Computational Isomorphisms in Classical Logic
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Description: Article by V. Danos, J. B. Joinet and H. Schellinx examining the categorical semantics of classical logic from a perspective inspired by linear logic.
CiteSeerX — Computational Isomorphisms in Classical Logic Computational Isomorphisms in Classical Logic (1996) Other Repositories/Bibliography by Vincent Danos , Jean-baptiste Joinet , Harold Schellinx , Mathematisch Instituut
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| Page title: | CiteSeerX — Computational Isomorphisms in Classical Logic |
| Keywords: | CiteSeerX, Vincent Danos, Jean-baptiste Joinet, Harold Schellinx, Mathematisch Instituut |
| Description: | CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We prove that any pair of derivations, without structural rules, of F ) G and G ) F , where F , G are rst-order formulas `without any qualities', in a constrained classical sequent calculus LK p , denes a computational isomorphism up to an equivalence on derivations based upon reversibility properties of logical rules. This result gives a rationale behind the success of Girard's denotational semantics for classical logic, in which all standard `linear' boolean equations are satised. 1 Introduction 1.1 A patch of paradise to be broadened In recent work [1] devoted to the proof theory of classical logic, we embarked on the project of overcoming the obstacles that prevent cut from being a decent binary operation on the set of classical sequent derivations. To clarify what we mean by decency, let us have a look at the world of simply typed -calculus, which, seen from a normalization-as-computation point of view, is something close to a patch of paradise. danos@logique... |
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| Date | activated: 14-Jul-1986 last updated: 22-May-2013 expires: 31-Jul-2014 |