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A Simplified and Improved Free-Variable Framework for Hilbert's epsilon as an Operator of Indefinite Committed Choice [article]

Claus-Peter Wirth
2017 arXiv   pre-print
We propose a new semantics for Hilbert's epsilon as a choice operator with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice,  ...  We present the most recent version of our free-variable framework for two-valued logics with properly improved functionality, but only two kinds of free variables left (instead of three): implicitly universally  ...  ., 2004 ] ), in this paper we significantly improve our semantic free-variable framework for two-valued logics: 1.  ... 
arXiv:1104.2444v9 fatcat:z4d4xpltd5ggpnriisvu37svfu

Hilbert's epsilon as an operator of indefinite committed choice

Claus-Peter Wirth
2008 Journal of Applied Logic  
Finally, we ask the question whether our epsilon within our free-variable framework can serve as a paradigm useful in the specification and computation of semantics of discourses in natural language.  ...  Semantically, this left the epsilon-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the epsilon as a choice operator.  ...  indefinite and committed choice ( § 2.4).  ... 
doi:10.1016/j.jal.2007.07.009 fatcat:ubqafkw57vffbmra6a3ndq6wpi

Choice Functions in Semantics

Klaus Heusinger, Ruth Kempson
2004 Research on Language and Computation  
A new operator is added to Jacobson's variable-free semantics of functional readings, which leads to an analysis of theses readings using the general Skolem function interpretation of wide-scope indefinites  ...  We give an intuitive motivation for the familiar discourse dynamic features of the use of these expressions, and, taking due account of the structuring of information in more involved contexts, account  ...  The author was also partly supported by the fund for the promotion of research at the Technion, research No. 120-042, and by an NWO grant for visiting the UiL OTS of the Utrecht University in summer 2001  ... 
doi:10.1007/s11168-004-0903-7 fatcat:ye4rpurgcfhebaxlijllutq54a

A Most Interesting, but Revoked Draft for Hilbert and Bernays' "Grundlagen der Mathematik" that never found its way into any publication, and 2 CV of Gisbert Hasenjaeger [article]

Claus-Peter Wirth
2021 arXiv   pre-print
In May 2017, we identified an incorrectly filed text in Bernays scientific legacy at the archive of the ETH Zurich as a candidate for the beginning of the revoked draft for the 1st edn. or of a revoked  ...  A third of a century later, Bernays preface to the 2nd edn. (1968) of the 1st vol. of Hilbert-Bernays mentions joint work of Hasenjaeger and Bernays on the second edition.  ...  A simplified and improved free-variable framework for Hilbert's epsilon as an operator of indefinite committed choice. IFCoLog J. of Logics and Their Applications, 4:435-526. Received Oct. 23, 2015.  ... 
arXiv:1803.01386v4 fatcat:ai5itqzjnzddpnum2shh5johua

John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis

Joseph F. Grcar
2011 SIAM Review  
Von Neumann once remarked that to found a mathematical theory one had to prove the first theorem, which he and Goldstine did for the accuracy of mechanized Gaussian elimination-but their paper was about  ...  be needed to use the new machines effectively and to guide the development of still faster computers.  ...  I thank the reviewers and editors for comments that improved the paper. I am grateful for help with images, interpretations, sources, and text that was generously given by W. Aspray  ... 
doi:10.1137/080734716 fatcat:6ymfptvzfrg7doc7ajv4iljk24

Theorem Proving in Lean

Jeremy Avigad, Leonardo De Moura, Soonho Kong
The gold standard for supporting a mathematical claim is to provide a proof, and twentieth-century developments in logic show most if not all conventional proof methods can be reduced to a small set of  ...  Other systems provide search procedures and decision procedures for specific languages and domains, such as linear or nonlinear expressions over the integers or the real numbers.  ...  Just as indefinite description is a weaker version of strong indefinite description, the some operator is a weaker version of the epsilon operator. It is sometimes easier to use.  ... 
doi:10.1184/r1/6492902.v1 fatcat:tjnxwlyc7zdn7hlq2jvotm3vke

9th International Conference on Types for Proofs and Programs LIPIcs-Leibniz International Proceedings in Informatics

Ralph Matthes, Aleksy Schubert, Ralph Matthes, Aleksy Schubert, Wolfgang Thomas, Rwth Aachen, Reinhard Wilhelm
2013 unpublished
The 19th International Conference on Types for Proofs and Programs (TYPES 2013) was held in Toulouse, France from April 22 to 26, 2013, consisting of the main conference and several satellite events.  ...  The following institutions helped with funding and/or in providing lecture halls and services that TYPES 2013 could take place (in alphabetic order):  ...  We gratefully acknowledge the anonymous referees for their careful reading of our paper and their many useful remarks and suggestions. In particular Lemma 35 strongly improved.  ...