David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Logica Universalis 1 (2):355-376 (2007)
. The term inversion principle goes back to Lorenzen who coined it in the early 1950s. It was later used by Prawitz and others to describe the symmetric relationship between introduction and elimination inferences in natural deduction, sometimes also called harmony. In dealing with the invertibility of rules of an arbitrary atomic production system, Lorenzen’s inversion principle has a much wider range than Prawitz’s adaptation to natural deduction. It is closely related to definitional reflection, which is a principle for reasoning on the basis of rule-based atomic definitions, proposed by Hallnäs and Schroeder-Heister. After presenting definitional reflection and the inversion principle, it is shown that the inversion principle can be formally derived from definitional reflection, when the latter is viewed as a principle to establish admissibility. Furthermore, the relationship between definitional reflection and the inversion principle is investigated on the background of a universalization principle, called the ω-principle, which allows one to pass from the set of all defined substitution instances of a sequent to the sequent itself.
|Keywords||Proof theory proof-theoretic semantics definitional reflection inversion principle admissibility inductive definition logic programming operative logic Lorenzen|
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Enrico Moriconi & Laura Tesconi (2008). On Inversion Principles. History and Philosophy of Logic 29 (2):103-113.
Luca Tranchini (2015). Harmonising Harmony. Review of Symbolic Logic 8 (3):411-423.
Wagner de Campos Sanz & Thomas Piecha (2009). Inversion by Definitional Reflection and the Admissibility of Logical Rules. Review of Symbolic Logic 2 (3):550-569.
Enrico Moriconi (2012). Steps Towards a Proof-Theoretical Semantics. Topoi 31 (1):67-75.
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