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

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
Volume276
DOIs
StatePublished - 1 Oct 2015

Funding

FundersFunder number
Israel Science Foundation280-10

    Keywords

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

    Fingerprint

    Dive into the research topics of 'A cut-free calculus for second-order Gödel logic'. Together they form a unique fingerprint.

    Cite this