Inference rules are logical principles that guide the process of drawing conclusions from premises. They are fundamental in fields like mathematics, computer science, and philosophy, helping to establish valid arguments and reasoning. Common examples include modus ponens and modus tollens, which allow one to infer new statements based on existing ones. These rules provide a structured way to evaluate the truth of statements and their relationships. By applying inference rules, one can systematically derive conclusions, ensuring that reasoning remains consistent and sound. This is essential for tasks such as proof construction and algorithm design.