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

In Sergei Artemov & Anil Nerode (eds.), Logical Foundations of Computer Science. Cham: pp. 156-176 (2020)
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This paper employs the linear nested sequent framework to design a new cut-free calculus (LNIF) for intuitionistic fuzzy logic---the first-order Goedel 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.
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