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A functional functional interpretation

Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2014
In this paper, we present a modern reformulation of the Dialectica interpretation based on the linearized version of de Paiva. Contrarily to Gödel's original translation which translated HA into system T, our presentation applies on untyped λ-terms and features nicer proof-theoretical properties.
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Functions and functional on finite systems

Journal of Symbolic Logic, 1992
The global function on finite systems is a new concept defined by Gurevich in [1] and discussed in [2] and [3]. In the last ten years this concept has become more and more useful in computer science and logic. Gurevich also pointed out the importance of global functionals on finite systems.
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The function of function

Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences, 2000
Abstract Contemporary analyses of biological function almost invariably advocate a naturalistic analysis, grounding biological functions in some feature of the mind-independent world. Many recent accounts suggest that no single analysis will be appropriate for all cases of use and that biological teleology should be split into several distinct ...
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Functional Equations and Distribution Functions

Results in Mathematics, 1994
Let \(a \in (0,1)\), \(N \in \mathbb{N} \backslash \{1\}\) and \(- 1 = \beta_0 \leq \beta_1 \leq \dots \leq \beta_{N - 1} = 1\). Then the functional equation \[ f(x) = {1 \over N} \sum^{N - 1}_{k = 0} f \left( {x - \beta_k \over a} \right) \] has a unique bounded solution \(f : \mathbb{R} \to \mathbb{R}\) vanishing on \((- \infty, -1/(1 - a))\) and ...
Borwein, Jonathan M., Girgensohn, Roland
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Generating Functions for Hermite Functions

Canadian Journal of Mathematics, 1959
Hermite's function Hn(x) is denned for all complex values of x and n bywhere F (α; γ; x) is Kummer's function with the customary indices omitted. It satisfies the differential equation1.1of whichis a second solution. Every solution of (1.1) is an entire function.
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The Wigner Function as Distribution Function

Foundations of Physics, 2006
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The Function of Function Words and Functional Categories

2005
This volume brings together papers which address a range of issues regarding the syntax of function words and functional categories in the Germanic languages. The works offered in this volume derive specifically from comparative studies of Germanic; at the same time they all bear directly on long-standing problems in syntactic theory and universal ...
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The Minimal Function of a BV Function

Results in Mathematics
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Jing Li, Feng Liu
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On the Distribution Function of Additive Functions

The Annals of Mathematics, 1946
The author extends his previous work on the distribution of values of additive arithmetical functions [J. Lond. Math. Soc. 13, 119--127 (1938; Zbl 0018.29301); Am. J. Math. 61, 713--721 (1939; Zbl 0022.00903) and Am. J. Math. 61, 722--725 (1939; Zbl 0022.01001)]. Many striking results are obtained.
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