A Basic {}ukasiewicz m-valued conditional logic

This paper is devoted to the construction of conditional logic system of {}ukasiewicz m-valued propositional logic. We construct conditional logic system {}CR based on {}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 {}CR cannot be generalized directly to variable strict conditionals, but they are stricter than classical conditionals.