History and Philosophy of Logic 29 (2):103-113 (2008)

Enrico Moriconi
University of Pisa
The idea of an ?inversion principle?, and the name itself, originated in the work of Paul Lorenzen in the 1950s, as a method to generate new admissible rules within a certain syntactic context. Some fifteen years later, the idea was taken up by Dag Prawitz to devise a strategy of normalization for natural deduction calculi (this being an analogue of Gentzen's cut-elimination theorem for sequent calculi). Later, Prawitz used the inversion principle again, attributing it with a semantic role. Still working in natural deduction calculi, he formulated a general type of schematic introduction rules to be matched ? thanks to the idea supporting the inversion principle ? by a corresponding general schematic Elimination rule. This was an attempt to provide a solution to the problem suggested by the often quoted note of Gentzen. According to Gentzen ?it should be possible to display the elimination rules as unique functions of the corresponding introduction rules on the basis of certain requirements?. Many people have since worked on this topic, which can be appropriately seen as the birthplace of what are now referred to as ?general elimination rules?, recently studied thoroughly by Sara Negri and Jan von Plato. In this study, we retrace the main threads of this chapter of proof-theoretical investigation, using Lorenzen's original framework as a general guide
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DOI 10.1080/01445340701830334
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References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Dag Prawitz - 1965 - Stockholm, Sweden: Dover Publications.
The Runabout Inference-Ticket.A. N. Prior - 1960 - Analysis 21 (2):38.
Ideas and Results in Proof Theory.Dag Prawitz & J. E. Fenstad - 1971 - Journal of Symbolic Logic 40 (2):232-234.
A Natural Extension of Natural Deduction.Peter Schroeder-Heister - 1984 - Journal of Symbolic Logic 49 (4):1284-1300.

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Citations of this work BETA

General-Elimination Harmony and the Meaning of the Logical Constants.Stephen Read - 2010 - Journal of Philosophical Logic 39 (5):557-576.
Classical Harmony and Separability.Julien Murzi - 2020 - Erkenntnis 85 (2):391-415.

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