David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
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.
Similar books and articles
Rachael Briggs (2009). Distorted Reflection. Philosophical Review 118 (1):59-85.
J. Ketland (2010). Truth, Conservativeness, and Provability: Reply to Cieslinski. Mind 119 (474):423-436.
Conor McHugh (2010). Self-Knowledge and the KK Principle. Synthese 173 (3):231 - 257.
Sara Negri (2002). Varieties of Linear Calculi. Journal of Philosophical Logic 31 (6):569-590.
Stephen Read (2010). General-Elimination Harmony and the Meaning of the Logical Constants. Journal of Philosophical Logic 39 (5):557-76.
Jonathan Weisberg (2007). Conditionalization, Reflection, and Self-Knowledge. Philosophical Studies 135 (2):179-97.
Peter Schroeder-Heister (1983). The Completeness of Intuitionistic Logic with Respect to a Validity Concept Based on an Inversion Principle. Journal of Philosophical Logic 12 (3):359 - 377.
Jeff Speaks (2011). Spectrum Inversion Without a Difference in Representation is Impossible. Philosophical Studies 156 (3):339-361.
Wagner Campos Sanz & Thomas Piecha (2009). Inversion by Definitional Reflection and the Admissibility of Logical Rules. Review of Symbolic Logic 2 (3):550-569.
Patrick Maher (1992). Diachronic Rationality. Philosophy of Science 59 (1):120-141.
Added to index2009-01-28
Total downloads22 ( #130,611 of 1,725,622 )
Recent downloads (6 months)6 ( #110,407 of 1,725,622 )
How can I increase my downloads?