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

10/15/2019

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by   Tim Lyon, et al.

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This paper employs the recently introduced 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.