  We add to intuitionistic logic infinitely many classical disjunctive
tautologies and use the Curry--Howard correspondence to obtain typed concurrent
$\lambda$-calculi; each of them features a specific communication mechanism,
including broadcasting and cyclic message-exchange, and enhanced expressive
power with respect to the $\lambda$-calculus. Moreover they all implement forms
of code mobility. Our results provide a first concurrent computational
interpretation for many propositional intermediate logics, classical logic
included.
