English

Classical Logic = Fibred MLL

Logic 2007-05-23 v1

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.]

Keywords

Cite

@article{arxiv.math/0504028,
  title  = {Classical Logic = Fibred MLL},
  author = {Dominic Hughes},
  journal= {arXiv preprint arXiv:math/0504028},
  year   = {2007}
}

Comments

2 pages. Accepted for short presentation at Logic in Computer Science '05