 Angell (1966, 1967a, 1978) refers to AT′ as the Law of Conditional Non-Contradiction. Usually, Abelard’s First Principle, ~((A → B) ∧ (A → ~B)) is considered as a principle of conditional non-contradiction and as such is endorsed by some philosophers, e.g., Gibbard (1981, p. 231), Lowe (1995, p. 47), and Bennett (2003, p. 84), without making any reference to connexive logic. Conditional non-contradiction fails, however, to be a valid principle in the semantics suggested by Stalnaker (1968) and Lewis (1973), cf. the discussion in Unterhuber 2013. The restrictedly connexive logics presented in Weiss 2019 that validate Aristotle’s theses, BTw, and BTw′ stand in the tradition of Stalnaker and Lewis and are given an algebraic semantics that builds on the algebraic semantics for conditional logics from Nute 1980.