## 1 Introduction
[19] also proposed implicit inference of logical information of articles using graph structures, and these approaches have made a certain degree of progress on various datasets. Previous research believes that an intuitive idea for identifying logical relationships between text units for this goal is to use discourse relations [20], such as words like \"because\" and \"therefore\" for cause-effect relationships, and \"if\" words to indicate hypothetical relations, and implicit logical relations brought about by punctuation. Modeling logical structure has proven to be one of the effective methods for enhancing logical reasoning for the widely used pre-trained models so far in the current reasoning task. However, all of the above approaches suffer from a certain degree of suboptimal generalization ability and overfitting. First, logical expression-based data enhancement methods still focus on sentence-level interactions between tokens, cannot capture abstract logical relations well, and are prone to overfitting during the training process. This results in sacrificing the accuracy of certain types of questions, such as deductive reasoning, in order to improve the accuracy of specific types of reasoning problems, such as inductive reasoning. Second, regarding neural networks based on graph structures, due to the structural specificity of graph data, the position information is actually lost during the processing. For language models due to their extensive use of Transformer architecture, absolute/relative position embedding are both important components of their encoding layer [21], because the parallel computing nature of Transformer also makes it lose position information, which is also important for understanding semantics. Third, most of the existing methods for graph structure use graph convolution, and the computed EDU Embedding is aggregated with the token Embedding of the pre-trained model and sent to the Bi-GRU [18; 22] or multi-headed attention mechanism [8; 23]. The simple aggregation of self and neighbor node information by averaging does not combine EDU-level granularity of discourse units with the attention mechanism. To address the above problems, we will improve three aspects of the construction of the discourse graph neural network, node encoding method, and graph reasoning calculation method, and propose a machine reading comprehension model, DaGATN, for logical reasoning multiple choice task. The main contributions are summarized as follows:1. To improve logical reasoning processes, we propose a discourse graph construction approach that uses punctuation and explicit connectives for node segmentation, aided by positional encoding. It uses the PDTB2.0 [24] to partition the context and answers into nodes. After that, to supplement the positional information missing in DAGN, the nodes are positional encoded according to their order in the original text to supplement the missing positional information. 2. In order to make the node position encoding imply both absolute and relative position information, we use a period function-based approach to encode the node position vectors in two-by-two groups for their dimensions. This ensures that each position vector is unique and bounded, while different position vectors can be obtained by linear transformation. The model is easier to generalize when dealing with position vectors and better handles sequences with inconsistent length and training data distribution. 3. In order to solve the problem that existing models such as DAGN, still have room to improve the message passing method, and make it more effectively perform message passing among nodes when performing graph reasoning, we design a discourse graph attention network based on a multi-head attention mechanism. By using attention weight coefficients to adaptively obtain information about neighboring nodes to simulate different degrees of focus on each condition during reasoning, we enhanced its performance on the inductive task.