Designing logical frameworks to reason about the properties of concurrent programs while accurately capturing the essence of concurrency is a challenging task. The main difficulties can be traced back to the syntactic constraints of the languages used for this purpose.

In this talk, I will present my ongoing line of research, which aims to provide a new computation-as-deduction paradigm for the study of concurrent programs. In particular, I will show you a non-commutative logic where we can interpret proofs as computation trees for the pi-calculus, and use proof nets to provide canonical representations of these trees modulo interleaving concurrency.

This work is based on joint works with Giulia Manara and Fabrizio Montesi