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