A semantic proof of strong cut-admissibility for first-order Gödel logic

Ori Lahav*, Arnon Avron

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We provide a constructive direct semantic proof of the completeness of the cut-free part of the hypersequent calculus HIF for the standard first-order Gödel logic (thereby proving both completeness of the calculus for its standard semantics, and the admissibility of the cut rule in the full calculus). The results also apply to derivations from assumptions (or 'non-logical axioms'), showing in particular that when the set of assumptions is closed under substitutions, then cuts can be confined to formulas occurring in the assumptions. The methods and results are then extended to handle the (Baaz) Delta connective as well.

Original languageEnglish
Pages (from-to)59-86
Number of pages28
JournalJournal of Logic and Computation
Volume23
Issue number1
DOIs
StatePublished - Feb 2013

Funding

FundersFunder number
Israel Science Foundation280-10

    Keywords

    • Cut-admissibility
    • First order Gödel logic
    • Fuzzy logic
    • Hypersequents
    • Intermediate logic
    • Non-classical logic
    • Proof-theory
    • Semantic proof

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