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

LogicalFactChecker: Leveraging Logical Operations for Fact Checking with Graph Module Network