A da L o GN : Adaptive Logic Graph Network for Reasoning-Based Machine Reading Comprehension (2022)

Abstract: Recent machine reading comprehension datasets such as ReClor and LogiQA require performing logical reasoning over text. Conventional neural models are insufficient for logical reasoning, while symbolic reasoners cannot directly apply to text. To meet the challenge, we present a neural-symbolic approach which, to predict an answer, passes messages over a graph representing logical relations between text units. It incorporates an adaptive logic graph network (AdaLoGN) which adaptively infers logical relations to extend the graph and, essentially, realizes mutual and iterative reinforcement between neural and symbolic reasoning. We also implement a novel subgraph-to-node message passing mechanism to enhance context-option interaction for answering multiple-choice questions. Our approach shows promising results on ReClor and LogiQA.

## introduction machine reading comprehension (mrc) has drawn much research attention. early mrc datasets are not difficult for state-of-the-art neural methods. indeed, bert @xcite has outperformed humans on squad @xcite . recent datasets become more challenging. for example, reclor @xcite and logiqa @xcite require understanding and reasoning over logical relations described in text, where neural methods showed unsatisfactory performance. for instance, consider the mrc task in figure 1 . the context consists of a set of textual propositions describing logical relations between elementary discourse units (edus) @xcite . for example, the first sentence describes an implication between two edus: "the company gets project a" implies that "product b can be put on the market on schedule". with the help of propositional calculus, humans can formalize propositions and then apply inference rules in proposi- figure 1 : an example mrc task (adapted from a task in logiqa). logical connectives are highlighted in italics. marks the correct answer. existing methods and limitations to solve it, conventional neural models are insufficient for providing the required reasoning capabilities, while symbolic reasoners cannot directly apply to unstructured text. one promising direction is to consider a neural-symbolic solution, such as the recent dagn method @xcite . it breaks down the context and each option into a set of edus and connects them with discourse relations as a graph. then it performs graph neural network (gnn) based reasoning to predict an answer. however, we identify two limitations in this method. l1: despite the graph representation, it is predominantly a neural method over discourse relations. it is debatable whether the required symbolic reasoning over logical relations (e.g., implication, negation) can be properly approximated. l2: the graph is often loosely connected and composed of long paths. node-to-node message passing implemented in existing gnn models @xcite @xcite is prone to provide insufficient interaction between the context and the option, which is critical to answering a multiple-choice question. our approach. while we follow the general framework of dagn, i.e., graph construction and then graph-based reasoning, we overcome its two limitations with a novel neural-symbolic approach. to address l1, figure 3 sketches out our idea. specifically, we propose to construct a text logic graph (tlg) representing edus and their logical relations as opposed to discourse relations, so we can explicitly perform symbolic reasoning to extend the tlg with inferred logical relations, as illustrated in figure 2 . the inferred relations may provide crucial connections to be used in the subsequent graph-based message passing, i.e., symbolic reasoning reinforces neural reasoning. further, while trivially computing and admitting the deductive closure may extend the tlg with irrelevant connections which would mislead message passing, we leverage signals from neural reasoning to adaptively admit relevant extensions, i.e., neural reasoning reinforces symbolic reasoning. moreover, we iterate the above mutual reinforcement by restarting inference in each iteration with signals from the previous iteration to accommodate corrections to the reasoning process and allow sufficient neural-symbolic interaction. to address l2, we aggregate the information in the context subgraph of tlg and employ a novel subgraph-to-node message passing mechanism to enhance the interaction from the holistic context subgraph to each node in the option subgraph, and vice versa, as illustrated in figure 2b . we incorporate the above two ideas into our new adaptive logic graph network (adalogn). to summarize, our technical contributions include • a novel neural-symbolic approach where neural and symbolic reasoning mutually and iteratively reinforce each other, and • a novel aggregation-based enhancement of message passing in graph-based neural reasoning. outline. we elaborate our approach in section 2, present experiments in section 3, discuss related work in section 4, and conclude in section 5. our code is available on github: https:// github.com/nju-websoft/adalogn . ## approach a mrc task c, q, o consists of a context c, a question q, and a set of options o. only one option in o is the correct answer to q given c. the goal of the task is to find this option. figure 4 outlines our implementation. for each option @xmath0, we generate the representations of c, q, o (i.e., g c , g q , g o , respectively) by a pretrained language model (section 2.1), and we construct a raw tlg where nodes (i.e., u 1 , . . . , u |v | ) represent edus extracted from c, q, o and edges represent their logical relations (section 2.2). with their initial representations (i.e., h ## conclusion to meet the challenge of reasoning-based mrc, we presented a neural-symbolic approach where neural and symbolic reasoning mutually and iteratively reinforce each other via our new adalogn model. we also enhanced graph-based neural reasoning with a novel subgraph-to-node message passing mechanism. since these ideas are quite general, we believe they have great potential for a variety of applications beyond mrc, e.g., link prediction. error analysis has revealed some shortcomings of our approach. currently we rely on syntactic tools to extract a raw tlg from text. we will explore other extraction methods to achieve a higher quality. we also plan to apply more inference rules and incorporate quantifiers to improve the expressivity of our symbolic reasoning.