Abstract
Information retrieval plays a crucial role in resource localization. Current dense retrievers retrieve the relevant documents within a corpus via embedding similarities, which compute similarities between dense vectors mainly depending on word co-occurrence between queries and documents, but overlook the real query intents. Thus, they often retrieve numerous irrelevant documents. Particularly in the scenarios of complex queries such as *negative-constraint queries*, their retrieval performance could be catastrophic. To address the issue, we propose a neuro-symbolic information retrieval method, namely \textbf\{NS-IR\}, that leverages first-order logic (FOL) to optimize the embeddings of naive natural language by considering the *logical consistency* between queries and documents. Specifically, we introduce two novel techniques, *logic alignment* and *connective constraint*, to rerank candidate documents, thereby enhancing retrieval relevance. Furthermore, we construct a new dataset