Authors: Heinrich Wansing and Zach Weber

Connexive logic has room for two pairs of universal and particular quantifiers: one pair, \(\forall\) and \(\exists\), are standard quantifiers; the other pair, \({A}\) and \({E}\), are unorthodox, but we argue, are well-motivated in the context of connexive logic. Both non-standard quantifiers have been introduced previously,

but in the context of connexive logic they have a natural semantic and proof-theoretic place, and plausible natural language readings. The result are logics which are negation inconsistent but non-trivial.