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Minimal Classical Logic and Control Operators Zena M. Ariola 1 and Hugo Herbelin 2
 

Summary: Minimal Classical Logic and Control Operators
Zena M. Ariola 1 and Hugo Herbelin 2
1 University of Oregon, Eugene, OR 97403, USA
ariola@cs.uoregon.edu
2 INRIA-Futurs, Parc Club Orsay Universite, 91893 Orsay Cedex, France
Hugo.Herbelin@inria.fr
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  corresponds to
minimal classical logic. A continuation constant must be added to  to get full classical logic.
We then map the extended  to a new theory of control, -C -top, which extends Felleisen's
reduction theory. -C -top allows one to distinguish between aborting and throwing to a
continuation. It is also in correspondence with the proofs of a re nement of Prawitz's natural
deduction.
1 Introduction
Traditionally, classical logic is de ned by extending intuitionistic logic with either Pierce's law,
excluded middle or the double negation law. We show that these laws are not equivalent and de ne
minimal classical logic, which validates Peirce's law but not Ex Falso Quodlibet (EFQ), i.e. the
law ? ! A. The notion is interesting from a computational point of view since it corresponds

  

Source: Ariola, Zena M. - Department of Computer and Information Science, University of Oregon

 

Collections: Computer Technologies and Information Sciences