An incompleteness theorem for conditional logic.
Donald E. Nute · Notre Dame Journal of Formal Logic · 1978
I will present a finitely axiomatized, non-strict extension of David Lewis' conditional logic VC which is incomplete with respect to Lewis' system of spheres semantics.In doing so, I will utilize a result by S. K. Thomason [5].I refer throughout this paper to logics which contain all the classical connectives and only one additional connective > (binary), no propositional constants, all classical tautologies, and which are closed under the rule of modus ponens (MP).I call such logics conditional.