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INVERSION BY DEFINITIONAL REFLECTION AND THE ADMISSIBILITY OF LOGICAL RULES

Published online by Cambridge University Press:  05 October 2009

WAGNER DE CAMPOS SANZ  and
THOMAS PIECHA
WAGNER DE CAMPOS SANZ*
Affiliation:
Faculdade de Filosofia, Universidade Federal de Goiás
THOMAS PIECHA*
Affiliation:
Wilhelm-Schickard-Institut, Universität Tübingen
*
*FACULDADE DE FILOSOFIA, UNIVERSIDADE FEDERAL DE GOIÁS, CEP 74001-970, GOIÂNIA, GO, BRAZIL E-mail:[email protected]
†WILHELM-SCHICKARD-INSTITUT, UNIVERSITÄT TÜBINGEN, SAND 13, 72076 TÜBINGEN, GERMANY E-mail:[email protected]
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Abstract

The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister (1990, 1991) proposed the principle of definitional reflection, which embodies basic ideas of inversion in the more general context of clausal definitions. For the context of admissibility statements, this has been further elaborated by Schroeder-Heister (2007). Using the framework of definitional reflection and its admissibility interpretation, we show that, in the sequent calculus of minimal propositional logic, the left introduction rules are admissible when the right introduction rules are taken as the definitions of the logical constants and vice versa. This generalizes the well-known relationship between introduction and elimination rules in natural deduction to the framework of the sequent calculus.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 3 , September 2009 , pp. 550 - 569
Copyright
Copyright © Association for Symbolic Logic 2009

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