Hohfeld's Cube

Abstract

Wesley N. Hohfeld’s eight fundamental jural relations can be represented as the eight corners of a single, unified logical structure: a cube. In this model, the front and back faces of the cube form two parallel squares of opposition, representing the two parties in a legal relationship. Jural correlatives are located on corresponding corners of these opposite faces, while jural opposites are placed on diagonals across each square face. The logical validity of this geometric arrangement is demonstrated by translating each jural relation into a symbolic deontic logic defined by three parameters: whether the relation is obligatory or permissive, whether a state of affairs will or will not be created, and which party acts as the agent. The resulting symbolic framework confirms that the relationships between the concepts on the cube—including contradictories, contraries, and subcontraries—align with the formal properties of a logical square of opposition. This model not only serves as a tool for clarifying complex legal analysis but also offers a potential framework for computational jurisprudence, allowing for analogical legal searches based on the binary values of the logical components. – AI-generated abstract.