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1,107
Dialectica Interpretation of Well-Founded 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 well-founded 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 well-founded 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 First-Order Classical Affine Logic
- In this volume
, 2006
"... Abstract. We give a Dialectica-style interpretation of first-order classical affine logic. By moving to a contraction-free logic, the translation (a.k.a. D-translation) of a firstorder formula into a higher-type ∃∀-formula can be made symmetric with respect to duality, including exponentials. It tur ..."
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Abstract. We give a Dialectica-style interpretation of first-order classical affine logic. By moving to a contraction-free logic, the translation (a.k.a. D-translation) of a firstorder formula into a higher-type ∃∀-formula can be made symmetric with respect to duality, including exponentials
Synthesis of moduli of uniform continuity by the Monotone Dialectica Interpretation
- in the proof-system 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 NbE-normal form by means of a recurrent partial NbE-normalization. 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 non-computational 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 non-computational 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 two-way 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 contrac-tion 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 contrac-tion 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 re-ducing it to a quantifier-free 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 re-ducing it to a quantifier-free theory with finite types. Like other functional interpretations (e.g. Kleene’s realizability
Results 1 - 10
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1,107
