We develop a method of reasoning using an incrementally constructed bipolar argumentation framework (BAF) aiming to apply computational argumentation to legal reasoning. A BAF that explains the judgment of a certain case is constructed based on the user’s knowledge and recognition. More specifically, a set of effective laws are derived as the conclusions from evidential facts recognized by the user, in a bottom-up manner; conversely, the evidences required to derive a new conclusion are identified if certain conditions are added, in a top-down manner. The BAF is incrementally constructed by repeated exercise of this bidirectional reasoning. The method provides support for those who are not familiar with the law, so that they can understand the judgment process and identify strategies that might allow them to win their case.