 Modern modal logic started as a syntactical enterprise with C.I. Lewis, who defined a series of axiom systems to capture notions of strict implication. In a similar vein, Lewis’ student E. Nelson came up with an axiom system from which Aristotle’s and Boethius’ theses can be derived. The system is called NL in Mares and Paoli 2019, where its axioms and inference rules are presented as follows (we here use schematic letters for arbitrary formulas instead of propositional variables and a different symbol for negation):