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arXiv · 1910.06657

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

Tim Lyon
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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.

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Tim Lyon. 2019-10-15. Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents. https://doi.org/10.1007/978-3-030-36755-8_11

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