Preconditionals
arXiv:2402.02296
Abstract
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.
Corrected TikZ code for right side of Figure 4. Forthcoming in The Logica Yearbook 2023, ed. Igor Sedlar, College Publications