 A system of connexive logic with an intuitively plausible possible worlds semantics using a binary relation between worlds has been introduced in Wansing 2005. In this paper it is observed that a modification of the falsification conditions for negated implications in possible worlds models for David Nelson’s constructive four-valued logic with strong negation results in a connexive logic, called C, which inherits from Nelson’s logic an interpretation in terms of information states pre-ordered by a relation of possible expansion of these states. For Nelson’s constructive logics see, for example, Almukdad and Nelson 1984, Gurevich 1977, Nelson 1949, Odintsov 2008, Routley 1974, Thomason 1969, Wansing 2001, Kamide and Wansing 2012.