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1 Department of Computer and Information Science 2 LOGICAL - Logic and computing UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR8623 3 Computer Science Department

Abstract : We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce-s law without enforcing Ex Falso Quodlibet. We show that a -natural- implementation of this logic is Parigot-s classical natural deduction. We then move on to the computational side and emphasize that Parigot-s lambda-mu corresponds to minimal classical logic. A continuation constant must be added to lambda-mu to get full classical logic. The extended calculus is isomorphic to a syntactical restriction of Felleisen-s theory of control that offers a more expressive reduction semantics. This isomorphic calculus is in correspondence with a refined version of Prawitz-s natural deduction.

keyword : callcc minimal logic intuitionistic logic classical logic

Autor: Zena Ariola - Hugo Herbelin - Amr Sabry -

Fuente: https://hal.archives-ouvertes.fr/


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