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Dialectica Interpretation of WellFounded Induction
 MATHEMATICAL LOGIC QUARTERLY, 12/11/2007
, 2007
"... From a classical proof that the gcd of natural numbers a1 and a2 is a linear combination of the two, we extract by Gödel’s Dialectica interpretation an algorithm computing the coefficients. The proof uses the minimum principle. We show generally how wellfounded recursion can be used to Dialectica i ..."
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From a classical proof that the gcd of natural numbers a1 and a2 is a linear combination of the two, we extract by Gödel’s Dialectica interpretation an algorithm computing the coefficients. The proof uses the minimum principle. We show generally how wellfounded recursion can be used to Dialectica
DIALECTICA INTERPRETATION WITH FINE COMPUTATIONAL CONTROL
"... Abstract. This paper is an attempt to refine Hernest’s [2] extension of Berger’s uniform quantifiers [1] to Gödel’s functional (Dialectica) interpretation [3]. We consider the possibility to switch on and off every computational component and explore possible applications of the refined interpretat ..."
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Abstract. This paper is an attempt to refine Hernest’s [2] extension of Berger’s uniform quantifiers [1] to Gödel’s functional (Dialectica) interpretation [3]. We consider the possibility to switch on and off every computational component and explore possible applications of the refined
The Dialectica Interpretation of FirstOrder Classical Affine Logic
 In this volume
, 2006
"... Abstract. We give a Dialecticastyle interpretation of firstorder classical affine logic. By moving to a contractionfree logic, the translation (a.k.a. Dtranslation) of a firstorder formula into a highertype ∃∀formula can be made symmetric with respect to duality, including exponentials. It tur ..."
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Abstract. We give a Dialecticastyle interpretation of firstorder classical affine logic. By moving to a contractionfree logic, the translation (a.k.a. Dtranslation) of a firstorder formula into a highertype ∃∀formula can be made symmetric with respect to duality, including exponentials
Synthesis of moduli of uniform continuity by the Monotone Dialectica Interpretation
 in the proofsystem MINLOG. Electronic Notes in Theoretical Computer Science
, 2007
"... We extract on the computer a number of moduli of uniform continuity for the first few elements of a sequence of closed terms t of Gödel’s T of type (N→N)→(N→N). The generic solution may then be quickly inferred by the human. The automated synthesis of such moduli proceeds from a proof of the heredi ..."
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’s monotone functional interpretation. This new version of the Monotone Dialectica produces terms in NbEnormal form by means of a recurrent partial NbEnormalization. Such partial evaluation is strictly necessary.
LIGHT DIALECTICA INTERPRETATION (A REVIEW OF DAN HERNEST’S PHD THESIS)
"... The present paper presents a review of Dan Herenst’s PhD thesis [3]. The author incorporates the noncomputational quantifiers, which were introduced by U. Berger [1], and investigates their properties with respect to Gödel’s Dialectica interpretation [4]. This paper is mainly concerned with the so ..."
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The present paper presents a review of Dan Herenst’s PhD thesis [3]. The author incorporates the noncomputational quantifiers, which were introduced by U. Berger [1], and investigates their properties with respect to Gödel’s Dialectica interpretation [4]. This paper is mainly concerned
Gödel's Dialectica interpretation and its twoway stretch
 in Computational Logic and Proof Theory (G. Gottlob et al eds.), Lecture Notes in Computer Science 713
, 1997
"... this article has appeared in Computational Logic and Proof Theory (Proc. 3 ..."
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this article has appeared in Computational Logic and Proof Theory (Proc. 3
An analysis of Gödel’s Dialectica interpretation via linear logic. Dialectica (2008) [to appear: for preprint see http://www.dcs.qmul.ac.uk/∼pbo
"... pbo Abstract. This article presents an analysis of Gödel’s Dialectica interpretation via a refinement of intuitionistic logic known as linear logic. Linear logic comes naturally into the picture once one observes that the structural rule of contraction is the main cause of the lack of symmetry in ..."
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pbo Abstract. This article presents an analysis of Gödel’s Dialectica interpretation via a refinement of intuitionistic logic known as linear logic. Linear logic comes naturally into the picture once one observes that the structural rule of contraction is the main cause of the lack of symmetry
Cartesian Closed Dialectica Categories
"... When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove (relative) consistency of first order arithmetic by reducing it to a quantifierfree theory with finite types. Like other functional interpretations (e.g. Kleene’s realizability in ..."
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When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove (relative) consistency of first order arithmetic by reducing it to a quantifierfree theory with finite types. Like other functional interpretations (e.g. Kleene’s realizability
Results 1  10
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1,107