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We give a new proof of a theorem of Mints that the positive fragment ofminimal predicate logic is decidable. The idea of the proof is to replace theeigenvariable condition of sequent calculus by an appropriate scopingmechanism. The algorithm given by this proof seems to be more practical thanthat given by the original proof. A naive implementation is given at the end ofthe paper. Another contribution is to show that this result extends to a largeclass of theories, including simple type theory (higherorder logic) andsecond-order propositional logic. We obtain this way a new proof of thedecidability of the inhabitation problem for positive types in system F.

Eigenvariables, bracketing and the decidability of positive minimal predicate logic