The phrase "by rights" is often used to express what should happen logically or morally. However, there are different ways to convey the same meaning using synonyms. Here are some examples: "according to justice," "as it should be," "in all fairness," "justifiably," "properly," "rightfully," and "deservedly." Each of these synonyms emphasizes the idea that something is true or should be done based on what is fair or right. Using synonyms like these can add variety to your writing and help you convey your message with precision and clarity.