相关论文: Quantitative classical realizability
Realizability, introduced by Kleene, can be understood as a concretization of the Brouwer-Heyting-Kolmogorov (BHK) interpretation of proofs, providing a framework to interpret mathematical statements and proofs in terms of their…
The method of realizability was first developed by Kleene and is seen as a way to extract computational content from mathematical proofs. Traditionally, these models only satisfy intuitionistic logic, however this method was extended by…
The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…
We show how the language of Krivine's classical realizability may be used to specify various forms of nondeterminism and relate them with properties of realizability models. More specifically, we introduce an abstract notion of…
This work introduces a novel framework of uniform realizability that unifies and generalizes various realizability interpretations of logic, particularly focussing on the treatment of atomic formulas and quantifiers. Traditional…
In an impressive series of papers, Krivine showed at the edge of the last decade how classical realizability provides a surprising technique to build models for classical theories. In particular, he proved that classical realizability…
Realizability notions in mathematical logic have a long history, which can be traced back to the work of Stephen Kleene in the 1940s, aimed at exploring the foundations of intuitionistic logic. Kleene's initial realizability laid the ground…
We describe a realizability framework for classical first-order logic in which realizers live in (a model of) typed {\lambda}{\mu}-calculus. This allows a direct interpretation of classical proofs, avoiding the usual negative translation to…
We study a classical realizability model (in the sense of J.-L. Krivine) arising from a model of untyped lambda calculus in coherence spaces. We show that this model validates countable choice using bar recursion and bar induction.
A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic. While…
J.L. Krivine developed a new method based on realizability to construct models of set theory where the axiom of choice fails. We attempt to recreate his results in classical settings, i.e. symmetric extensions. We also provide a new…
We develop a notion of realizability for Classical Linear Logic based on a concurrent process calculus.
We present a sequent calculus for abstract focussing, equipped with proof-terms: in the tradition of Zeilberger's work, logical connectives and their introduction rules are left as a parameter of the system, which collapses the synchronous…
In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel…
We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by…
In Hayashi and Leigh (2024), the authors formulate classical number realisability for first-order arithmetic and a corresponding axiomatic system based on Krivine's classical realisability interpretation. This paper presents a…
We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one,…
We give a method to transform into programs, classical proofs using a well ordering of the reals. The technics uses a generalization of Cohen's forcing and the theory of classical realizability introduced by the author.
We prove the following completeness result about classical realizability: given any Boolean algebra with at least two elements, there exists a Krivine-style classical realizability model whose characteristic Boolean algebra is elementarily…
We use the technique of "classical realizability" to build new models of ZF + DC in which R is not well ordered. This gives new relative consistency results, probably not obtainable by forcing. This gives also a new method to get programs…