[FOM] Gentzen sequent calculus or ND system for Kleene's 3-valued logics

Arnon Avron aa at tau.ac.il
Fri May 1 15:36:19 EDT 2015

Dear Neil,

You can find a cut-free Gentzen sequent calculus for Kleene's strong 
3-valued logic in Section 4.1 of my paper:
Natural 3-valued Logics--- Characterization and Proof Theory
Journal of Symbolic Logic 56,  276-294 (1991).

(The paper treats only the propositional case, but
it is obvious how to extend the cut-free system there to the
first-order level).

Whether this is the optimal reference I cannot judge (and I am not
so objective about this issue...)



On Thu, Apr 30, 2015 at 01:13:15PM +0000, Tennant, Neil wrote:
> Could any fom-er be so kind as to provide an optimal reference for a (complete) Gentzen sequent calculus (and/or natural-deduction system) for Kleene's 3-valued logic (weak or strong)?---preferably, one for which a cut-elimination (resp., normalization) theorem is proved?
> Neil Tennant

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