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

TL;DR

This paper develops a new m-valued conditional logic system based on { extL}ukasiewicz logic, extending classical semantics to an m-valued setting and proving key logical properties.

Contribution

It introduces the { extL}CR system, generalizes world semantics to m-valued logic, and establishes its soundness, completeness, and finite model property.

Findings

The { extL}CR system is sound and complete.

World semantics are successfully generalized to m-valued logic.

Conditionals in { extL}CR are stricter than classical conditionals.

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.