On the Computational Representation of Classical Logical Connectives

Many programming calculi have been designed to have a Curry-Howard correspondence with a classical logic. We investigate the effect that different choices of logical connective have on such calculi, and the resulting computational content. We identify two connectives ‘if-and-only-if’ and ‘exclusive or’ whose computational content is not well known, and whose cut elimination rules are non-trivial to define. In the case of the former, we define a term calculus and show that the computational content of several other connectives can be simulated. We show this is possible even for connectives not logically expressible with ‘if-and-only-if’.