Advances in Natural Deduction: A Celebration of Dag - download pdf or read online

By Luiz Carlos Pereira, Edward Hermann Haeusler, Valeria de Paiva

ISBN-10: 9400775474

ISBN-13: 9789400775473

ISBN-10: 9400775482

ISBN-13: 9789400775480

This selection of papers, celebrating the contributions of Swedish philosopher Dag Prawitz to facts concept, has been assembled from these awarded on the average Deduction convention equipped in Rio de Janeiro to honour his seminal study. Dag Prawitz’s paintings kinds the root of intuitionistic sort idea and his inversion precept constitutes the root of most up-to-date debts of proof-theoretic semantics in good judgment, Linguistics and Theoretical laptop Science.

The diversity of contributions comprises fabric at the extension of usual deduction with higher-order ideas, instead of higher-order connectives, and a paper discussing the appliance of average deduction ideas to facing equality in predicate calculus. the amount maintains with a key bankruptcy summarizing paintings at the extension of the Curry-Howard isomorphism (itself a spinoff of the paintings on typical deduction), through equipment of type idea which have been effectively utilized to linear good judgment, in addition to many different contributions from very hot gurus. With an illustrious team of members addressing a wealth of themes and functions, this quantity is a beneficial addition to the libraries of teachers within the a number of disciplines whose improvement has been given extra scope via the methodologies provided by means of common deduction. the amount is consultant of the wealthy and sundry instructions that Prawitz paintings has encouraged within the region of usual deduction.

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Konstruktive Begründung der Mathematik. Mathematische Zeitschrift, 53, 162–202. 14. Lorenzen, P. (1955). Einführung in die operative Logik und Mathematik (2nd ed 1969). Berlin: Springer. 15. Martin-Löf, P. (1984). Intuitionistic Type Theory. Napoli: Bibliopolis. 28 P. Schroeder-Heister 16. , & Tesconi, L. (2008). On inversion principles. History and Philosophy of Logic, 29, 103–113. 17. , & von Plato, J. (2001). Structural Proof Theory. Cambridge: Cambridge University Press. 18. Olkhovikov, G. , & Schoeder-Heister, P.

Tesconi, L. (2004). Strong Normalization Theorem for Natural Deduction with General Elimination Rules. Ph. D. thesis: University of Pisa. 44. Wansing, H. (1993). The Logic of Information Structures. Berlin: Springer (Lecture Notes in Artificial Intelligence, Vol. 681). Revisiting Zucker’s Work on the Correspondence Between Cut-Elimination and Normalisation Christian Urban Abstract Zucker showed that in the fragment of intuitionistic logic whose formulae are build up from ∧, → and ⇒ only, every reduction sequence in natural deduction corresponds to a reduction sequence in the sequent calculus and vice versa.

Revisiting Zucker’s Work 35 More recently, Negri and von Plato [12] describe a natural deduction system with a particular formulation for the elimination rules—they are called general elimination rules. For this system a positive answer to the correspondence question can be given. However, we find it is questionable to make the natural deduction calculus to be ‘sequent-calculus-like’, meaning that many proofs are distinguished that differ only in the order of some inference rules. There is also work by Ungar [16] that modifies the natural deduction calculus for obtaining a positive answer to the correspondence question.

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Advances in Natural Deduction: A Celebration of Dag Prawitz's Work by Luiz Carlos Pereira, Edward Hermann Haeusler, Valeria de Paiva

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