If the law embodies a culture of implicity, logic’s orientation displays an enthusiasm for the explicit. Logicians put a premium on precision and exactitude, and they reserve a special place for definitions, both biconditional and implicit. It has a considerable bearing on the two-solitudes phenomenon that, for over a century, mainstream logic has been part of mathematics. As the name suggests, mathematical logic serves the interests of mathematics, and its methods are themselves imbued with richly mathematical content. Certainly it would take only the most monomaniacal of mathematical logicians to propose that the logic of legal reasoning is a Boolean lattice or that the secrets of legal relevance are best revealed in a possible worlds semantics for relevant logic. But logic has come a long way in the past 40 years, spurred by developments in computer science, AI, logic programming, dynamic and deontic logics and logics of practical reasoning in which there have been repeated attempts to reconnect with human reasoning in real-life situations. Any number of successes (or partial successes) have already been claimed by theorists working in what collectively has been called the New Logic. It is here that the two-solitudes phenomenon makes least sense, and it is here that prospects of rapprochement are at their best. In companion articles, we have recently explored the logical structure of probability in legal reasoning, as well as the abductive character of the criminal proof standard; In each case, we have attempted to bring to bear upon these legal issues resources from the New Logic. In the present essay we try our hand at relevance.