Post Completeness in Conditional Logic

A logic is Post complete if it is consistent but has no consistent proper extensions.

In this article, we systematically investigate the Post complete extensions of certain basic conditional logics.

We identify all of the finitely many regular and normal Post complete conditional logics, and prove analogues of Makinson's embedding theorems.

We also show that certain basic conditional logics have uncountably many Post complete extensions for which closure under some, but not necessarily all, rules peculiar to the conditional are relaxed.

We reflect on what our results tell us about the structure of certain lattices of conditional logics and also draw some morals for multimodal logic.