Strict-Tolerant Conditional Logics

We construct a conditional logic using selection models in a three-valued setting. When the selection function selects an empty set, the corresponding conditional is neither true nor false. The semantic consequence is defined as in Strict-Tolerant logic. The resulting logic validates Conditional Excluded Middle without assuming that a selection function always chooses a single world, reconciling Stalnaker and Lewis. We give a labelled sequent calculus for the logic and consider three extensions of it. It turns out two extensions are strongly connexive, hyperconnexive, superconnexive, and almost totally connexive.