## S. Baratella and A. Masini.
A proof-theoretic investigation of a logic of positions.
*Annals of Pure and Applied Logic*, 123:135-162, 2003.

We introduce an extension of natural deduction that is
suitable for dealing with modal operators and
induction. We provide a proof reduction system and we
prove a strong normalization theorem for an
intuitionistic calculus. As a consequence we obtain a
purely syntactic proof of consistency. We also present
a classical calculus and we relate provability in the
two calculi by means of an adequate formula
translation.

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