A cut-free calculus for second-order Gödel logic

Ori Lahav*, Arnon Avron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Abstract We prove that the extension of the known hypersequent calculus for standard first-order Gödel logic with usual rules for second-order quantifiers is sound and (cut-free) complete for Henkin-style semantics for second-order Gödel logic. The proof is semantic, and it is similar in nature to Schütte and Tait's proof of Takeuti's conjecture.

Original languageEnglish
Article number6737
Pages (from-to)1-30
Number of pages30
JournalFuzzy Sets and Systems
StatePublished - 1 Oct 2015


FundersFunder number
Israel Science Foundation280-10


    • Cut-admissibility
    • Fuzzy logics
    • Gödel logic
    • Non-classical logics
    • Non-deterministic semantics
    • Proof theory
    • Second-order logic


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