 If property (iii) is generalized to arbitrary formulas A and B, it is called the variable sharing property or variable sharing principle, which is generally seen as a necessary condition on a logic to count as a relevance logic (see the entry  logic: relevance).  So-called containment logics (also called Parry systems or systems of analytic implication, see Parry 1933, Anderson and Belnap 1975, Fine 1986, Ferguson 2015), satisfy the strong relevance requirement that if ⊢ A → B, then every propositional variable of B is also a propositional variable of A. The variable sharing property indicates a content connection between A and B if B is derivable from A (or, semantically, A entails B). The properties (i) and (ii) may be viewed to express a content connection requirement on the derivability relation in a negative way. If one wants to express these constraints in terms of the provability of object language formulas, one naturally arrives at Aristotle’s and Boethius’ theses.