Logical rules are core tools for knowledge acquisition and decision support, providing clear explanations for reasoning tasks. This paper focuses on the problem of mining rules from text. Current methods primarily rely on knowledge graphs and statistical techniques, with two main limitations: (1) They struggle to effectively mine rules from rich text resources in the absence of structured data, and (2) statistical methods often miss semantically meaningful but infrequent rules. To address these challenges, we propose an application-driven framework to mine rules of interest to users from text, leveraging semantic-relational logic to ensure rule validity. This framework first applies a fine-tuned textual entailment model to select conditions based on the application aims. It then applies contrapositive reasoning to determine whether further rule expansion is necessary, ensuring the completeness of the conditions. We evaluated our framework on real-world textual datasets, applying the mined rules to knowledge graph inference tasks. Our approach surpassed existing rule-mining methods on Hit@N and MRR metrics, demonstrating its effectiveness.