Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents

Tim Lyon

doi:10.1007/978-3-030-36755-8_11

paper

Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents

arXiv:1910.06657 · doi:10.1007/978-3-030-36755-8_11

Abstract

This paper employs the linear nested sequent framework to design a new cut-free calculus LNIF for intuitionistic fuzzy logic--the first-order Gödel 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.

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)