Classical Logic = Fibred MLL

Abstract

This paper represents classical propositional proofs as *combinatorial proofs*, which are more abstract than proof nets: superposition (contraction/weakening) is modelled mathematically, as a lax form of fibration, rather than syntactically (as in proof nets, which involve contraction and weakening nodes). A combinatorial proof is a `fibred' multiplicative linear proof net, hence the slogan in the title. Cut elimination retains its richness from sequent calculus: its non-determinism does not collapse to become confluent. [Note: this is merely a 2-page synopsis, accepted for a short presentation at Logic in Computer Science '05.]