In this paper, we address the issue of using logic rules to explain the results from legal case retrieval. The task is critical to legal case retrieval because the users (e.g., lawyers or judges) are highly specialized and require the system to provide logic, faithful, and interpretable explanations before making legal decisions. Recently, research efforts have been made to learn explainable legal case retrieval models. However, these methods usually select rationales (key sentences) from the legal cases as explanations, failing to provide faithful and logicly correct explanations. In this paper, we propose Neural-Symbolic enhanced Legal Case Retrieval (NS-LCR), a framework that explicitly conducts reasoning on the matching of legal cases through learning case-level and law-level logic rules. The learned rules are then integrated into the retrieval process in a neuro-symbolic manner. Benefiting from the logic and interpretable nature of the logic rules, NS-LCR is equipped with built-in faithful explainability. We also show that NS-LCR is a model-agnostic framework that can be plug-in for multiple legal retrieval models. To demonstrate the superiority of NS-LCR, we extend the benchmarks of LeCaRD and ELAM with manually annotated logic rules and propose a new explainability measure based on Large Language Models (LLMs). Extensive experiments show that NS-LCR can achieve state-of-the-art ranking performances, and the empirical analysis also showed that NS-LCR is capable of providing faithful explanations for legal case retrieval.

One typical approach to long-form document matching is first conducting alignment between cross-document sentence pairs, and then aggregating all of the sentence-level matching signals. However, this approach could be problematic because the alignment between documents is partial — despite two documents as a whole are well-matched, most of the sentences could still be dissimilar. Those dissimilar sentences lead to spurious sentence-level matching signals which may overwhelm the real ones, increasing the difficulties of learning the matching function. Therefore, accurately selecting the key sentences for document matching is becoming a challenging issue. To address the issue, we propose a novel matching approach that equips existing document matching models with an Optimal Partial Transport (OPT) based component, namely OPT-Match, which selects the sentences that play a major role in matching. Enjoying the partial transport properties of OPT, the selected key sentences can not only effectively enhance the matching accuracy, but also be explained as the rationales for the matching results. Extensive experiments on four publicly available datasets demonstrated that existing methods equipped with OPT-Match consistently outperformed the corresponding underlying methods. Evaluations also showed that the key sentences selected by OPT-Match were consistent with human-provided rationales.

One approach to matching texts from asymmetrical domains is projecting the input sequences into a common semantic space as feature vectors upon which the matching function can be readily defined and learned. In real-world matching practices, it is often observed that with the training goes on, the feature vectors projected from different domains tend to be indistinguishable. The phenomenon, however, is often overlooked in existing matching models. As a result, the feature vectors are constructed without any regularization, which inevitably increases the difficulty of learning the downstream matching functions. In this paper, we propose a novel match method tailored for text matching in asymmetrical domains, called WD-Match. In WD-Match, a Wasserstein distance-based regularizer is defined to regularize the features vectors projected from different domains. As a result, the method enforces the feature projection function to generate vectors such that those correspond to different domains cannot be easily discriminated. The training process of WD-Match amounts to a game that minimizes the matching loss regularized by the Wasserstein distance. WD-Match can be used to improve different text matching methods, by using the method as its underlying matching model. Four popular text matching methods have been exploited in the paper. Experimental results based on four publicly available benchmarks showed that WD-Match consistently outperformed the underlying methods and the baselines.