We build a Kleene realizability semantics for the two-level Minimalist Foundation MF, ideated by Maietti and Sambin in 2005 and completed by Maietti in 2009. Thanks to this semantics we prove that both levels of MF are consistent with the formal Church Thesis CT. Since MF consists of two levels, an intensional one, called mTT, and an extensional one, called emTT, linked by an interpretation, it...

We develop a notion of realizability for Classical Linear Logic based on a concurrent process calculus.