Results 11 to 20 of about 344,169 (311)
A constructive proof of Simpson’s Rule [PDF]
Journal of Logic and Analysis, 2012 For most purposes, one can replace the use of Rolle's theorem and the mean value theorem, which are not constructively valid, by the law of bounded change. The proof of two basic results in numerical analysis, the error term for Lagrange interpolation and Simpson's rule, however seem to require the full strength of the classical Rolle's Theorem.
Coquand, T., Spitters, B.
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Constructive Proof of the Carpenter's Theorem [PDF]
Canadian Mathematical Bulletin, 2014 AbstractWe give a constructive proof of the carpenter’s theorem due to Kadison. Unlike the original proof, our approach also yields the real case of this theorem.
Bownik, Marcin, Jasper, John
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Proof Search in Constructive Logics [PDF]
, 1999 We present an overview of some sequent calculi organised not for "theorem-proving" but for proof search, where the proofs themselves (and the avoidance of known proofs on backtracking) are objects of interest. The main calculus discussed is that of Herbelin [1994] for intuitionistic logic, which extends methods used in hereditary Harrop logic ...
Pinto, Luís F., Dyckhoff, Roy
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Proofs as Spatio-Temporal Processes
Philosophia Scientiæ, 2014 The concept of proof can be studied from many different perspectives. Many types of proofs have been developed throughout history such as apodictic, dialectical, formal, constructive and non-constructive proofs, proofs by visualisation, assumption-based ...
Petros Stefaneas, Ioannis M. Vandoulakis
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Formalizing Constructive Quantifier Elimination in Agda [PDF]
Electronic Proceedings in Theoretical Computer Science, 2018 In this paper a constructive formalization of quantifier elimination is presented, based on a classical formalization by Tobias Nipkow. The formalization is implemented and verified in the programming language/proof assistant Agda.
Jeremy Pope
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Al-Lisaniyyat, 2022 The aim of our paper is to present the Constructive Type Theory (CTT) and some related concepts for the Swedish logician Per Martin Löf, who constructed a formal logic system in order to establish a philosophical foundation of constructive mathematics ...
Terkia Mechouet, Farid Zidani
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Infinite Towers of Galois Defect Extensions of Kaplansky Fields
Annales Mathematicae Silesianae, 2018 We give conditions for Kaplansky fields to admit infinite towers of Galois defect extensions of prime degree. As proofs of the presented facts are constructive, this provides examples of constructions of infinite towers of Galois defect extensions of ...
Blaszczok Anna
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Strong Normalization for HA + EM1 by Non-Deterministic Choice [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 We study the strong normalization of a new Curry-Howard correspondence for HA + EM1, constructive Heyting Arithmetic with the excluded middle on Sigma01-formulas.
Federico Aschieri
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Hölder, Mach, and the Law of the Lever: A Case of Well-founded Non-controversy
Philosophia Scientiæ, 2013 Otto Hölder’s reply to Mach’s renowned critique of the Archimedean proof of the Law of the Lever is analyzed and contextutalized as part of Hölder’s epistemological theory.
Oliver Schlaudt
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Hereditary Substitution for the λΔ-Calculus [PDF]
Electronic Proceedings in Theoretical Computer Science, 2013 Hereditary substitution is a form of type-bounded iterated substitution, first made explicit by Watkins et al. and Adams in order to show normalization of proof terms for various constructive logics.
Harley Eades, Aaron Stump
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