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.
Keywords
Cite
@article{arxiv.2407.19221,
title = {A Basic {\L}ukasiewicz m-valued conditional logic},
author = {Shuquan Huo},
journal= {arXiv preprint arXiv:2407.19221},
year = {2024}
}
Comments
p.1 This research was supported by Major Program of National Fund of Philosophy and Social Science of China (18ZDA032) ; p.8 Proposition 2.8 can be applied to {\L}CR.; p.12 By calculating or referring to the properties of MV-algebra.;The validity of this step can be verified by a + {\pounds} b Vy({\psi}) and the property of MV-algebra ( cf.[5, p.10])