TITLE: Is there a decision procedure for intuitionistic propositional logic?
QUESTION [13 upvotes]: Is intutionistic propositional logic decidable?  If so, what is a decision procedure for it, like tableaux for classical propositional logic?
EDIT: In the first revision I mistook "predicate" for "propositional".

REPLY [13 votes]: Gentzen was the first to show decidability. Papers about 1990 by Jörg Hudelmaier (giving an O(n log n)-space decision procedure) and by myself (Roy Dyckhoff) should be studied by anyone interested in using such a procedure. These show (following earlier work of Vorob'ev in 1950) how to avoid loop-checking in a root-first sequent calculus search. Avoiding back-tracking is a harder problem... The appropriate calculus G4ip is covered in the standard text, Basic Proof Theory.  The ILTP library at Potsdam (maintained by Jens Otten) links to implementations and classes of problems. Use of large Heyting algebras isn't really the best way to do it...