A Basic {\L}ukasiewicz m-valued conditional logic

Abstract

This paper is devoted to the construction of conditional logic system of {\L}ukasiewicz m-valued propositional logic. We construct conditional logic system {\L}CR based on {\L}ukasiewicz m-valued propositional logic. We construct world semantics for the system by generalizing conditional and accessibility relation from classical bivalent to m-valued, and prove its soundness, completeness and finite model property. Conditionals of {\L}CR cannot be generalized directly to variable strict conditionals, but they are stricter than classical conditionals.