker, a neural network approach capable of leveraging logical operations for fact checking. It achieves the state-of-the-art performance on TABFACT, a large-scale, benchmark dataset built for verifying a textual statement with semi-structured tables. This is achieved by a graph module network built upon the Transformer-based architecture. With a textual statement and a table as the input, LogicalFactChecker automatically derives a program (a.k.a. logical form) of the statement in a semantic parsing manner. A heterogeneous graph is then constructed to capture not only the structures of the table and the program, but also the connections between inputs with different modalities. Such a graph reveals the related contexts of each word in the statement, the table and the program. The graph is used to obtain graph-enhanced contextual representations of words in Transformer-based architecture. After that, a program-driven module network is further introduced to exploit the hierarchical structure of the program, where semantic compositionality is dynamically modeled along the program structure with a set of function-specific modules. Ablation experiments suggest that both the heterogeneous graph and the module network are important to obtain strong results.

Fact checking is a challenging task because verifying the truthfulness of a claim requires reasoning about multiple retrievable evidence. In this work, we present a method suitable for reasoning about the semantic-level structure of evidence. Unlike most previous works, which typically represent evidence sentences with either string concatenation or fusing the features of isolated evidence sentences, our approach operates on rich semantic structures of evidence obtained by semantic role labeling. We propose two mechanisms to exploit the structure of evidence while leveraging the advances of pre-trained models like BERT, GPT or XLNet. Specifically, using XLNet as the backbone, we first utilize the graph structure to re-define the relative distances of words, with the intuition that semantically related words should have short distances. Then, we adopt graph convolutional network and graph attention network to propagate and aggregate information from neighboring nodes on the graph. We evaluate our system on FEVER, a benchmark dataset for fact checking, and find that rich structural information is helpful and both our graph-based mechanisms improve the accuracy. Our model is the state-of-the-art system in terms of both official evaluation metrics, namely claim verification accuracy and FEVER score.