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Intelim Rules for Classical Connectives

Chapter
Part of the Outstanding Contributions to Logic book series (OCTR, volume 3)

Abstract

We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted (but more often used) context of set/formula sequents, as also in the intermediate set/formula-or-empty context.

Keywords

Intelim rules Introduction rules Elimination rules Classical logic Truth-functional connectives 

Notes

Acknowledgments

Thanks to Lloyd Humberstone and to Frederik van de Putte for incisive comments and vigorous criticism over several drafts. Peter Schroeder-Heister’s counsel from a proof-theoretic perspective was of great assistance, and the searching remarks of two anonymous referees also helped improve the text. Finally, thanks to the Editor for his patience with repeated post-final refinements.

References

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Philosophy, Logic and Scientific MethodLondon School of EconomicsLondonUK

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