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On cut elimination in the presence of perice rule

Archive for Mathematical Logic 26 (1):147-164 (1987)

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An Alternative Normalization of the Implicative Fragment of Classical Logic.Branislav Boričić & Mirjana Ilić - 2015 - Studia Logica 103 (2):413-446.details A normalizable natural deduction formulation, with subformula property, of the implicative fragment of classical logic is presented. A traditional notion of normal deduction is adapted and the corresponding weak normalization theorem is proved. An embedding of the classical logic into the intuitionistic logic, restricted on propositional implicational language, is described as well. We believe that this multiple-conclusion approach places the classical logic in the same plane with the intuitionistic logic, from the proof-theoretical viewpoint. Download Export citation Bookmark 1 citation
Dag Prawitz on Proofs and Meaning.Heinrich Wansing (ed.) - 2014 - Cham, Switzerland: Springer.details This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an (...) Download Export citation Bookmark
Necessity of Thought.Cesare Cozzo - 2015 - In Heinrich Wansing (ed.), Dag Prawitz on Proofs and Meaning. Cham, Switzerland: Springer. pp. 101-20.details The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. (...) Download Export citation Bookmark 6 citations
A New Normalization Strategy for the Implicational Fragment of Classical Propositional Logic.Luiz C. Pereira, Edward H. Haeusler, Vaston G. Costa & Wagner Sanz - 2010 - Studia Logica 96 (1):95-108.details The introduction and elimination rules for material implication in natural deduction are not complete with respect to the implicational fragment of classical logic. A natural way to complete the system is through the addition of a new natural deduction rule corresponding to Peirce's formula → A) → A). E. Zimmermann [6] has shown how to extend Prawitz' normalization strategy to Peirce's rule: applications of Peirce's rule can be restricted to atomic conclusions. The aim of the present paper is to extend (...) Download Export citation Bookmark 4 citations

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