Judges sometimes make mistakes. We propose JUST, a logical framework within which judges can record propositions about a case and witness statements where a witness says that certain propositions are true or false. JUST allows the judge (or a jury) to assign a rating of credibility to witness statements. A world is an assignment of true/false to each proposition, which is required to satisfy case-specific integrity constraints. We first develop JUST ’s explicit algorithm, which calculates the k most likely worlds without using independence assumptions between propositions. The judge may use these calculated top-k most likely worlds to make her final decision. For this computation, JUST  uses a suite of “combination” functions. We also develop JUST ’s implicit algorithm, which is far more efficient. We test JUST on 5 real-world court cases and 19 TV court cases, showing that JUST works well in practice.