Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents
Abstract
This paper employs the linear nested sequent framework to design a new cut-free calculus LNIF for intuitionistic fuzzy logic--the first-order G\"odel logic characterized by linear relational frames with constant domains. Linear nested sequents--which are nested sequents restricted to linear structures--prove to be a well-suited proof-theoretic formalism for intuitionistic fuzzy logic. We show that the calculus LNIF possesses highly desirable proof-theoretic properties such as invertibility of all rules, admissibility of structural rules, and syntactic cut-elimination.
Keywords
Cite
@article{arxiv.1910.06657,
title = {Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents},
author = {Tim Lyon},
journal= {arXiv preprint arXiv:1910.06657},
year = {2020}
}
Comments
Appended version of the paper "Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents", accepted to the International Symposium on Logical Foundations of Computer Science (LFCS 2020)