Inversion by definitional reflection and the admissibility of logical rules: Inversion by definitional reflection

Review of Symbolic Logic 2 (3):550-569 (2009)

The inversion principle for logical rules expresses a relationship between introduction and elimination rules for logical constants. Hallnäs & Schroeder-Heister 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. 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.
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DOI 10.1017/S1755020309990165
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References found in this work BETA

Structural Proof Theory.Sara Negri, Jan von Plato & Aarne Ranta - 2001 - Cambridge University Press.
Proof Theory for Admissible Rules.Rosalie Iemhoff & George Metcalfe - 2009 - Annals of Pure and Applied Logic 159 (1-2):171-186.
Natural Deduction with General Elimination Rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.

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Citations of this work BETA

Characterizing Generics Are Material Inference Tickets: A Proof-Theoretic Analysis.Preston Stovall - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy:1-37.
Definitional Reflection and Basic Logic.Peter Schroeder-Heister - 2013 - Annals of Pure and Applied Logic 164 (4):491-501.

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