Abstract 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. With the sequent calculus in hand, we show the decidability of two systems. It turns out that two extensions are strongly connexive, hyperconnexive, superconnexive and almost totally connexive. We compare our logics with other connexive conditional logics and show the philosophical consequence concerning paraconsistency and überconsistency.

We introduce a new belief revision operator called evaluative multiple revision. Belief states in the revision are belief bases with core beliefs. New information that triggers the revision is evaluated beliefs, some of which are evaluated by the core beliefs as plausible and the others implausible. We characterize this operator by axiomatic postulates in the AGM (named after the three authors, i. e. C.E. Alchourrón, P. Gärdenfors, and D. Makinson, in literature of belief revision) style. Two functional constructions are given for the operator based on evaluative kernel sets and evaluative remainder sets, respectively, with representation theorems proved. We also compare some related works with ours and show the generality of the operator.