Results 1  10
of
2,433,288
On proof mining by cutelimination
"... Abstract. We present cutelimination as a method of proof mining, in the sense that hidden mathematical information can be extracted by eliminating lemmas from proofs. We present reductive methods for cutelimination and the method ceres (cutelimination by resolution). A comparison of ceres with red ..."
Abstract
 Add to MetaCart
known proof of the infinitude of primes by Fürstenberg; this proof uses topological lemmas based on arithmetic progressions. These topological lemmas of the proof are eliminated by ceres and Euclid’s construction of primes is extracted. We also touch the problem of cutelimination by resolution on induction
Semantic techniques for cutelimination . . .
, 2004
"... This paper is part of an ongoing effort to examine the role of extensionality in higherorder logic and provide tools for analyzing higherorder calculi. In an earlier paper, we have presented eight classes of higher order models with respect to various combinations of Boolean extensionality and t ..."
Abstract
 Add to MetaCart
and three forms of functional extensionality. Furthermore, we have developed a methodology of abstract consistency methods (by providing the necessary model existence theorems) needed to analyze completeness of higherorder calculi with respect to these model classes. This framework, employs a strong
Completeness and CutElimination in the . . .
, 2004
"... In this paper we give a semantic proof of cutelimination for ICTT. ICTT is an intuitionistic formulation of Church's theory of types defined by Miller, Scedrov, Nadathur and Pfenning in the late 1980s. It is the basis for the *prolog programming language. Our approach, extending techniques of ..."
Abstract
 Add to MetaCart
In this paper we give a semantic proof of cutelimination for ICTT. ICTT is an intuitionistic formulation of Church's theory of types defined by Miller, Scedrov, Nadathur and Pfenning in the late 1980s. It is the basis for the *prolog programming language. Our approach, extending techniques
A firstorder primaldual algorithm for convex problems with applications to imaging
, 2010
"... In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering in this paper ..."
Abstract

Cited by 435 (20 self)
 Add to MetaCart
In this paper we study a firstorder primaldual algorithm for convex optimization problems with known saddlepoint structure. We prove convergence to a saddlepoint with rate O(1/N) in finite dimensions, which is optimal for the complete class of nonsmooth problems we are considering
Strong Normalisation of CutElimination in Classical Logic
, 2000
"... In this paper we present a strongly normalising cutelimination procedure for classical logic. This procedure adapts Gentzen's standard cutreductions, but is less restrictive than previous strongly normalising cutelimination procedures. In comparison, for example, with works by Dragalin and D ..."
Abstract

Cited by 44 (4 self)
 Add to MetaCart
In this paper we present a strongly normalising cutelimination procedure for classical logic. This procedure adapts Gentzen's standard cutreductions, but is less restrictive than previous strongly normalising cutelimination procedures. In comparison, for example, with works by Dragalin
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
Abstract

Cited by 546 (25 self)
 Add to MetaCart
Least fixpoints as meanings of recursive definitions.
Strong CutElimination, Coherence, and Nondeterministic Semantics
"... Abstract. An (n, k)ary quantifier is a generalized logical connective, binding k variables and connecting n formulas. Canonical systems with (n, k)ary quantifiers form a natural class of Gentzentype systems which in addition to the standard axioms and structural rules have only logical rules in w ..."
Abstract
 Add to MetaCart
in such systems. We show that the following properties of a canonical system G with arbitrary (n, k)ary quantifiers are equivalent: (i) G is coherent, (ii) G admits strong cutelimination, and (iii) G has a strongly characteristic twovalued generalized nondeterministic matrix. In addition, we define simple
Domain names  Implementation and Specification
 RFC883, USC/Information Sciences Institute
, 1983
"... This RFC describes the details of the domain system and protocol, and assumes that the reader is familiar with the concepts discussed in a companion RFC, "Domain Names Concepts and Facilities " [RFC1034]. The domain system is a mixture of functions and data types which are an official pr ..."
Abstract

Cited by 715 (9 self)
 Add to MetaCart
This RFC describes the details of the domain system and protocol, and assumes that the reader is familiar with the concepts discussed in a companion RFC, "Domain Names Concepts and Facilities " [RFC1034]. The domain system is a mixture of functions and data types which are an official
Nullstellensatz and Positivstellensatz from cutelimination
"... We give in this article an effective proof of Hilbert's nullstellensatz and KrivineStengle's positivstellensatz using the cut elimination theorem for sequent calculus. The proof is very similar to the current techniques in constructive algebraic geometry by Henri Lombardi, but seems more ..."
Abstract
 Add to MetaCart
We give in this article an effective proof of Hilbert's nullstellensatz and KrivineStengle's positivstellensatz using the cut elimination theorem for sequent calculus. The proof is very similar to the current techniques in constructive algebraic geometry by Henri Lombardi, but seems more
Cutelimination for a logic with definitions and induction
 Theoretical Computer Science
, 1997
"... In order to reason about specifications of computations that are given via the proof search or logic programming paradigm one needs to have at least some forms of induction and some principle for reasoning about the ways in which terms are built and the ways in which computations can progress. The l ..."
Abstract

Cited by 72 (22 self)
 Add to MetaCart
that this logic has a number of applications. In this paper we prove the cutelimination theorem for F Oλ ∆IN, adapting a technique due to Tait and MartinLöf. This cutelimination proof is technically interesting and significantly extends previous results of this kind. 1
Results 1  10
of
2,433,288