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Classical Logic = Fibred MLL | Dominic Hughes
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1 Apr 2005 | Subject: | Logic MSC-class: 03B05; 03F52 | math.LO | 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.] | Source: | arXiv, math.LO/0504028 | Services: | Forum | Review | PDF | Favorites |
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