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A natural interpretation of classical proofs
, 2002
"... A natural interpretation of classical proofs ..."
Classical proof forestry
 Annals of Pure and Applied Logic
"... Classical proof forests are a proof formalism for firstorder classical logic based on Herbrand’s Theorem and backtracking games in the style of Coquand. First described by Miller in a cutfree setting as an economical representation of firstorder and higherorder classical proof, defining features ..."
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Classical proof forests are a proof formalism for firstorder classical logic based on Herbrand’s Theorem and backtracking games in the style of Coquand. First described by Miller in a cutfree setting as an economical representation of firstorder and higherorder classical proof, defining
Classical Proofs and Programs
"... Contents 1 Introduction 1 2 General Background 2 2.1 Godel's System T . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Intuitionistic Arithmetic for Functionals . . . . . . . . . . . . . . 6 2.3 Program Extraction from Constructive Proofs . . . . . . . . . . . 7 2.4 Example: Fibona ..."
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: Fibonacci Numbers . . . . . . . . . . . . . . . . . . . . 13 3 Computational Content of Classical Proofs 14 3.1 Definite and Goal Formulas . . . . . . . . . . . . . . . . . . . . . 14 3.2 Computational Content . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Example: Fibonacci Numbers Again
Minimal from Classical Proofs
"... It is well known that any proof can be transformed into a unique normal form with respect to ficonversion. Using jexpansion we can then construct the long normal form, where all minimal formulas are atomic. We are interested in the problem of how to find proofs in minimal logic, from a somewhat pr ..."
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practical point of view. * In particular we want to make use of existing theorem provers based on classical logic. So our problem is to review under what circumstances a classical proof can be converted into a proof in minimal logic, and moreover to describe reasonable algorithms which do this conversion. A
Quantum versus classical proofs and advice
 In preparation
, 2006
"... Abstract: This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA = QCMA. We prove three results about this question. First, we give a “quantum oracle separation ” between QMA and QCMA. More concretely, we show that any quantum algorithm ..."
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Cited by 30 (16 self)
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Abstract: This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA = QCMA. We prove three results about this question. First, we give a “quantum oracle separation ” between QMA and QCMA. More concretely, we show that any quantum
The Frame Problem and the Semantics of Classical Proofs
"... We outline the logic of current approaches to the socalled “frame problem ” (that is, the problem of predicting change in the physical world by using logical inference), and we show that these approaches are not completely extensional since none of them is closed under uniform substitution. The und ..."
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world data, it nevertheless remains obscure both what the logical form of this realworld data might be, and also how such data actually interacts with logical deduction. We show, using work of McCain and Turner, that this data can be captured using the semantics of classical proofs developed by Bellin
Denotations for classical proofs  Preliminary results
, 1992
"... This paper addresses the problem of extending the formulaeastypes principle to classical logic. More precisely, we introduce a typed lambdacalculus (LK ! ) whose inhabited types are exactly the implicative tautologies of classical logic and whose type assignment system is a classical sequent c ..."
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This paper addresses the problem of extending the formulaeastypes principle to classical logic. More precisely, we introduce a typed lambdacalculus (LK ! ) whose inhabited types are exactly the implicative tautologies of classical logic and whose type assignment system is a classical sequent
Classical Proofs via Basic Logic
 IN PROCEEDINGS OF THE CSL '97
, 1997
"... Cutelimination, besides being an important tool in prooftheory, plays a central role in the proofsasprograms paradigm. In recent years this approach has been extended to classical logic (cf. Girard 1991, Parigot 1991, and recently Danos Joinet Schellinx 1997). This paper introduces a new sequent ..."
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Cited by 3 (1 self)
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Cutelimination, besides being an important tool in prooftheory, plays a central role in the proofsasprograms paradigm. In recent years this approach has been extended to classical logic (cf. Girard 1991, Parigot 1991, and recently Danos Joinet Schellinx 1997). This paper introduces a new sequent
Polarized and Focalized Linear and Classical Proofs
, 2000
"... We give the precise correspondence between polarized linear logic and polarized classical logic. The properties of focalization and reversion of linear proofs [AP91, Gir91a, DJS97] are at the heart of our analysis: we show that the tqprotocol of normalization (dened in [DJS97]) for the classical sy ..."
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We give the precise correspondence between polarized linear logic and polarized classical logic. The properties of focalization and reversion of linear proofs [AP91, Gir91a, DJS97] are at the heart of our analysis: we show that the tqprotocol of normalization (dened in [DJS97]) for the classical
Results 1  10
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515,201