  In recent work, we introduced a new semantics for conditionals, covering a
large class of what we call preconditionals. In this paper, we undertake an
axiomatic study of preconditionals and subclasses of preconditionals. We then
prove that any bounded lattice equipped with a preconditional can be
represented by a relational structure, suitably topologized, yielding a single
relational semantics for conditional logics normally treated by different
semantics, as well as generalizing beyond those semantics.
