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A Term Assignment for Polarized Bi-intuitionistic Logic and its Strong Normalization

Biasi C., Aschieri F.

Fundamenta Informaticae

2008

Vol. 84, nr 2

185-205

We propose a term assignment (let calculus) for Intuitionistic Logic for Pragmatics ILP_AC, a polarized sequent calculus which includes ordinary positive intuitionistic logic LJ its dual LJ and dual negations ( )^ which allow a formula to "communicate" with its dual fragment. We prove the strong normalization property for the term assignment which follows by soundly translating the let calculus into simply typed l calculus with pairings and projections. A new and simple proof of strong normalization for the latter is also provided.