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How is the idea of permission in deontic logic related to Wesley Newcomb Hohfeld’s legal concept of privilege?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Applied logic Aristotle, marble portrait bust, Roman copy (2nd century bce) of a Greek original (c. 325 bce); in the Museo Nazionale Romano, Rome.

In the study of applied logic, the relationship between deontic logic and the legal theory of Wesley Newcomb Hohfeld is significant. Hohfeld, a U.S. legal scholar, developed a framework of fundamental legal conceptions that, while originally presented informally, shares deep structural connections with contemporary deontic logic.1

Specifically, the deontic logician’s concept of permission—often expressed by the operator $P$ —is considered a generalization of Hohfeld’s legal concept of privilege. Both frameworks attempt to systematize normative concepts, such as obligation and permission, by analyzing the logical relations between them.213

A shared challenge between these two approaches is the perceived weakness of the notion of permission. In deontic logic, permission is sometimes criticized as being "unduly weak" because it lacks the specificity found in more complex legal or moral contexts. By treating the deontic operator for permission as a generalization of Hohfeld’s privilege, logicians can better bridge the gap between abstract logical formulas and the practical, nuanced conceptualizations used in law.1