A comparison of connexive logics

The most widespread criterion for the admission of a logic into the connexive family is the satisfaction of the pairs of formulas known as Aristotle's and Boethius' theses, along with the non-symmetry of implication. In this paper, we discuss whether this is enough to characterize a connexive logic or if more can be said about the issue. Our strategy is the following: first, we introduce a logic that has origins and motivations that have little to do with connexive logic. We then present a list of additional criteria found scattered throughout the literature on connexivity and propose to use this list to compare this logic and some of the well-known non-bivalent truth-functional connexive logics. This comparison gives us several interesting results: when every condition is given the same weight, the introduced logic can score as high as some of the well-known systems. Furthermore, a connection between the satisfaction of the most conditions and the loss of intuitiveness or an increase in the complexity of certain structural properties of the system seems to arise. We take these results to motivate the more general open problem of finding the most adequate way of judging systems of connexive logic.